TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60039 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (0ms).
 | – Problem 2 was processed with processor BackwardsNarrowing (2ms).
 |    | – Problem 5 was processed with processor BackwardsNarrowing (5ms).
 |    |    | – Problem 6 was processed with processor BackwardsNarrowing (8ms).
 |    |    |    | – Problem 7 was processed with processor BackwardsNarrowing (6ms).
 |    |    |    |    | – Problem 8 was processed with processor BackwardsNarrowing (10ms).
 |    |    |    |    |    | – Problem 9 was processed with processor BackwardsNarrowing (13ms).
 |    |    |    |    |    |    | – Problem 10 was processed with processor BackwardsNarrowing (14ms).
 |    |    |    |    |    |    |    | – Problem 11 was processed with processor BackwardsNarrowing (17ms).
 |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor BackwardsNarrowing (19ms).
 |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor BackwardsNarrowing (24ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor BackwardsNarrowing (68ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor BackwardsNarrowing (29ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor BackwardsNarrowing (70ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor BackwardsNarrowing (44ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor BackwardsNarrowing (99ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor BackwardsNarrowing (116ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor BackwardsNarrowing (66ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor BackwardsNarrowing (127ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor BackwardsNarrowing (87ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor BackwardsNarrowing (162ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor BackwardsNarrowing (362ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 remains open; application of the following processors failed [BackwardsNarrowing (505ms), BackwardsNarrowing (308ms), BackwardsNarrowing (582ms), BackwardsNarrowing (366ms), BackwardsNarrowing (376ms), BackwardsNarrowing (461ms), BackwardsNarrowing (415ms), BackwardsNarrowing (705ms), BackwardsNarrowing (427ms), BackwardsNarrowing (735ms), BackwardsNarrowing (489ms), BackwardsNarrowing (670ms), BackwardsNarrowing (545ms), BackwardsNarrowing (575ms), BackwardsNarrowing (600ms), BackwardsNarrowing (612ms), BackwardsNarrowing (1005ms), BackwardsNarrowing (705ms), BackwardsNarrowing (742ms), BackwardsNarrowing (853ms), BackwardsNarrowing (841ms), BackwardsNarrowing (1296ms), BackwardsNarrowing (832ms), BackwardsNarrowing (967ms), BackwardsNarrowing (893ms), BackwardsNarrowing (948ms), BackwardsNarrowing (1544ms), BackwardsNarrowing (1028ms), BackwardsNarrowing (651ms), BackwardsNarrowing (773ms), BackwardsNarrowing (800ms), BackwardsNarrowing (841ms), BackwardsNarrowing (870ms), BackwardsNarrowing (1478ms), BackwardsNarrowing (965ms), BackwardsNarrowing (582ms), BackwardsNarrowing (926ms), BackwardsNarrowing (804ms), BackwardsNarrowing (758ms)].
 | – Problem 3 was processed with processor SubtermCriterion (0ms).
 | – Problem 4 was processed with processor SubtermCriterion (0ms).

The following open problems remain:

Open Dependency Pair Problem 2

Dependency Pairs

if_gcd#(true, x, y) → gcd#(minus(x, y), y)if_gcd#(false, x, y) → gcd#(minus(y, x), x)
gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: minus, 0, s, le, if_gcd, false, true, pred, gcd

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

gcd#(s(x), s(y)) → le#(y, x)if_gcd#(true, x, y) → gcd#(minus(x, y), y)
le#(s(x), s(y)) → le#(x, y)minus#(x, s(y)) → minus#(x, y)
if_gcd#(false, x, y) → minus#(y, x)minus#(x, s(y)) → pred#(minus(x, y))
if_gcd#(true, x, y) → minus#(x, y)if_gcd#(false, x, y) → gcd#(minus(y, x), x)
gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: 0, minus, le, s, if_gcd, true, false, pred, gcd

Strategy

The following SCCs where found

le#(s(x), s(y)) → le#(x, y)
minus#(x, s(y)) → minus#(x, y)
if_gcd#(true, x, y) → gcd#(minus(x, y), y)if_gcd#(false, x, y) → gcd#(minus(y, x), x)
gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))

Problem 2: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(true, x, y) → gcd#(minus(x, y), y)if_gcd#(false, x, y) → gcd#(minus(y, x), x)
gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: minus, 0, s, le, if_gcd, false, true, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(true, x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(minus(true, 0), x, y) 
if_gcd#(pred(s(true)), x, y) 
if_gcd#(le(0, _x21), x, y) 
if_gcd#(gcd(0, true), x, y) 
Thus, the rule if_gcd#(true, x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(0, true), x, y) → gcd#(minus(x, y), y)if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)

Problem 5: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(0, true), x, y) → gcd#(minus(x, y), y)if_gcd#(false, x, y) → gcd#(minus(y, x), x)
if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: 0, minus, le, s, if_gcd, true, false, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(0, true), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(0, minus(true, 0)), x, y) 
if_gcd#(gcd(0, le(0, _x41)), x, y) 
if_gcd#(minus(gcd(0, true), 0), x, y) 
if_gcd#(pred(s(gcd(0, true))), x, y) 
if_gcd#(gcd(pred(s(0)), true), x, y) 
if_gcd#(gcd(0, gcd(0, true)), x, y) 
if_gcd#(gcd(minus(0, 0), true), x, y) 
if_gcd#(gcd(0, pred(s(true))), x, y) 
if_gcd#(gcd(gcd(0, 0), true), x, y) 
Thus, the rule if_gcd#(gcd(0, true), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(minus(0, 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)

Problem 6: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(minus(0, 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)
gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: minus, 0, s, le, if_gcd, false, true, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(minus(0, 0), true), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) 
if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) 
if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) 
if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) 
if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) 
if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) 
if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) 
if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) 
if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) 
if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) 
if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) 
if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) 
if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) 
if_gcd#(gcd(minus(minus(0, 0), 0), true), x, y) 
if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) 
Thus, the rule if_gcd#(gcd(minus(0, 0), true), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)

Problem 7: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(minus(minus(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: 0, minus, le, s, if_gcd, true, false, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(0, pred(s(true))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) 
if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) 
if_gcd#(gcd(0, pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) 
if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) 
if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) 
if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) 
if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) 
if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) 
if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) 
if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) 
if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) 
if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) 
if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) 
Thus, the rule if_gcd#(gcd(0, pred(s(true))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)

Problem 8: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(minus(minus(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)if_gcd#(false, x, y) → gcd#(minus(y, x), x)
if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: minus, 0, s, le, if_gcd, false, true, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(0, pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) 
if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) 
if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) 
if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) 
if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) 
if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) 
if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) 
if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) 
if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) 
if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) 
if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) 
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) 
if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) 
if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) 
if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) 
Thus, the rule if_gcd#(gcd(0, pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)

Problem 9: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: 0, minus, le, s, if_gcd, true, false, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) 
if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) 
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) 
if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) 
if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) 
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) 
if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) 
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) 
if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) 
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) 
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) 
if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) 
if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) 
if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) 
if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) 
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) 
if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) 
if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) 
Thus, the rule if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)

Problem 10: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(minus(minus(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: minus, 0, s, le, if_gcd, false, true, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(minus(minus(0, 0), 0), true), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) 
if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) 
if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) 
if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) 
if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) 
if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) 
if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) 
if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) 
if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) 
if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) 
if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) 
if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) 
if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) 
if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) 
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) 
if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) 
if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) 
if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) 
if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) 
if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) 
Thus, the rule if_gcd#(gcd(minus(minus(0, 0), 0), true), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)

Problem 11: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: 0, minus, le, s, if_gcd, true, false, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) 
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) 
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) 
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) 
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) 
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) 
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) 
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) 
Thus, the rule if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)

Problem 12: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(false, x, y) → gcd#(minus(y, x), x)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: minus, 0, s, le, if_gcd, false, true, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) 
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) 
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) 
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) 
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) 
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) 
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) 
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) 
Thus, the rule if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)

Problem 13: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(false, x, y) → gcd#(minus(y, x), x)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: 0, minus, le, s, if_gcd, true, false, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(pred(minus(s(0), pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(gcd(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(pred(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) 
if_gcd#(gcd(minus(pred(minus(s(0), 0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) 
if_gcd#(gcd(minus(s(0), s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(gcd(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) 
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) 
if_gcd#(gcd(pred(s(pred(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) 
if_gcd#(minus(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) 
if_gcd#(gcd(gcd(0, pred(minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) 
if_gcd#(gcd(pred(minus(minus(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(0, gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true)))))), x, y) 
if_gcd#(pred(s(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) 
if_gcd#(gcd(pred(minus(s(minus(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) 
if_gcd#(gcd(pred(minus(gcd(0, s(0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(gcd(0, minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) 
Thus, the rule if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(minus(s(0), 0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(pred(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(s(0), s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(minus(s(0), 0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(minus(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(minus(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(gcd(0, s(0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(gcd(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)

Problem 14: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(gcd(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(minus(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(0, s(0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(s(0), s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(pred(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(minus(s(0), 0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(minus(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: minus, 0, s, le, if_gcd, false, true, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, true)))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, true))), 0)))), x, y) 
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, true)), 0))), 0)), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, true)), 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), minus(0, 0))))), x, y) 
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, true)), 0))))), x, y) 
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, true)))), 0)))), x, y) 
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) 
if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), 0), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, le(0, _x111))), 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) 
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), gcd(0, 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, true)), 0), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), pred(s(0)))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, true), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, true)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(true)))), 0)))), x, y) 
Thus, the rule if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, true)), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, true), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, le(0, _x111))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, true)), 0))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, true))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)

Problem 15: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(gcd(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(gcd(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, true), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(minus(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, le(0, _x111))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(0, s(0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(s(0), s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(pred(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, true)), 0))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, true))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, true)), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(minus(s(0), 0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(minus(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: 0, minus, le, s, if_gcd, true, false, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)))), x, y) 
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(le(0, _x121), 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) 
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) 
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) 
if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) 
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))))), x, y) 
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)))), x, y) 
Thus, the rule if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(le(0, _x121), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)

Problem 16: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(gcd(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(gcd(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, true), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(minus(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, le(0, _x111))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(gcd(0, s(0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(false, x, y) → gcd#(minus(y, x), x)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(le(0, _x121), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(s(0), s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(pred(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, true)), 0))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, true))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, true)), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(minus(s(0), 0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(minus(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: minus, 0, s, le, if_gcd, false, true, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) 
if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) 
if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) 
if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) 
Thus, the rule if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)

Problem 17: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(gcd(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, true), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(minus(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, le(0, _x111))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(0, s(0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(le(0, _x121), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(s(0), s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(pred(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, true)), 0))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, true))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, true)), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(minus(s(0), 0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(minus(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: 0, minus, le, s, if_gcd, true, false, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) 
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) 
if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) 
if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) 
if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) 
if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) 
Thus, the rule if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)

Problem 18: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(gcd(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, true), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(minus(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, le(0, _x111))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(0, s(0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(le(0, _x121), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(s(0), s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(pred(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, true)), 0))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, true))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, true)), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(minus(s(0), 0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(minus(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: minus, 0, s, le, if_gcd, false, true, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) 
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) 
if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) 
Thus, the rule if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) → gcd#(minus(x, y), y)

Problem 19: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(minus(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, le(0, _x111))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(0, s(0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(le(0, _x121), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(s(0), s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, true)), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(minus(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(gcd(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, true), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(pred(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, true)), 0))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, true))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(minus(s(0), 0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: 0, minus, le, s, if_gcd, true, false, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(minus(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(pred(s(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(gcd(0, pred(pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(minus(pred(s(s(minus(0, 0)))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(gcd(0, s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(minus(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) 
if_gcd#(pred(s(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(pred(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(0, gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(pred(s(0)), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, gcd(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(gcd(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(pred(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) 
if_gcd#(minus(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, pred(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) 
if_gcd#(gcd(minus(pred(pred(s(s(minus(0, 0))))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(gcd(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(gcd(0, pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(gcd(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) 
Thus, the rule if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(minus(0, 0)))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, pred(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(gcd(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(minus(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(pred(s(0)), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, gcd(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(s(minus(0, 0))))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(0, s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)

Problem 20: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(minus(0, 0)))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(minus(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(pred(s(0)), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(minus(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, le(0, _x111))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(0, s(0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(false, x, y) → gcd#(minus(y, x), x)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(le(0, _x121), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(s(0), s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, true)), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, pred(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(minus(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(gcd(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(gcd(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))if_gcd#(gcd(pred(s(pred(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(minus(0, 0))))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, true), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(gcd(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, gcd(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(pred(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, true)), 0))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, true))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(minus(s(0), 0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: minus, 0, s, le, if_gcd, false, true, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(pred(pred(gcd(0, gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(minus(pred(pred(gcd(0, s(s(0))))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, pred(s(s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(pred(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(minus(pred(gcd(0, s(s(0)))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(0, gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(gcd(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(gcd(0, pred(gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(gcd(0, 0), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(s(pred(pred(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(pred(s(0)), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(pred(s(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) 
if_gcd#(minus(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(gcd(s(0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(minus(0, 0), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(gcd(0, s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, gcd(s(s(0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(pred(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) 
if_gcd#(pred(s(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(gcd(0, pred(pred(gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(minus(s(0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(pred(s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
Thus, the rule if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(minus(s(0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(gcd(0, 0), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(gcd(0, s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(minus(0, 0), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(gcd(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(pred(s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, pred(s(s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(gcd(0, s(s(0)))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(pred(s(0)), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, gcd(s(s(0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(gcd(0, s(s(0))))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(pred(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(gcd(s(0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)

Problem 21: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(minus(0, 0)))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(minus(0, 0), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(minus(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(gcd(0, 0), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(pred(s(0)), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(gcd(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(minus(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, le(0, _x111))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(0, s(0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(gcd(s(0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(le(0, _x121), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(s(0), s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, true)), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, pred(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(pred(s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(minus(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(gcd(0, s(s(0))))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(minus(s(0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(gcd(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(gcd(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))if_gcd#(gcd(pred(s(pred(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, pred(s(s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(s(minus(0, 0))))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(gcd(0, s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, true), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(pred(s(0)), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(pred(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, gcd(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(pred(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, true)), 0))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, true))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(minus(s(0), 0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(gcd(0, s(s(0)))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, gcd(s(s(0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: 0, minus, le, s, if_gcd, true, false, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(gcd(0, 0))), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, minus(0, 0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(pred(s(0)), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, gcd(0, 0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), gcd(0, minus(true, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(minus(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) 
if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0))), 0))), x, y) 
if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) 
if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(gcd(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0))), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, pred(s(0))), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(gcd(0, 0), gcd(0, minus(true, 0))))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(gcd(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) 
if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) 
Thus, the rule if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, gcd(0, 0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, minus(0, 0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(gcd(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(minus(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, pred(s(0))), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(pred(s(0)), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(gcd(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(gcd(0, 0))), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(gcd(0, 0), gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)

Problem 22: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(minus(0, 0)))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(minus(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(minus(0, 0), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(minus(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(gcd(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(gcd(0, 0), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(pred(s(0)), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(gcd(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(minus(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, le(0, _x111))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(0, s(0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(gcd(s(0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(le(0, _x121), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(s(0), s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, true)), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, pred(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(pred(s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(minus(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(gcd(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(gcd(0, s(s(0))))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(minus(s(0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(gcd(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(gcd(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(gcd(pred(s(pred(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, pred(s(s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(s(minus(0, 0))))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(gcd(0, 0), gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(gcd(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(gcd(0, s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, true), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(pred(s(0)), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(pred(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, gcd(0, 0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, gcd(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, minus(0, 0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(pred(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(minus(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, true)), 0))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(pred(s(0)), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(gcd(0, 0))), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, true))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(0, s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, pred(s(0))), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(minus(s(0), 0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(gcd(0, s(s(0)))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, gcd(s(s(0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: minus, 0, s, le, if_gcd, false, true, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) 
if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) 
if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) 
Thus, the rule if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)

Problem 23: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(minus(0, 0)))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(minus(0, 0), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(minus(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(gcd(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(gcd(0, 0), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(pred(s(0)), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(gcd(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(minus(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, le(0, _x111))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(0, s(0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(gcd(s(0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(le(0, _x121), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(s(0), s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, true)), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, pred(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(pred(s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(minus(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(gcd(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(gcd(0, s(s(0))))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(minus(s(0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(gcd(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(gcd(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))if_gcd#(gcd(pred(s(pred(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, pred(s(s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(s(minus(0, 0))))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(gcd(0, 0), gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(gcd(0, s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, true), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(pred(s(0)), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(pred(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, gcd(0, 0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, gcd(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, minus(0, 0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(pred(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(minus(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, true)), 0))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(pred(s(0)), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(gcd(0, 0))), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, true))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(0, s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, pred(s(0))), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(minus(s(0), 0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(gcd(0, s(s(0)))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, gcd(s(s(0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: 0, minus, le, s, if_gcd, true, false, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(pred(minus(s(s(0)), s(0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(0)), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) 
if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(0)), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) 
if_gcd#(minus(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), gcd(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(minus(pred(minus(s(s(0)), 0)), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(pred(minus(s(s(0)), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(s(pred(pred(minus(s(s(0)), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(pred(s(s(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(minus(pred(pred(minus(s(s(0)), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(minus(0, 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(pred(s(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(gcd(s(0), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(gcd(s(s(0)), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(minus(s(s(0)), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(0)), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(pred(s(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(minus(s(0), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), minus(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), pred(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) 
if_gcd#(gcd(pred(pred(pred(s(minus(s(s(0)), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) 
Thus, the rule if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(minus(s(s(0)), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(pred(s(s(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(0)), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(s(0), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(0)), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(minus(0, 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(minus(s(s(0)), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(0)), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(minus(s(s(0)), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(0)), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(s(0)), s(0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), gcd(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(0)), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), minus(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(minus(s(0), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), pred(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(minus(s(s(0)), 0)), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(pred(s(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(minus(s(s(0)), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)

Problem 24: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(minus(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, minus(s(0), 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(pred(s(0))), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(gcd(0, pred(minus(s(s(pred(s(0)))), 0)))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), minus(0, 0)))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(gcd(0, 0), 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), gcd(0, pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(minus(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, gcd(0, s(0)))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(gcd(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(gcd(0, pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(gcd(0, s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, pred(s(0))))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(0, gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(pred(s(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(minus(s(0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(pred(s(s(0))), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(gcd(0, 0), minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, gcd(0, 0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(s(pred(s(0)))), s(0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(pred(s(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(pred(s(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(pred(s(pred(s(0)))))))), 0), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(pred(s(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(pred(s(s(pred(s(0)))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0)))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(pred(s(pred(s(0))))), 0)))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(pred(s(0)), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(pred(s(0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(pred(gcd(s(0), 0)))), 0)))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(minus(pred(gcd(0, s(0))), 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(gcd(0, 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(gcd(0, minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(false, x, y) → gcd#(minus(y, x), x)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(s(pred(s(0)))), s(0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), pred(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), pred(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(gcd(s(0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(minus(s(s(pred(s(0)))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(pred(s(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), gcd(0, pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(0, pred(s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(gcd(0, s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(gcd(s(pred(s(0))), 0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(s(0), s(0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), gcd(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), gcd(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(minus(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, pred(s(0))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(gcd(0, true), 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(minus(gcd(0, s(0)), 0)))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, pred(s(gcd(0, minus(true, 0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(minus(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(gcd(0, 0))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(le(0, _x141), 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(minus(gcd(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(gcd(0, pred(s(pred(s(0))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), minus(pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(gcd(0, s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), minus(pred(s(0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), minus(pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(minus(pred(minus(s(s(pred(s(0)))), 0)), 0)), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(pred(s(pred(s(0)))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(minus(0, 0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(minus(0, 0), s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(s(0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, gcd(s(0), 0))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(gcd(0, 0)), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, pred(s(0))))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(pred(s(0)))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(minus(s(pred(gcd(0, s(0)))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), minus(0, 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(minus(s(gcd(0, minus(true, 0))), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(gcd(s(s(pred(s(0)))), 0), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(pred(gcd(s(0), 0)))), 0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(gcd(0, s(pred(s(0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(minus(s(0), 0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, minus(s(0), 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, minus(s(0), 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), gcd(0, 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(pred(s(s(0))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(le(0, _x21), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(0, 0)), minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(0)), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, pred(s(0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(pred(s(0)), minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(minus(s(s(pred(gcd(0, s(0))))), 0)), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, gcd(s(0), 0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(minus(s(s(pred(s(0)))), 0)), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, pred(s(0))), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(minus(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(minus(0, 0))))), 0), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(pred(s(s(s(pred(s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(le(0, _x61)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(s(pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(gcd(0, s(s(0))))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(minus(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(s(0), 0)))), 0), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(minus(0, 0)), 0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, pred(s(0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(pred(s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(pred(s(0)), s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, pred(s(0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(minus(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(minus(0, 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(pred(s(s(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), minus(pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(0, gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(0)), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(minus(0, 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), gcd(0, minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(gcd(0, 0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(pred(s(s(pred(gcd(s(0), 0)))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(gcd(s(0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(gcd(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(pred(s(0)), s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(pred(s(0))))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(pred(minus(s(s(pred(s(0)))), 0))))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(pred(s(0)), 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(pred(s(true)), 0))))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(minus(0, 0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(minus(s(pred(gcd(s(0), 0))), 0)), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(pred(s(0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(pred(s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), minus(0, 0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(gcd(0, 0), gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(minus(s(0), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(gcd(s(0), 0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(gcd(s(0), 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(pred(s(true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), minus(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), pred(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), pred(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(gcd(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(gcd(0, 0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(gcd(0, 0), s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(s(0)))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(pred(s(0)), minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, pred(s(0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), s(0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), pred(s(0)))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(minus(s(pred(s(0))), 0)), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), gcd(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(minus(s(0), 0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(minus(0, minus(0, 0)), 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(pred(s(0))))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(pred(s(0)), s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(pred(s(pred(s(0)))))))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, le(0, _x81)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), pred(s(0))))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(minus(pred(s(0)), 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(gcd(s(0), 0)))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(pred(s(0)))))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, gcd(s(0), 0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, true), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(minus(s(s(pred(gcd(0, s(0))))), 0)), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(minus(s(s(pred(gcd(0, s(0))))), 0)), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(minus(pred(s(0)), 0))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(pred(s(s(pred(gcd(s(0), 0)))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, pred(s(s(0))))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(pred(s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(pred(s(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(minus(pred(s(0)), 0))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(minus(0, 0)), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(pred(s(0)), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), gcd(0, 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(minus(s(s(pred(s(0)))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(0, gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(minus(s(s(pred(s(0)))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x171), 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(le(0, _x171), 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, gcd(s(true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(gcd(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(pred(gcd(s(0), 0))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(gcd(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, gcd(0, minus(true, 0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(minus(0, 0)))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(minus(pred(gcd(0, s(0))), 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), minus(0, 0))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(s(pred(s(0))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), minus(0, 0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(minus(s(s(pred(s(0)))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(s(pred(gcd(0, s(0))))), s(0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(s(0)))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(s(pred(gcd(0, s(0))))), s(0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(le(0, _x141), 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(s(pred(gcd(s(0), 0)))), s(0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(pred(s(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(s(pred(gcd(s(0), 0)))), s(0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(minus(0, 0), 0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(gcd(s(pred(s(0))), 0)), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(pred(s(0)))), 0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(minus(0, 0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(minus(0, 0))), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(minus(pred(s(0)), 0))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(pred(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(minus(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(pred(s(0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(s(pred(gcd(0, s(0))))), s(0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(pred(s(0)))), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), gcd(0, pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, minus(pred(s(gcd(0, minus(true, 0)))), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, pred(pred(minus(s(s(pred(s(0)))), 0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, pred(s(true))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(gcd(0, s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, pred(s(0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(pred(gcd(s(0), 0))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), pred(s(0))))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(pred(s(pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(pred(s(0))))), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(gcd(0, 0))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, gcd(0, minus(true, 0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(minus(s(s(0)), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, pred(s(0)))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(gcd(0, s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(s(pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, gcd(0, minus(true, 0)))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(pred(s(0)), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(minus(0, 0), gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(le(0, _x171), 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(pred(s(0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(gcd(0, s(true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(minus(s(pred(s(0))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(minus(s(s(pred(s(0)))), 0))))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(minus(pred(s(0)), 0))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(pred(s(s(0)))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(minus(0, 0)), 0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(minus(s(pred(s(0))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(gcd(0, s(s(0)))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(pred(s(0)), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(pred(s(s(0))), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0)))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(minus(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(minus(0, 0)))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(pred(s(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(minus(s(s(pred(s(0)))), 0), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), gcd(0, pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(gcd(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0)))))), 0)), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(pred(s(s(0))))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(minus(0, 0))))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), gcd(0, 0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(gcd(0, pred(s(0))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(gcd(0, s(pred(gcd(0, s(0)))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0)), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(pred(s(pred(s(0)))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(minus(s(pred(gcd(s(0), 0))), 0)), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, gcd(0, s(s(0)))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(pred(gcd(s(0), 0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(pred(s(0))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), minus(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(pred(s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(pred(s(0)), s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(0, 0), true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(pred(s(pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(gcd(0, pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(minus(0, 0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(minus(s(s(pred(s(0)))), 0)), 0)), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(pred(s(pred(s(0)))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(pred(s(0)), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(0, s(pred(s(pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(minus(0, 0), 0), true)), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(0, minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(minus(s(s(pred(s(0)))), 0)), 0)), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(minus(0, 0), s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(minus(0, 0)))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(pred(s(gcd(s(0), 0)))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(minus(0, 0), minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, minus(0, 0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, le(0, _x81))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(pred(s(pred(s(0)))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(minus(s(s(pred(gcd(s(0), 0)))), 0), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(pred(s(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(pred(s(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(pred(gcd(0, s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(minus(0, 0))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(0, 0), true), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(minus(pred(minus(s(s(pred(s(0)))), 0)), 0)), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(minus(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(minus(s(0), 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(minus(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(minus(s(s(pred(s(0)))), s(0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(minus(0, 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), minus(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(pred(s(pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(pred(s(pred(s(0))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x161), 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(0, s(0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(s(s(pred(s(pred(s(0)))))), 0))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(pred(s(true)), 0)))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(pred(s(0)))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(gcd(s(s(pred(s(0)))), 0), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(pred(s(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(minus(s(0), 0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(gcd(0, s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(pred(s(pred(s(0)))), 0))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0)))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(pred(s(s(0)))))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), minus(0, 0)))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(pred(s(s(pred(s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(gcd(0, 0), s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(gcd(0, 0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(gcd(0, 0), s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(gcd(0, 0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), pred(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(pred(s(s(pred(s(0)))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), pred(s(0)))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(pred(s(true)), 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(pred(s(0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(gcd(0, pred(s(0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(pred(s(0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(gcd(0, s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(s(pred(gcd(0, s(0)))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0)), 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(pred(s(0)), minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, minus(0, pred(s(0)))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, minus(0, 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(pred(pred(minus(s(s(pred(s(0)))), 0))))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), minus(0, 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), pred(s(0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, minus(s(0), 0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(pred(s(s(pred(s(0)))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(gcd(0, pred(s(0))))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), gcd(0, 0)))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0)))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(s(pred(gcd(0, s(0))))), s(0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(pred(s(s(pred(s(0)))))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, pred(s(minus(true, 0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), gcd(0, 0)), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(minus(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0)))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(pred(gcd(s(0), 0)))), 0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(gcd(0, pred(gcd(0, s(0)))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(minus(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(pred(s(s(pred(s(0)))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, true)), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(gcd(0, 0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), pred(s(0))))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(pred(s(s(pred(s(0)))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), minus(0, 0)), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(minus(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, pred(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(pred(s(s(true)))), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), pred(s(minus(0, 0))))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(minus(s(pred(gcd(0, s(0)))), 0)), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(pred(s(s(pred(gcd(0, s(0))))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(minus(s(gcd(0, minus(true, 0))), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(gcd(0, s(pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), minus(pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(gcd(0, s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(gcd(0, 0)))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), minus(0, 0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(minus(s(0), 0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(minus(s(true), 0)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, gcd(s(0), 0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, pred(s(pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(if_gcd(false, 0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), 0), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(gcd(0, pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(minus(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(minus(0, 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(s(s(pred(s(pred(s(0)))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), pred(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(pred(s(0))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), gcd(0, 0))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(minus(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(pred(s(0)), _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, le(0, _x101)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, le(0, _x81))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), minus(gcd(0, minus(true, 0)), 0)), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(pred(s(0))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(minus(true, 0), 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(gcd(0, pred(s(pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, minus(0, 0)))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(le(0, _x161), 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(gcd(0, s(0)))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), gcd(0, pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(gcd(s(pred(gcd(s(0), 0))), 0)), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(0)), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(pred(s(s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(gcd(s(s(pred(s(0)))), 0), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(pred(s(gcd(0, 0))), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(minus(0, 0), minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(0, minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(pred(s(0)), 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(gcd(0, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(gcd(0, 0)), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(gcd(0, 0), true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(pred(s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(minus(s(s(pred(s(0)))), s(0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(pred(s(0)), 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(0, gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(gcd(0, pred(minus(s(s(pred(s(0)))), 0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(pred(s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0)), 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(minus(s(s(pred(s(0)))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(gcd(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(0, 0), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)gcd#(s(x), s(y)) → if_gcd#(le(y, x), s(x), s(y))
if_gcd#(gcd(minus(pred(s(pred(pred(minus(s(s(pred(s(0)))), 0))))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(pred(s(s(0))))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, pred(s(s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, gcd(0, s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(gcd(0, pred(minus(s(s(pred(s(0)))), 0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, gcd(s(0), 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(if_gcd(true, s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(minus(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(pred(s(pred(s(0))))))), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(minus(0, minus(0, 0)), 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(minus(s(pred(s(0))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(minus(0, 0))))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(pred(gcd(0, s(true))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(gcd(0, minus(true, 0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(pred(minus(s(s(pred(s(0)))), 0))))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(minus(s(0), 0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(minus(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(pred(gcd(s(0), 0)))), 0)))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(pred(s(pred(s(0))))), 0)))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, pred(s(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(gcd(s(0), 0)))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(pred(s(0)))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(minus(pred(minus(s(s(pred(s(0)))), 0)), 0)), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(pred(s(s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(pred(s(pred(s(0)))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(0, pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(s(pred(s(0))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(gcd(0, s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(gcd(0, 0), gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(gcd(0, 0)))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(gcd(0, 0), s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(s(pred(s(0))), 0)), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, gcd(0, minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(pred(s(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(minus(0, 0), minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, minus(0, 0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(pred(s(gcd(s(s(pred(gcd(0, s(0))))), 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(s(pred(s(0)))), s(0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(pred(s(0))), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(minus(s(pred(gcd(0, s(0)))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(minus(s(pred(gcd(0, s(0)))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(minus(0, 0))))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(gcd(0, s(s(pred(s(0))))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(0)), gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(gcd(0, pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(le(0, _x201))), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(minus(true, 0), 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, gcd(0, 0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(minus(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(gcd(0, minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), gcd(0, pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(gcd(0, 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(gcd(0, minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(s(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(s(0), 0)))), 0), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(pred(s(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(gcd(0, minus(s(s(pred(s(0)))), 0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(pred(s(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(0, s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(pred(gcd(s(0), 0))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(gcd(0, s(0))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(gcd(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, gcd(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), gcd(0, pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(minus(s(pred(s(0))), 0)))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(minus(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, minus(0, 0)), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, pred(s(0))))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(gcd(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0)))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(gcd(0, pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(gcd(0, s(s(pred(s(0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(minus(gcd(0, gcd(0, true)), 0))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(minus(0, 0), 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(minus(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(s(pred(gcd(0, s(0))))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(s(pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(minus(s(s(pred(gcd(s(0), 0)))), 0), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(s(0)))), 0), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(pred(s(0)), minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, pred(s(0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(minus(s(pred(s(0))), 0)), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(gcd(0, 0), s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(minus(pred(s(0)), 0))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(minus(gcd(0, s(0)), 0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(gcd(0, s(s(0))))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(pred(s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(minus(pred(s(0)), 0))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), minus(0, 0))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(gcd(0, 0)), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(minus(s(pred(gcd(s(0), 0))), 0)), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(minus(s(pred(s(0))), 0)))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, 0), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(pred(s(0))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, gcd(s(0), 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, gcd(s(0), 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, pred(s(minus(true, 0))))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(pred(s(pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(s(gcd(0, le(0, _x81)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), minus(pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(minus(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), 0), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(gcd(s(pred(s(0))), 0)))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(pred(s(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(minus(s(0), 0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(gcd(s(0), 0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(gcd(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(gcd(s(s(pred(gcd(0, s(0))))), 0), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x161), 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(minus(gcd(0, minus(true, 0)), 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, pred(s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, minus(0, gcd(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(gcd(0, 0), minus(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(pred(s(s(s(pred(s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(pred(s(pred(s(0))))))), 0)), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(minus(s(0), 0)), 0), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(gcd(0, 0))))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(s(s(pred(s(pred(s(0)))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, pred(s(gcd(0, minus(true, 0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(minus(s(0), 0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(gcd(0, minus(s(s(pred(s(0)))), 0)))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(pred(s(s(s(pred(gcd(s(0), 0)))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, pred(gcd(s(0), 0))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(minus(0, 0))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(minus(gcd(0, s(0)), 0)))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(minus(0, 0), s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(minus(gcd(0, minus(true, 0)), 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(true, 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(0)), 0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(pred(s(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(minus(pred(gcd(s(0), 0)), 0))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(s(pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(s(pred(s(0)))), s(0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(gcd(s(0), 0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, gcd(0, 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0)))), 0)))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), 0), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(s(0)), s(0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(gcd(s(0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(minus(s(0), 0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(minus(s(s(pred(gcd(0, s(0))))), 0), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(minus(pred(gcd(0, s(0))), 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(minus(pred(gcd(0, s(0))), 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(gcd(s(0), 0)))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(minus(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(gcd(0, 0))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, gcd(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(minus(0, 0), 0)), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(0, gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(0, 0), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(s(pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(pred(s(0)))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(0, pred(s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, pred(gcd(s(0), 0))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(pred(s(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(gcd(0, 0), s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(gcd(0, 0)))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(s(s(minus(0, 0))))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(gcd(0, true), 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(minus(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(minus(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(minus(s(s(pred(s(0)))), 0))))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(gcd(0, minus(true, 0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(minus(s(0), 0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), minus(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), minus(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(pred(s(gcd(s(0), 0)))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(pred(s(0)), 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(0, s(pred(s(pred(s(0))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), minus(pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(pred(s(0)))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, minus(minus(0, 0), 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(0)), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), gcd(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(pred(s(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), pred(s(0)))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(0, s(pred(s(0))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(pred(s(s(s(pred(s(0)))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(gcd(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(pred(s(s(pred(s(0)))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(0, 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(minus(0, 0), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0)), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(gcd(s(pred(gcd(0, s(0)))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(s(pred(gcd(0, s(0)))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(pred(s(s(0)))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(pred(s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), 0), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(gcd(s(pred(s(0))), 0)), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(s(pred(s(0)))))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(pred(s(s(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(gcd(0, 0), 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, gcd(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), minus(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), minus(pred(s(gcd(0, gcd(0, true)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(s(0)))))), 0))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(gcd(0, s(s(pred(gcd(0, s(0)))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(minus(s(s(0)), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(pred(s(pred(s(0))))))), 0)), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(minus(s(s(pred(s(0)))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(gcd(0, s(s(0)))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(pred(s(s(0)))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), gcd(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(pred(s(0)), 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(pred(s(0)), 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(minus(s(pred(s(0))), 0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(minus(0, 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, minus(true, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), pred(s(0))))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(pred(s(true)), 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(pred(s(pred(s(0)))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(pred(s(0))))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(minus(s(s(pred(s(0)))), 0), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(pred(s(s(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(pred(s(s(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), minus(pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), pred(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(gcd(0, s(s(0)))), 0)), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, minus(s(true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(pred(s(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, pred(s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), pred(s(0)))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), 0), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(s(pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(pred(s(pred(s(0)))), 0))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(minus(gcd(0, s(true)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(minus(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0)))))), 0)), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(0)), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, gcd(0, 0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(gcd(0, 0), minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(pred(s(pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(gcd(0, s(pred(s(0))))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(gcd(0, pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(s(pred(gcd(s(0), 0)))), s(0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, pred(s(true))), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(minus(true, 0), 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(pred(s(s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(pred(gcd(s(0), 0)))), 0)))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(pred(s(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(minus(0, 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(gcd(s(gcd(0, minus(true, 0))), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(minus(0, minus(0, 0)), 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(s(pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, true)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(pred(s(0)), true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(minus(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0)), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(gcd(s(pred(gcd(0, s(0)))), 0)), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(s(0)))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(pred(s(0)))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), pred(s(0))))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(minus(0, 0))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, minus(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(pred(s(true)))), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, le(0, _x81))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), minus(pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, minus(pred(s(true)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), minus(0, 0)))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(gcd(s(0), 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(pred(s(true)), 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(pred(s(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(pred(s(pred(s(0))))), 0)))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), gcd(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(pred(s(s(0)))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(pred(s(0))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(pred(s(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(minus(s(0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(gcd(0, s(0)), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(minus(s(s(pred(gcd(s(0), 0)))), 0))))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(minus(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(minus(0, 0))))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), s(0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(0, true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(pred(s(s(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(minus(s(0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), minus(pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(pred(s(0))))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(gcd(0, s(0)), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(pred(s(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(minus(s(0), 0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(gcd(0, 0)), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(minus(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(pred(s(pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(s(s(minus(0, 0))))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(gcd(0, minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, pred(s(0))))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, pred(s(0))), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(pred(s(0)), minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(0, 0), pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), minus(0, 0)))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(gcd(0, s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), gcd(0, 0)))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, pred(s(0))), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, pred(s(true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), pred(s(0))))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), pred(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), gcd(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(pred(s(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(minus(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(gcd(0, s(0))), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(gcd(0, s(0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(minus(s(s(pred(gcd(0, s(0))))), 0)), 0)), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(gcd(0, s(s(0)))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(pred(s(pred(s(0))))), 0)))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x171), 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(minus(s(s(pred(s(0)))), 0))))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(gcd(0, s(pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), gcd(0, 0)))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(pred(s(pred(s(0)))))), 0))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0)))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, minus(0, 0)))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(pred(s(0)))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(gcd(0, s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(pred(s(0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), gcd(0, 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(gcd(s(0), 0), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, gcd(s(0), 0))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(gcd(0, 0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, pred(s(0))))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(minus(s(s(pred(s(0)))), 0), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(minus(s(s(pred(gcd(s(0), 0)))), 0), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, true)), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), minus(0, 0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), gcd(0, minus(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(minus(pred(gcd(s(0), 0)), 0))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), minus(pred(s(gcd(0, true))), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, le(0, _x81)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0)))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(minus(s(0), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, minus(gcd(0, minus(pred(s(true)), 0)), 0)), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(s(minus(gcd(0, gcd(0, true)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), minus(0, 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(minus(0, 0), 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(gcd(0, s(true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(pred(s(0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(pred(s(0)), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), pred(s(0))))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(gcd(0, 0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(gcd(0, 0), s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(pred(s(0)))), 0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), s(0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(minus(s(s(0)), 0)), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(gcd(0, s(0)), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(gcd(0, 0), 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(minus(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0)))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(pred(s(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(minus(pred(gcd(s(0), 0)), 0))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(pred(s(0)), true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(minus(gcd(0, true), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(minus(0, 0)), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(pred(gcd(s(0), 0)))), 0)))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(pred(s(s(s(pred(s(0)))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(0), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(0)), gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(minus(gcd(0, s(0)), 0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(minus(gcd(0, s(0)), 0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(pred(s(s(0))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(minus(0, 0), 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(0, pred(gcd(0, s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(minus(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), minus(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(0, s(minus(0, 0)))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), gcd(0, 0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(minus(true, 0))), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(pred(s(0))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(pred(s(s(gcd(0, minus(true, 0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(minus(s(s(pred(gcd(s(0), 0)))), 0)), 0)), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), pred(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(minus(0, 0)))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, gcd(s(s(0)), 0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(pred(minus(s(s(pred(s(0)))), 0))))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(minus(gcd(0, s(0)), 0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(gcd(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(minus(s(s(pred(s(0)))), s(0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(pred(s(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), pred(s(0))))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(gcd(s(0), 0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(minus(gcd(s(0), 0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(pred(s(s(s(pred(gcd(0, s(0))))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(pred(s(0)))))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, le(0, _x81)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(minus(s(s(pred(s(0)))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(minus(0, 0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(minus(0, 0), s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(minus(0, 0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(minus(0, 0), s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(gcd(0, s(s(0))))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), gcd(0, pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(gcd(0, s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(gcd(0, s(s(0))))), 0), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(pred(s(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(pred(s(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(gcd(0, s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(pred(s(0)), s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, pred(s(s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(pred(s(minus(s(s(pred(s(0)))), 0))))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(s(0)))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), le(0, _x41)), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0)), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(gcd(0, 0), 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(s(0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(gcd(0, s(s(0))))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(gcd(0, true)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(gcd(0, s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(gcd(0, s(pred(s(0))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(pred(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(pred(s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(pred(s(0)), s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(pred(s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(pred(s(0)), s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(s(pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, 0), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(0, gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), gcd(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(gcd(0, 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, gcd(s(s(0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(gcd(s(0), 0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), gcd(0, pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(pred(s(s(0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(pred(s(s(0)))), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(minus(s(s(0)), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(minus(pred(gcd(0, s(0))), 0))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(minus(0, minus(0, 0)), 0), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), minus(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), minus(0, 0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(pred(gcd(s(0), 0))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, true), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(minus(0, 0)))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(gcd(0, 0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(pred(s(0)), s(true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(gcd(0, s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(pred(s(0)))))), 0))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(gcd(0, 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(0, gcd(gcd(0, 0), gcd(0, minus(true, 0)))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), minus(0, 0)))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(pred(s(0)), le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(minus(0, 0), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, pred(s(s(0))))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(pred(s(0)))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, pred(pred(minus(s(s(pred(s(0)))), 0)))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(minus(pred(s(0)), 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), minus(0, 0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(minus(gcd(s(0), 0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), gcd(0, pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, s(0))), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(minus(0, 0), 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(gcd(s(true), 0)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(minus(s(s(pred(s(0)))), 0), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(pred(s(s(pred(gcd(s(0), 0)))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(gcd(0, 0), s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(gcd(0, s(gcd(0, minus(true, 0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, minus(pred(s(gcd(0, minus(true, 0)))), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0)))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x181), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, gcd(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(minus(s(s(pred(gcd(s(0), 0)))), 0)), 0)), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(pred(s(0)))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(minus(0, 0)), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(s(0))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(pred(s(gcd(0, minus(true, 0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(minus(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(gcd(0, 0)))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(gcd(s(0), 0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(gcd(0, pred(pred(minus(s(s(pred(s(0)))), 0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(s(pred(gcd(s(0), 0))), 0)), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(gcd(s(pred(s(0))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(gcd(0, 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, gcd(0, 0)), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, gcd(0, 0)))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(gcd(0, 0), minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(gcd(0, 0), s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(minus(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(pred(s(s(0)))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(minus(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(minus(s(s(pred(gcd(0, s(0))))), 0)), 0)), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(pred(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(minus(s(s(pred(gcd(s(0), 0)))), 0))))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(minus(s(0), 0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, 0), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(gcd(0, s(pred(s(0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(s(0), 0)))), 0), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), s(0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(minus(s(0), 0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, gcd(0, s(0)))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(pred(s(s(s(pred(gcd(s(0), 0)))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(pred(gcd(s(0), 0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(minus(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(gcd(0, s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(gcd(0, minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, pred(s(0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, le(0, _x111))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(gcd(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(pred(s(true)), 0))))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(pred(s(true)), 0))))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(s(gcd(0, le(0, _x81)))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), pred(s(gcd(0, minus(true, 0))))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(pred(s(s(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, minus(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(le(0, _x121), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(gcd(0, 0), _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(minus(0, minus(0, 0)), 0), true), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), minus(pred(s(0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(0, gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(pred(s(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), minus(pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(gcd(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(gcd(0, s(s(pred(s(0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(minus(0, 0), pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(minus(pred(s(0)), 0))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(minus(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(gcd(0, pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(gcd(0, 0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(gcd(0, 0))), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(gcd(0, le(0, _x81))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(minus(s(0), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(minus(s(0), 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(minus(s(s(pred(gcd(s(0), 0)))), 0))))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(s(s(pred(s(pred(s(0)))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(pred(s(0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(minus(pred(s(0)), 0))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(pred(s(pred(s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(pred(s(pred(s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), gcd(0, minus(true, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, minus(s(0), 0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), minus(pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(pred(s(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), gcd(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), gcd(0, pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(gcd(s(0), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(s(s(pred(s(pred(s(0)))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(minus(0, 0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(s(0))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(minus(0, 0), s(true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(pred(s(0)))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(minus(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, pred(s(s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(s(s(minus(0, 0))), 0))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(s(0), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(gcd(0, pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, minus(0, 0)), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(gcd(s(0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(minus(0, 0)))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(minus(0, 0), s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(gcd(s(0), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(0))), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(gcd(0, s(0)))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(0, gcd(s(s(pred(gcd(0, s(0))))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(minus(0, 0), gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(gcd(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0)), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(pred(s(s(pred(s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(gcd(s(pred(s(0))), 0)), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(gcd(s(pred(s(0))), 0)))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(gcd(s(0), 0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(pred(s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(pred(s(s(s(pred(gcd(s(0), 0)))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(pred(s(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, minus(0, 0)), gcd(0, 0)), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, minus(s(0), 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), minus(pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), gcd(0, 0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(0, s(s(0))), 0))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, gcd(0, true))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(pred(s(pred(s(0))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(minus(0, 0))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(gcd(0, 0), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(pred(s(s(pred(gcd(0, s(0))))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0)))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(gcd(0, s(pred(gcd(0, s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, pred(s(0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(gcd(0, true), 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, pred(s(0))), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(s(minus(true, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(pred(s(s(s(pred(s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))), 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(gcd(s(0), 0)))))))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(minus(s(pred(s(0))), 0)), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(s(s(0)))), 0), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(pred(s(0)), minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, pred(s(0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(minus(s(0), 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(gcd(0, true))), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(pred(s(0)))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(minus(0, 0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(minus(0, 0), s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(gcd(0, 0))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(gcd(0, s(gcd(0, minus(true, 0)))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(pred(s(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0)))), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(s(pred(gcd(0, s(0))))), s(0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, pred(s(true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(minus(minus(0, 0), 0), true))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(minus(s(s(pred(s(0)))), 0)), 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(s(gcd(minus(0, 0), true)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(0, s(gcd(0, gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(le(0, _x181), 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(s(s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, pred(s(minus(0, 0)))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), pred(s(0))))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(s(gcd(0, gcd(0, true))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), minus(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(minus(0, minus(0, 0)))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, true)), 0)))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(pred(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(pred(s(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(0, pred(s(gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(gcd(0, minus(s(s(pred(s(0)))), 0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), gcd(0, pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(gcd(0, le(0, _x81))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), s(0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), minus(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)), 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(minus(s(s(pred(gcd(0, s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, minus(0, 0)))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(minus(0, 0), minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, minus(0, 0)), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(minus(0, 0), _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, s(minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(0, gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), gcd(0, 0)))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(minus(0, 0), gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(0, gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(minus(pred(gcd(0, s(0))), 0))), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), gcd(0, true)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(gcd(0, s(true))), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), 0), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(pred(s(gcd(gcd(0, 0), gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(minus(s(0), 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(minus(s(0), 0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, le(s(0), s(_x91)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(pred(s(gcd(0, minus(true, 0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(minus(s(s(pred(s(0)))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(minus(s(pred(gcd(0, s(0)))), 0)), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(minus(s(0), 0)), pred(s(gcd(0, gcd(0, true))))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(gcd(0, 0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), pred(s(0))))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(minus(s(s(pred(s(0)))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(gcd(0, pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, gcd(0, pred(s(0)))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(pred(s(s(0)))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(pred(s(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, 0), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(minus(s(pred(gcd(0, s(0)))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), gcd(0, pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(minus(0, minus(0, 0)), 0))), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(minus(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(pred(s(s(pred(s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), gcd(0, 0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(s(pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, gcd(s(0), 0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), gcd(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, le(0, _x41)), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), s(0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(s(gcd(0, le(0, _x81))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), minus(0, 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(minus(s(s(pred(gcd(s(0), 0)))), 0)), 0)), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(gcd(0, 0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), gcd(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(gcd(s(pred(gcd(0, s(0)))), 0)), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(minus(s(s(pred(s(0)))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(pred(s(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(gcd(0, minus(0, minus(0, 0))), 0), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(minus(0, 0))), 0))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(pred(s(0)))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(pred(s(gcd(gcd(0, 0), gcd(0, minus(true, 0))))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(s(s(pred(s(pred(s(0)))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(minus(s(0), 0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(0, 0)), 0), minus(true, 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(minus(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(pred(pred(minus(s(s(pred(s(0)))), 0))))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(minus(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(gcd(0, 0), gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(pred(s(minus(s(s(pred(s(0)))), 0))))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(pred(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(pred(s(s(0))), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(0, 0), pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, minus(0, 0)), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(pred(s(pred(s(0))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, pred(s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(gcd(s(pred(gcd(0, s(0)))), 0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, pred(s(s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, pred(s(s(0))))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, pred(gcd(0, s(le(0, _x81))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(pred(s(s(minus(0, 0)))), 0)), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, pred(gcd(s(0), 0))))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(le(0, _x131), 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), pred(s(minus(0, 0))))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, gcd(minus(0, 0), true))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(gcd(s(pred(gcd(s(0), 0))), 0)), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), gcd(0, pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(minus(0, 0))), 0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(pred(s(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(s(0), 0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(pred(s(s(s(pred(s(0)))))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(pred(s(minus(s(s(0)), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(minus(s(0), 0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(minus(gcd(s(0), 0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(s(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(s(gcd(0, true)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(pred(s(pred(s(0)))))))), 0), pred(gcd(0, gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(pred(s(s(gcd(0, minus(true, 0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(minus(0, 0))), pred(minus(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(minus(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), gcd(0, pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(pred(s(s(gcd(0, true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(minus(0, 0), pred(s(0))), true), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(pred(s(s(s(pred(s(0)))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, pred(s(s(s(0))))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(gcd(0, s(0))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(s(true), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0)))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(gcd(0, pred(s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(gcd(s(gcd(0, minus(true, 0))), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(pred(s(s(0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(gcd(s(0), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(pred(s(gcd(s(0), 0)))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(0, minus(true, pred(s(0)))), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, minus(gcd(pred(s(0)), minus(true, 0)), 0)), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(gcd(0, s(0)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(minus(0, minus(pred(s(0)), 0)), 0), true), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(s(0)), 0), pred(s(minus(gcd(0, gcd(0, true)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(le(0, _x151), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), gcd(0, 0))))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(minus(s(0), 0)))), pred(s(gcd(0, gcd(0, true))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(s(s(minus(0, 0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(0)))))), pred(gcd(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(pred(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(minus(s(s(pred(gcd(0, s(0))))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(pred(s(minus(s(s(pred(s(0)))), 0))))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(minus(s(pred(s(0))), 0)), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(s(minus(0, 0)), 0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(minus(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), 0))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(pred(s(0)), 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(pred(s(0))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(pred(s(gcd(0, 0))), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(minus(gcd(s(minus(gcd(gcd(pred(s(0)), 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(s(pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(gcd(0, gcd(0, gcd(0, true))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(minus(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), 0), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(s(pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, pred(s(minus(true, 0))))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(s(0))), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(pred(s(0)))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(gcd(0, s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(gcd(0, s(minus(0, 0)))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, gcd(0, 0)))))), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(gcd(0, pred(s(s(true)))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, pred(s(gcd(0, minus(true, 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(minus(s(pred(s(pred(s(0))))), 0)))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(gcd(0, s(0))))))))), pred(gcd(0, gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(gcd(0, s(s(0))))))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, pred(s(le(0, _x81))))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), gcd(0, 0)))), pred(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(0, 0), pred(gcd(s(gcd(0, true)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(gcd(0, pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0)))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(gcd(0, pred(s(0))))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(0, gcd(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(gcd(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(pred(s(pred(s(0)))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(minus(s(0), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(0, gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(pred(s(gcd(0, s(0))))))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(pred(s(0))), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(s(gcd(0, minus(le(0, _x81), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(pred(s(0)), 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, minus(s(s(pred(s(0)))), 0)))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(s(pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0))))))), pred(s(0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), pred(s(minus(0, 0)))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(pred(s(0)), minus(true, pred(s(0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(minus(s(0), 0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), gcd(0, 0)), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(minus(pred(s(true)), 0), 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(gcd(s(s(pred(gcd(0, s(0))))), 0), 0))), pred(gcd(pred(pred(s(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(s(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(s(minus(pred(s(gcd(0, gcd(0, true)))), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(pred(s(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(s(0)))), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(s(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0)))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(gcd(pred(s(pred(minus(s(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), minus(0, 0)))), 0)))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), minus(0, 0)))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(pred(s(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, minus(0, 0)))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, pred(s(0))), gcd(0, minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(pred(s(0)), minus(true, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, pred(s(0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(0, s(0))))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(0)))), pred(gcd(0, gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(gcd(s(0), 0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), pred(s(0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(gcd(0, s(s(0))))), pred(gcd(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(gcd(0, 0), 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(0)), 0))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(pred(gcd(0, s(0))))))))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(minus(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(gcd(s(0), 0)))), gcd(0, 0)))), pred(minus(gcd(pred(s(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))))), pred(s(0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(pred(pred(minus(s(s(pred(s(0)))), 0))))), pred(gcd(pred(s(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), minus(0, 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(minus(minus(s(s(pred(s(0)))), 0), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(pred(s(0)))), 0))), pred(gcd(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, pred(s(0))))))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(s(0)), pred(gcd(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(minus(s(s(pred(s(0)))), 0))), 0), pred(gcd(pred(gcd(s(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, minus(0, 0))))), 0)), 0))), x, y) → gcd#(minus(x, y), y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: minus, 0, s, le, if_gcd, false, true, pred, gcd

Strategy

The left-hand side of the rule if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(gcd(0, pred(s(s(minus(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(minus(pred(pred(s(s(minus(0, 0))))), 0), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(gcd(s(minus(0, 0)), 0)))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(0, gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)))), x, y) 
if_gcd#(minus(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), 0), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(0, gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), minus(pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), 0)), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, minus(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(minus(s(s(minus(0, 0))), 0))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), gcd(0, 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(gcd(0, s(minus(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(pred(s(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(minus(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, gcd(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(pred(s(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), minus(0, 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, pred(s(0))))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(s(pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))))), x, y) 
if_gcd#(gcd(pred(s(pred(pred(s(s(minus(0, 0))))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(gcd(0, minus(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(gcd(0, 0), minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(minus(0, 0), minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(le(0, _x161), 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(s(s(minus(0, 0))), 0))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(pred(s(s(minus(0, 0))))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(minus(s(minus(0, 0)), 0)))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(minus(0, 0), 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(pred(s(s(s(minus(0, 0))))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0)))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(pred(s(0)), minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(gcd(0, 0), 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(pred(s(minus(0, 0))))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), gcd(0, pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(pred(s(0)), 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), pred(s(0))))), x, y) 
if_gcd#(gcd(pred(minus(pred(s(s(minus(0, 0)))), 0)), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(gcd(0, pred(pred(s(s(minus(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0)), 0))), x, y) 
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0))), x, y) 
Thus, the rule if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y) is replaced by the following rules:
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), gcd(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(minus(pred(pred(s(s(minus(0, 0))))), 0), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(gcd(0, 0), minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(gcd(0, pred(s(s(minus(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), gcd(0, pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(0, gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, minus(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(pred(s(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(pred(s(s(minus(0, 0))))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), pred(s(0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(pred(s(0)), minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(gcd(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(minus(gcd(0, gcd(0, minus(true, 0))), 0), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), gcd(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(minus(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(s(pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(0, gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(gcd(0, minus(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, minus(gcd(0, minus(true, 0)), 0)), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(minus(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), 0), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(minus(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(s(minus(0, 0)), 0)))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, gcd(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, pred(s(gcd(0, minus(true, 0))))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(s(pred(pred(s(s(minus(0, 0))))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(pred(s(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, pred(s(minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), pred(s(0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(minus(pred(s(s(minus(0, 0)))), 0)), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(pred(s(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(gcd(0, minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(gcd(0, true), 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(gcd(0, s(minus(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(gcd(0, s(minus(gcd(0, gcd(0, minus(true, 0))), 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(minus(0, 0), minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), minus(0, 0))), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0))), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(minus(true, 0), 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(pred(s(0)), minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, pred(s(0))))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(s(s(minus(0, 0))), 0))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(pred(s(gcd(0, gcd(0, minus(true, 0))))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(minus(s(s(minus(0, 0))), 0))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), minus(pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0)), 0)), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, pred(s(0))))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), minus(0, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), minus(0, 0)))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(minus(0, 0), 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(pred(s(true)), 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(minus(s(minus(0, 0)), 0)))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(gcd(0, 0), minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(le(0, _x161), 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, gcd(0, 0)))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(pred(s(minus(0, 0))))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(pred(s(0)), 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, gcd(0, minus(true, 0)))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(pred(s(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(gcd(0, 0), gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, pred(s(minus(true, 0))))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(pred(s(0)), gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), gcd(0, 0))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(gcd(0, pred(pred(s(s(minus(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(pred(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), pred(s(0)))), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(gcd(0, s(s(minus(0, 0)))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(pred(s(s(s(minus(0, 0))))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(minus(0, 0), minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, minus(0, 0)))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)if_gcd#(gcd(pred(pred(s(s(minus(0, 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(minus(0, 0), gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)
if_gcd#(gcd(pred(pred(s(s(minus(gcd(0, 0), 0))))), pred(gcd(gcd(0, minus(s(minus(gcd(0, gcd(0, minus(true, 0))), 0)), 0)), 0))), x, y) → gcd#(minus(x, y), y)

Problem 3: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

minus#(x, s(y)) → minus#(x, y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: 0, minus, le, s, if_gcd, true, false, pred, gcd

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

minus#(x, s(y)) → minus#(x, y)

Problem 4: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

le#(s(x), s(y)) → le#(x, y)

Rewrite Rules

le(0, y) → truele(s(x), 0) → false
le(s(x), s(y)) → le(x, y)pred(s(x)) → x
minus(x, 0) → xminus(x, s(y)) → pred(minus(x, y))
gcd(0, y) → ygcd(s(x), 0) → s(x)
gcd(s(x), s(y)) → if_gcd(le(y, x), s(x), s(y))if_gcd(true, x, y) → gcd(minus(x, y), y)
if_gcd(false, x, y) → gcd(minus(y, x), x)

Original Signature

Termination of terms over the following signature is verified: 0, minus, le, s, if_gcd, true, false, pred, gcd

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

le#(s(x), s(y)) → le#(x, y)