TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60001 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (135ms).
 | – Problem 2 was processed with processor ForwardNarrowing (6ms).
 |    | – Problem 3 was processed with processor ForwardNarrowing (4ms).
 |    |    | – Problem 4 was processed with processor ForwardNarrowing (2ms).
 |    |    |    | – Problem 5 was processed with processor ForwardNarrowing (1ms).
 |    |    |    |    | – Problem 6 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    | – Problem 7 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (45ms).
 |    |    |    |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (49ms).
 |    |    |    |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (93ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (187ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (323ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 remains open; application of the following processors failed [ForwardNarrowing (312ms), ForwardNarrowing (247ms), ForwardNarrowing (402ms), ForwardNarrowing (131ms), ForwardNarrowing (426ms), ForwardNarrowing (341ms), ForwardNarrowing (366ms), ForwardNarrowing (278ms), ForwardNarrowing (369ms), ForwardNarrowing (299ms), ForwardNarrowing (78ms), ForwardNarrowing (137ms), ForwardNarrowing (146ms), ForwardNarrowing (239ms), ForwardNarrowing (410ms), ForwardNarrowing (431ms), ForwardNarrowing (147ms), ForwardNarrowing (243ms), ForwardNarrowing (339ms), ForwardNarrowing (97ms), ForwardNarrowing (166ms), ForwardNarrowing (446ms), ForwardNarrowing (448ms), ForwardNarrowing (timeout)].

The following open problems remain:

Open Dependency Pair Problem 2

Dependency Pairs

app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(plus, app(s, x)), y) → app#(s, app(app(plus, x), y))app#(app(plus, app(s, x)), y) → app#(plus, x)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: plus, app, 0, inc, s, map, curry, cons, nil

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

inc# → app#(s, 0)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(plus, app(s, x)), y) → app#(plus, x)app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)
inc# → app#(curry, plus)app#(app(app(curry, g), x), y) → app#(app(g, x), y)
app#(app(plus, app(s, x)), y) → app#(s, app(app(plus, x), y))inc# → app#(map, app(app(curry, plus), app(s, 0)))
inc# → app#(app(curry, plus), app(s, 0))app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The following SCCs where found

app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(plus, app(s, x)), y) → app#(s, app(app(plus, x), y))app#(app(plus, app(s, x)), y) → app#(plus, x)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))

Problem 2: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(plus, app(s, x)), y) → app#(s, app(app(plus, x), y))app#(app(plus, app(s, x)), y) → app#(plus, x)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(plus, app(s, x)), y) → app#(s, app(app(plus, x), y)) is 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
app#(s, _x31) 
app#(s, app(s, app(app(plus, _x32), _x31))) 
Thus, the rule app#(app(plus, app(s, x)), y) → app#(s, app(app(plus, x), y)) is replaced by the following rules:
app#(app(plus, app(s, app(s, _x32))), _x31) → app#(s, app(s, app(app(plus, _x32), _x31)))app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)

Problem 3: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(plus, app(s, app(s, _x32))), _x31) → app#(s, app(s, app(app(plus, _x32), _x31)))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(app(curry, g), x), y) → app#(g, x)app#(app(plus, app(s, x)), y) → app#(plus, x)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)
app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: plus, app, 0, inc, s, map, curry, cons, nil

Strategy

The right-hand side of the rule app#(app(plus, app(s, app(s, _x32))), _x31) → app#(s, app(s, app(app(plus, _x32), _x31))) is 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
app#(s, app(s, _x61)) 
app#(s, app(s, app(s, app(app(plus, _x62), _x61)))) 
Thus, the rule app#(app(plus, app(s, app(s, _x32))), _x31) → app#(s, app(s, app(app(plus, _x32), _x31))) is replaced by the following rules:
app#(app(plus, app(s, app(s, 0))), _x61) → app#(s, app(s, _x61))app#(app(plus, app(s, app(s, app(s, _x62)))), _x61) → app#(s, app(s, app(s, app(app(plus, _x62), _x61))))

Problem 4: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(plus, app(s, app(s, 0))), _x61) → app#(s, app(s, _x61))app#(app(plus, app(s, x)), y) → app#(plus, x)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))
app#(app(plus, app(s, app(s, app(s, _x62)))), _x61) → app#(s, app(s, app(s, app(app(plus, _x62), _x61))))app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(plus, app(s, app(s, 0))), _x61) → app#(s, app(s, _x61)) is 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
Thus, the rule app#(app(plus, app(s, app(s, 0))), _x61) → app#(s, app(s, _x61)) is deleted.

Problem 5: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(plus, app(s, x)), y) → app#(plus, x)app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)
app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)app#(app(plus, app(s, app(s, app(s, _x62)))), _x61) → app#(s, app(s, app(s, app(app(plus, _x62), _x61))))
app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)
app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: plus, app, 0, inc, s, map, curry, cons, nil

Strategy

The right-hand side of the rule app#(app(plus, app(s, x)), y) → app#(plus, x) is 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
Thus, the rule app#(app(plus, app(s, x)), y) → app#(plus, x) is deleted.

Problem 6: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))
app#(app(plus, app(s, app(s, app(s, _x62)))), _x61) → app#(s, app(s, app(s, app(app(plus, _x62), _x61))))app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(plus, app(s, app(s, app(s, _x62)))), _x61) → app#(s, app(s, app(s, app(app(plus, _x62), _x61)))) is 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
app#(s, app(s, app(s, app(s, app(app(plus, _x72), _x71))))) 
app#(s, app(s, app(s, _x71))) 
Thus, the rule app#(app(plus, app(s, app(s, app(s, _x62)))), _x61) → app#(s, app(s, app(s, app(app(plus, _x62), _x61)))) is replaced by the following rules:
app#(app(plus, app(s, app(s, app(s, 0)))), _x71) → app#(s, app(s, app(s, _x71)))app#(app(plus, app(s, app(s, app(s, app(s, _x72))))), _x71) → app#(s, app(s, app(s, app(s, app(app(plus, _x72), _x71)))))

Problem 7: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(plus, app(s, app(s, app(s, 0)))), _x71) → app#(s, app(s, app(s, _x71)))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(app(curry, g), x), y) → app#(g, x)app#(app(plus, app(s, app(s, app(s, app(s, _x72))))), _x71) → app#(s, app(s, app(s, app(s, app(app(plus, _x72), _x71)))))
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)
app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: plus, app, 0, inc, s, map, curry, cons, nil

Strategy

The right-hand side of the rule app#(app(plus, app(s, app(s, app(s, 0)))), _x71) → app#(s, app(s, app(s, _x71))) is 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
Thus, the rule app#(app(plus, app(s, app(s, app(s, 0)))), _x71) → app#(s, app(s, app(s, _x71))) is deleted.

Problem 8: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(plus, app(s, app(s, app(s, app(s, _x72))))), _x71) → app#(s, app(s, app(s, app(s, app(app(plus, _x72), _x71)))))app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)
app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)
app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(plus, app(s, app(s, app(s, app(s, _x72))))), _x71) → app#(s, app(s, app(s, app(s, app(app(plus, _x72), _x71))))) is 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
app#(s, app(s, app(s, app(s, _x101)))) 
app#(s, app(s, app(s, app(s, app(s, app(app(plus, _x102), _x101)))))) 
Thus, the rule app#(app(plus, app(s, app(s, app(s, app(s, _x72))))), _x71) → app#(s, app(s, app(s, app(s, app(app(plus, _x72), _x71))))) is replaced by the following rules:
app#(app(plus, app(s, app(s, app(s, app(s, 0))))), _x101) → app#(s, app(s, app(s, app(s, _x101))))app#(app(plus, app(s, app(s, app(s, app(s, app(s, _x102)))))), _x101) → app#(s, app(s, app(s, app(s, app(s, app(app(plus, _x102), _x101))))))

Problem 9: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(plus, app(s, app(s, app(s, app(s, 0))))), _x101) → app#(s, app(s, app(s, app(s, _x101))))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(app(curry, g), x), y) → app#(g, x)app#(app(plus, app(s, app(s, app(s, app(s, app(s, _x102)))))), _x101) → app#(s, app(s, app(s, app(s, app(s, app(app(plus, _x102), _x101))))))
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)
app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: plus, app, 0, inc, s, map, curry, cons, nil

Strategy

The right-hand side of the rule app#(app(plus, app(s, app(s, app(s, app(s, 0))))), _x101) → app#(s, app(s, app(s, app(s, _x101)))) is 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
Thus, the rule app#(app(plus, app(s, app(s, app(s, app(s, 0))))), _x101) → app#(s, app(s, app(s, app(s, _x101)))) is deleted.

Problem 10: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(plus, app(s, app(s, app(s, app(s, app(s, _x102)))))), _x101) → app#(s, app(s, app(s, app(s, app(s, app(app(plus, _x102), _x101))))))app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)
app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)
app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(plus, app(s, app(s, app(s, app(s, app(s, _x102)))))), _x101) → app#(s, app(s, app(s, app(s, app(s, app(app(plus, _x102), _x101)))))) is 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
app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111))))))) 
app#(s, app(s, app(s, app(s, app(s, _x111))))) 
Thus, the rule app#(app(plus, app(s, app(s, app(s, app(s, app(s, _x102)))))), _x101) → app#(s, app(s, app(s, app(s, app(s, app(app(plus, _x102), _x101)))))) is replaced by the following rules:
app#(app(plus, app(s, app(s, app(s, app(s, app(s, 0)))))), _x111) → app#(s, app(s, app(s, app(s, app(s, _x111)))))app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))

Problem 11: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(plus, app(s, app(s, app(s, app(s, app(s, 0)))))), _x111) → app#(s, app(s, app(s, app(s, app(s, _x111)))))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(app(curry, g), x), y) → app#(g, x)app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)
app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))
app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)
app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: plus, app, 0, inc, s, map, curry, cons, nil

Strategy

The right-hand side of the rule app#(app(plus, app(s, app(s, app(s, app(s, app(s, 0)))))), _x111) → app#(s, app(s, app(s, app(s, app(s, _x111))))) is 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
Thus, the rule app#(app(plus, app(s, app(s, app(s, app(s, app(s, 0)))))), _x111) → app#(s, app(s, app(s, app(s, app(s, _x111))))) is deleted.

Problem 12: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x))
app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x)) is 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
app#(cons, _x31) 
app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32))) 
app#(cons, app(app(_x31, _x33), _x32)) 
app#(cons, app(s, app(app(plus, _x32), _x31))) 
app#(cons, nil) 
Thus, the rule app#(app(map, f), app(app(cons, x), xs)) → app#(cons, app(f, x)) is replaced by the following rules:
app#(app(map, app(plus, app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(map, _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, _x31), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))

Problem 13: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(app(curry, g), x), y) → app#(g, x)app#(app(map, app(app(curry, _x31), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)
app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))
app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, app(plus, app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(map, _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: plus, app, 0, inc, s, map, curry, cons, nil

Strategy

The right-hand side of the rule app#(app(map, app(app(curry, _x31), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32)) is 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
app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32)) 
app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42))) 
app#(cons, app(app(_x41, _x43), _x42)) 
app#(cons, _x41) 
app#(cons, app(_x51, _x32)) 
app#(cons, app(s, app(app(plus, _x42), _x41))) 
app#(cons, app(app(app(_x51, _x53), _x52), _x32)) 
app#(cons, nil) 
app#(cons, app(nil, _x32)) 
app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32)) 
Thus, the rule app#(app(map, app(app(curry, _x31), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32)) is replaced by the following rules:
app#(app(map, app(app(curry, app(plus, 0)), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(map, app(app(curry, plus), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, map), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, map), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, plus), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(map, _x51)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(plus, app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(app(curry, app(app(curry, _x51), _x53)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(curry, _x41)), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))

Problem 14: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(map, app(app(curry, app(plus, 0)), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(map, app(app(curry, app(map, _x51)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(map, app(app(curry, app(plus, app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(app(curry, app(curry, _x41)), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, _x51), _x53)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))
app#(app(map, app(plus, app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(app(curry, g), x), y) → app#(app(g, x), y)
app#(app(map, app(app(curry, plus), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(map, _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, map), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, map), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, plus), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(map, app(app(curry, app(plus, 0)), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32)) is 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
app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42))) 
app#(cons, app(app(_x41, _x43), _x42)) 
app#(cons, app(s, app(app(plus, _x42), _x41))) 
app#(cons, _x41) 
app#(cons, nil) 
Thus, the rule app#(app(map, app(app(curry, app(plus, 0)), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32)) is replaced by the following rules:
app#(app(map, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)

Problem 15: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(curry, _x41)), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, _x51), _x53)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))
app#(app(map, app(app(curry, plus), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(map, _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, map), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)app#(app(map, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(app(curry, g), x), y) → app#(g, x)app#(app(map, app(app(curry, app(map, _x51)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(plus, app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(app(curry, g), x), y) → app#(app(g, x), y)
app#(app(map, app(plus, app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, map), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, plus), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: plus, app, 0, inc, s, map, curry, cons, nil

Strategy

The right-hand side of the rule app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, nil), xs)) → app#(cons, nil) is 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
Thus, the rule app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, nil), xs)) → app#(cons, nil) is deleted.

Problem 16: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)
app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, _x51), _x53)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(map, app(app(curry, app(curry, _x41)), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))
app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)app#(app(map, app(app(curry, plus), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, map), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(map, _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)
app#(app(map, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(map, app(app(curry, app(map, _x51)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)
app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, app(plus, app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, map), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, plus), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(map, app(app(curry, app(curry, _x41)), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42)) is 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
app#(cons, _x31) 
app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42)) 
app#(cons, app(_x51, _x42)) 
app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32))) 
app#(cons, app(app(_x31, _x33), _x32)) 
app#(cons, app(s, app(app(plus, _x32), _x31))) 
app#(cons, nil) 
app#(cons, app(app(app(_x51, _x53), _x52), _x42)) 
app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42)) 
app#(cons, app(nil, _x42)) 
Thus, the rule app#(app(map, app(app(curry, app(curry, _x41)), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42)) is replaced by the following rules:
app#(app(map, app(app(curry, app(curry, app(map, _x51))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(app(curry, app(curry, plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(curry, app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(curry, app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(curry, plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(curry, app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(curry, app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))

Problem 17: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(map, app(app(curry, app(curry, app(map, _x51))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, _x51), _x53)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))
app#(app(map, app(app(curry, plus), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(curry, app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(map, _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, map), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)
app#(app(map, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(map, app(app(curry, app(curry, app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(map, _x51)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(plus, app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(curry, app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(curry, app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(app(curry, g), x), y) → app#(app(g, x), y)
app#(app(map, app(plus, app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(curry, plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(curry, app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, map), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, plus), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(curry, plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: plus, app, 0, inc, s, map, curry, cons, nil

Strategy

The right-hand side of the rule app#(app(map, app(app(curry, app(curry, app(map, _x51))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42)) is 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
Thus, the rule app#(app(map, app(app(curry, app(curry, app(map, _x51))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42)) is deleted.

Problem 18: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)
app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, _x51), _x53)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))
app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)app#(app(map, app(app(curry, app(curry, app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(app(curry, plus), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, map), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(map, _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)app#(app(map, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(app(curry, g), x), y) → app#(g, x)app#(app(map, app(app(curry, app(curry, app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(map, _x51)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)
app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(app(curry, app(curry, app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(curry, app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, app(plus, app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(curry, plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(curry, app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, map), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, plus), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(curry, plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(map, app(app(curry, app(app(curry, _x51), _x53)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32)) is 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
app#(cons, app(app(app(_x61, _x63), _x62), _x32)) 
app#(cons, app(app(_x41, _x43), _x42)) 
app#(cons, app(app(nil, _x52), _x32)) 
app#(cons, app(_x61, _x32)) 
app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32)) 
app#(cons, app(app(_x71, _x52), _x32)) 
app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32)) 
app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32)) 
app#(cons, app(nil, _x32)) 
app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32)) 
app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32)) 
Thus, the rule app#(app(map, app(app(curry, app(app(curry, _x51), _x53)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32)) is replaced by the following rules:
app#(app(map, app(app(curry, app(app(curry, curry), _x41)), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(map, _x71)), nil)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, plus), 0)), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))app#(app(map, app(app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))app#(app(map, app(app(curry, app(app(curry, map), _x61)), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))
app#(app(map, app(app(curry, app(app(curry, plus), app(s, _x62))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, app(s, _x72))), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, _x61)), _x63)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, map), _x61)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))

Problem 19: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(map, app(app(curry, app(app(curry, curry), _x41)), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))app#(app(map, app(app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)
app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))app#(app(map, app(app(curry, plus), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, app(curry, app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(map, _x71)), nil)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x52), _x32))
app#(app(map, app(app(curry, map), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(map, _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, plus), app(s, _x62))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, _x61)), _x63)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))
app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)app#(app(map, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(app(curry, g), x), y) → app#(g, x)app#(app(map, app(app(curry, app(app(curry, plus), 0)), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))
app#(app(map, app(app(curry, app(app(curry, map), _x61)), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, app(app(curry, app(curry, app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(map, _x51)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, app(s, _x72))), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)
app#(app(map, app(app(curry, app(plus, app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(curry, app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(curry, app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(plus, app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, app(app(curry, app(curry, plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(curry, app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, map), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, plus), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(curry, plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)app#(app(map, app(app(curry, app(app(curry, map), _x61)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: plus, app, 0, inc, s, map, curry, cons, nil

Strategy

The right-hand side of the rule app#(app(map, app(app(curry, app(app(curry, curry), _x41)), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42)) is 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
app#(cons, _x31) 
app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42)) 
app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32))) 
app#(cons, app(_x51, _x42)) 
app#(cons, app(app(_x31, _x33), _x32)) 
app#(cons, app(s, app(app(plus, _x32), _x31))) 
app#(cons, nil) 
app#(cons, app(app(app(_x51, _x53), _x52), _x42)) 
app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42)) 
app#(cons, app(nil, _x42)) 
Thus, the rule app#(app(map, app(app(curry, app(app(curry, curry), _x41)), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42)) is replaced by the following rules:
app#(app(map, app(app(curry, app(app(curry, curry), app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, curry), app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, curry), app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, app(app(curry, curry), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(app(curry, curry), plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(app(curry, curry), plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, curry), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(app(curry, curry), app(map, _x51))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))

Problem 20: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(map, app(app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))
app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)
app#(app(map, app(app(curry, plus), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(map, _x71)), nil)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, plus), app(s, _x62))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, _x61)), _x63)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)
app#(app(map, app(app(curry, app(app(curry, curry), app(map, _x51))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(app(curry, plus), 0)), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))
app#(app(map, app(app(curry, app(app(curry, map), _x61)), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, app(app(curry, app(curry, app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(map, _x51)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)
app#(app(map, app(app(curry, app(plus, app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(curry, app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(curry, app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, curry), app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(plus, app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(app(curry, g), x), y) → app#(app(g, x), y)
app#(app(map, app(app(curry, app(app(curry, curry), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, plus), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(curry, plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, map), _x61)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, curry), plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))
app#(app(map, app(app(curry, app(curry, app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, curry), app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(map, _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, map), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(app(curry, g), x), y) → app#(g, x)app#(app(map, app(app(curry, app(app(curry, app(plus, app(s, _x72))), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(curry, plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(curry, app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, app(app(curry, curry), app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, map), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(app(curry, curry), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32)) is 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
app#(cons, app(app(app(_x61, _x63), _x62), _x32)) 
app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42))) 
app#(cons, app(app(_x41, _x43), _x42)) 
app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32)) 
app#(cons, app(_x61, _x32)) 
app#(cons, _x41) 
app#(cons, app(s, app(app(plus, _x42), _x41))) 
app#(cons, nil) 
app#(cons, app(nil, _x32)) 
app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32)) 
Thus, the rule app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32)) is replaced by the following rules:
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, _x61), _x63))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), map)), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(map, _x61))), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), map)), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, _x41))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, app(s, _x62)))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(map, _x61))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))

Problem 21: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(map, app(app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))app#(app(plus, app(s, 0)), _x31) → app#(s, _x31)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, _x61), _x63))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))app#(app(map, app(app(curry, plus), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, app(app(curry, app(map, _x71)), nil)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(map, _x61))), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, plus), app(s, _x62))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, _x61)), _x63)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))app#(app(map, f), app(app(cons, x), xs)) → app#(map, f)
app#(app(map, app(app(curry, app(app(curry, curry), app(map, _x51))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(app(curry, plus), 0)), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))
app#(app(map, app(app(curry, app(map, _x51)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(curry, app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(app(curry, map), _x61)), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)
app#(app(map, app(app(curry, app(plus, app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(curry, app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(curry, app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, app(plus, app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, curry), app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, _x41))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, curry), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, plus), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(curry, plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, map), _x61)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)
app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, curry), plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))app#(app(map, app(app(curry, app(curry, app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), map)), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, curry), app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(map, _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, map), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, app(s, _x62)))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(map, _x61))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(app(curry, g), x), y) → app#(g, x)app#(app(map, app(app(curry, app(app(curry, app(plus, app(s, _x72))), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(curry, plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), map)), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, curry), app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(curry, app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, map), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, curry), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: plus, app, 0, inc, s, map, curry, cons, nil

Strategy

The right-hand side of the rule app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32)) is 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
app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42))) 
app#(cons, app(app(_x41, _x43), _x42)) 
app#(cons, _x41) 
app#(cons, app(s, app(app(plus, _x42), _x41))) 
app#(cons, nil) 
Thus, the rule app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32)) is replaced by the following rules:
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(map, _x41))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))

Problem 22: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(map, _x51)))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, plus), app(s, _x42)))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(map, _x61))), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, plus))), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(map, _x61)), app(app(cons, _x63), _x62)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x52), _x42))app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(curry, app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(app(curry, curry), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, plus), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), plus)), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, app(s, 0)))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))
app#(app(map, app(app(curry, app(curry, plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(app(curry, map), _x61)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), 0))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), map)), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(app(curry, app(curry, plus)), 0)), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72)))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x62), _x32))app#(app(map, app(plus, app(s, 0))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))
app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, 0))))), _x91)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, _x91)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, plus)), app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(map, _x71))), app(app(cons, _x73), _x72))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(curry, app(curry, app(plus, app(s, _x52))))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))app#(app(map, app(app(curry, plus), app(s, app(s, 0)))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, _x81)))
app#(app(map, app(app(curry, app(curry, app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, plus), app(s, app(s, _x72)))), _x71)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x72), _x71))), _x32))
app#(app(map, app(map, _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, app(s, _x62)))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))
app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(map, _x41))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(map, _x61))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(curry, _x41)), _x43))), _x42)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, app(s, _x92)))))), _x91)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(app(plus, _x92), _x91)))), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(map, _x51))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, map))), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(plus, app(s, _x72))), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), _x41))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(map, _x61)), nil))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(nil, _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, app(curry, app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, _x51))), _x53)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, _x71), _x73)), _x72))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, _x72))), _x71))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x62), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(curry, app(curry, app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(curry, app(curry, map))), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(curry, app(curry, app(map, _x51)))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(curry, app(curry, app(curry, _x41)))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(curry, app(curry, app(app(curry, _x51), _x53)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, app(s, app(s, _x82))))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x82), _x81)))))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, curry), _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, map), _x41))), app(app(cons, _x43), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(app(curry, _x51), _x53)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, app(s, 0)))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, _x81)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, 0))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))
app#(app(map, app(plus, app(s, app(s, _x62)))), app(app(cons, _x61), xs)) → app#(cons, app(s, app(s, app(app(plus, _x62), _x61))))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), plus)), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, app(app(curry, app(curry, map)), _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, 0)))), _x81)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, map), _x41))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, plus), 0)), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, plus))), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(curry, app(curry, map))), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(curry, app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(app(curry, map), _x61)), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, app(app(curry, app(plus, app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(plus, 0)), _x71))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x62), _x32))app#(app(app(curry, g), x), y) → app#(app(g, x), y)
app#(app(map, app(app(curry, app(app(curry, curry), app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(app(curry, _x61), _x63)), _x62))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, map))), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, app(app(curry, plus), app(s, app(s, app(s, _x82))))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x82), _x81)))))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x71)), nil))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x62), _x32))
app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), map)), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(curry, _x51)), _x53))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(curry, app(curry, plus))), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(plus, 0)), _x61))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x61, _x52), _x42))app#(app(map, app(app(curry, app(app(curry, curry), app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), map)), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, map), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(plus, app(s, _x62))), _x61))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(app(plus, _x62), _x61)), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(curry, _x31)))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(app(curry, g), x), y) → app#(g, x)app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(curry, _x41))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, plus), app(s, 0))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, map), _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, app(s, _x72)))), _x71)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), map)), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(curry, plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, plus), 0))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))
app#(app(map, app(app(curry, app(app(curry, curry), app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(map, _x51))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(app(curry, _x71), _x73))), _x72)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x62), _x32))app#(app(map, app(app(curry, map), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, app(s, _x52))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(app(curry, app(curry, app(map, _x71))), nil)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x62), _x32))

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(map, _x51)))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42)) is 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
Thus, the rule app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(map, _x51)))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42)) is deleted.

Problem 23: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, plus), app(s, _x42)))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(map, _x61))), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, map), _x41)), app(app(cons, _x43), _x42)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(map, _x61)), app(app(cons, _x63), _x62)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x52), _x42))
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(curry, app(app(curry, map), _x41))), app(app(cons, _x43), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, map), _x61)))), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), _x41))), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(curry, _x41)), _x43))), _x42)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, app(s, _x92)))))), _x91)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(app(plus, _x92), _x91)))), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, app(s, _x62)))), _x61))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x62), _x61))), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, plus)), app(s, app(s, _x82))))), _x81))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x82), _x81))), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), _x41))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, 0))), app(map, _x31))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, _x43), _x42)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, _x41))), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, app(curry, plus)), app(s, app(s, _x62)))), app(app(cons, _x61), xs)) → app#(cons, app(s, app(s, app(app(plus, _x62), _x61))))
app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), _x61))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x61, _x52), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, 0))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, _x51))), _x53)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, curry), _x31)), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), map)), _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, plus)))), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, plus), app(s, 0))))), _x71)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x71), _x32))app#(app(map, app(app(curry, app(curry, app(curry, map))), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(curry, app(curry, app(map, _x51)))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(curry, app(curry, app(curry, _x41)))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, plus), 0))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, map), _x41))), app(app(cons, _x43), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(map, _x51)))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, app(s, 0)))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, _x81)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(app(curry, _x51), _x53)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, plus)), app(s, 0)))), _x81))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, app(s, _x52))))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72))))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, 0))), _x61))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, _x61), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), plus)), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(curry, map)), _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(map, _x61)), nil)), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(nil, _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, 0))), app(map, _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), 0))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, map), _x41))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, app(map, _x61)), nil))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(nil, _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, plus), 0)), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, app(s, app(s, 0)))), _x101))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(s, _x101)), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, map), _x61)), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, app(app(curry, app(curry, app(curry, map))), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(plus, app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(app(curry, g), x), y) → app#(app(g, x), y)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, plus)), 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(app(curry, _x61), _x63)), _x62)), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, 0)))), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, map)), _x41))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, app(s, _x62))), _x61)), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(app(plus, _x62), _x61)), _x52), _x42))app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(map, _x71))), nil))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, map), _x61))), app(app(cons, _x63), _x62)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, app(app(curry, app(app(curry, curry), app(plus, app(s, 0)))), _x61)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, _x61), _x42))
app#(app(map, app(app(curry, app(curry, app(curry, plus))), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(plus, 0)), _x61))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x61, _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, plus))), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, curry), app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, map), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, map)), _x51))), nil))), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, map))), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, map), _x61)))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, plus)), 0))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), plus)), 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, map), _x61))), nil))), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(curry, _x41))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, plus), app(s, 0))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(map, _x51))), nil))), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, plus))), app(s, app(s, _x62)))), app(app(cons, _x61), xs)) → app#(cons, app(s, app(s, app(app(plus, _x62), _x61))))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, plus), app(s, _x62)))), _x61))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, app(s, _x72)))), _x71)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, plus), 0))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, app(s, 0)))), _x81))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))app#(app(map, app(app(curry, map), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x51)), nil))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(curry, _x61)), _x63)))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(curry, app(app(curry, curry), _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, 0)))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(curry, _x31))), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(map, _x51))))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(map, _x61)), app(app(cons, _x63), _x62))), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x52), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, app(map, _x61)), app(app(cons, _x63), _x62)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x52), _x42))
app#(app(map, app(app(curry, app(curry, app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(map, _x51))))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, plus)), app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, map), _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), map)), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, 0)))), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(app(curry, _x51), _x53))))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, plus)), 0)), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72)))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x62), _x32))app#(app(map, app(app(curry, app(curry, plus)), app(s, 0))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))
app#(app(map, app(plus, app(s, 0))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))
app#(app(map, app(app(curry, app(app(curry, app(curry, plus)), app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, 0))))), _x91)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, _x91)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(map, _x71))), app(app(cons, _x73), _x72))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, 0))), app(app(curry, _x31), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, app(s, app(s, app(s, _x102))))), _x101))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(s, app(s, app(app(plus, _x102), _x101)))), _x52), _x42))app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(curry, app(curry, app(plus, app(s, _x52))))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(app(curry, curry), plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(curry, app(app(curry, map), _x41))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(plus, app(s, _x52)))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(curry, _x51))), _x53))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, map)), _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(plus, 0)), _x51))), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))
app#(app(map, app(app(curry, plus), app(s, app(s, 0)))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, _x81)))app#(app(map, app(app(curry, app(app(curry, plus), app(s, app(s, _x72)))), _x71)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x72), _x71))), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(plus, app(s, _x72))), _x71))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, app(s, _x62)))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))
app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(map, _x41))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(plus, 0)), _x71)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(map, _x51))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, map))), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(curry, app(app(curry, app(curry, _x41)), _x43))), _x42)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, map), _x41)), nil))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, app(s, _x72))), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(app(curry, _x71), _x73))), _x72))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x62), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, plus), 0))), _x61))), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(map, _x61)), nil))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(nil, _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), 0))), app(map, _x41))), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(curry, app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, map)))), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, 0)))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(curry, _x31))))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, _x71), _x73)), _x72))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, curry), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, app(s, app(s, _x82))))), _x81))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x82), _x81))), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, _x72))), _x71))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x62), _x32))app#(app(map, app(app(curry, app(curry, app(curry, app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), app(plus, app(s, app(s, _x62))))), _x61)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x62), _x61))), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, curry), _x41))), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, plus))), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, plus), app(s, _x42))), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(plus, app(s, app(s, _x102)))), _x101)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(s, app(app(plus, _x102), _x101))), _x52), _x32))
app#(app(map, app(app(curry, app(curry, app(curry, app(app(curry, _x51), _x53)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, plus))), app(s, 0))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, curry), _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, app(s, app(s, _x82))))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x82), _x81)))))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, plus), 0)), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, 0))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))
app#(app(map, app(plus, app(s, app(s, _x62)))), app(app(cons, _x61), xs)) → app#(cons, app(s, app(s, app(app(plus, _x62), _x61))))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, 0)))), _x81)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))
app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, plus))), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43))), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))app#(app(map, app(app(curry, app(curry, app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(curry, app(app(curry, plus), app(s, _x42)))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(plus, 0)), _x71))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x62), _x32))
app#(app(map, app(app(curry, app(curry, app(app(curry, app(app(curry, _x61), _x63)), _x62))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), 0))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(app(curry, _x61), _x63)), _x62))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x52), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(map, _x51))), app(app(cons, _x53), _x52)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, plus), app(s, app(s, app(s, _x102))))))), _x101)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(app(plus, _x102), _x101)))), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(curry, _x41)), _x43)), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, map))), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, app(app(curry, plus), app(s, app(s, app(s, _x82))))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x82), _x81)))))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x71)), nil))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x62), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(map, _x71))), app(app(cons, _x73), _x72)))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), 0))), app(plus, app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), map)), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(plus, 0))), _x71))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(curry, _x51)), _x53))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, map))), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, plus), app(s, app(s, 0)))))), _x101)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, _x101)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), map)), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(plus, app(s, _x62))), _x61))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(app(plus, _x62), _x61)), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, curry), _x41)))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(curry, _x31)))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, 0))), app(plus, app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72)))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(app(curry, g), x), y) → app#(g, x)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(plus, app(s, _x72)))), _x71))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, map), _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(curry, plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), map)), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(curry, app(app(curry, _x71), _x73))), _x72)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(map, _x51))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, app(s, _x52))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, plus), 0)))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, app(curry, app(map, _x71))), nil)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x62), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(plus, 0)), _x71))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, map)), _x51))), app(app(cons, _x53), _x52)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(plus, 0))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), _x41))), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42)) is 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
app#(cons, _x31) 
app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42)) 
app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32))) 
app#(cons, app(_x51, _x42)) 
app#(cons, app(app(_x31, _x33), _x32)) 
app#(cons, app(s, app(app(plus, _x32), _x31))) 
app#(cons, nil) 
app#(cons, app(app(app(_x51, _x53), _x52), _x42)) 
app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42)) 
app#(cons, app(nil, _x42)) 
Thus, the rule app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), _x41))), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42)) is replaced by the following rules:
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(map, _x51)))), nil))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(app(curry, _x51), _x53)))), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), map))), _x31))), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(map, _x51)))), app(app(cons, _x53), _x52)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), map))), _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(plus, app(s, _x52))))), _x51))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(curry, _x31)))), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), plus))), 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), plus))), app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(plus, 0)))), _x51))), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))

Problem 24: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, plus), app(s, _x42)))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, app(s, _x42))))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(map, _x61))), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(map, _x51)))), app(app(cons, _x53), _x52)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, map), _x41)), app(app(cons, _x43), _x42)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(map, _x61)), app(app(cons, _x63), _x62)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(curry, app(app(curry, map), _x41))), app(app(cons, _x43), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43)))), _x42)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, map), _x41)))), app(app(cons, _x43), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, map), _x61)))), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(map, _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, map)))), _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(curry, _x41)), _x43)))), _x42)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(curry, _x41)), _x43))), _x42)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, _x43), _x42)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, curry), _x31)), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), map)), _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, app(plus, app(s, _x72))), _x71)), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, plus)))), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), map))), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), map))), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(map, _x31))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, plus), app(s, 0))))), _x71)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x71), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, app(s, _x32))))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, app(map, _x51))))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(map, _x41)))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(curry, app(curry, map))), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, map)))), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(curry, app(curry, app(map, _x51)))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, plus), 0)), _x61))), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, app(plus, app(s, _x52)))))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(curry, app(curry, app(curry, _x41)))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, plus), 0))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, plus))), 0)), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(plus, app(s, app(s, app(s, _x72)))))), app(app(cons, _x71), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x72), _x71)))))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(plus, app(s, app(s, 0))))), app(app(cons, _x71), xs)) → app#(cons, app(s, app(s, _x71)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, map), _x41))), app(app(cons, _x43), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(map, _x51)))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(app(curry, _x51), _x53)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, app(s, 0)))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, _x81)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(curry, plus)), app(s, app(s, 0)))), app(app(cons, _x71), xs)) → app#(cons, app(s, app(s, _x71)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, 0))), app(plus, 0)))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), plus))), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, app(s, _x52))))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, plus)), app(s, 0)))), _x81))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72))))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, 0))), _x61))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, _x61), _x42))
app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), plus))), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), plus)), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(plus, app(s, app(s, _x52)))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, plus))), app(s, _x62))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(curry, map)), _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(map, _x61)), nil)), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(nil, _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, 0))), app(map, _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), 0))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, plus), 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(plus, 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, map), _x41))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(curry, app(app(curry, app(map, _x61)), nil))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(nil, _x52), _x42))app#(app(map, app(app(curry, app(app(curry, plus), 0)), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), app(s, _x42))))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, app(s, app(s, 0)))), _x101))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(s, _x101)), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, map), _x61)), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, app(app(curry, app(curry, app(curry, map))), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(map, _x41)))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(plus, app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(app(curry, curry), app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(app(curry, g), x), y) → app#(app(g, x), y)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, plus)), 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(plus, 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(app(curry, _x61), _x63)), _x62)), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, app(s, app(s, 0))))), _x101))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(s, app(s, _x101))), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, 0)))), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, _x61)))), _x63)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, map)), _x41))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(plus, 0)))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(curry, plus)), app(s, app(s, app(s, _x72))))), app(app(cons, _x71), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x72), _x71)))))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, app(s, _x62))), _x61)), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(app(plus, _x62), _x61)), _x52), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, plus)))), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(map, _x71))), nil))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x62), _x32))
app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(app(curry, _x51), _x53)))), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(plus, app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(plus, app(s, 0)))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), plus))), 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, map), _x61))), app(app(cons, _x63), _x62)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, app(app(curry, app(app(curry, curry), app(plus, app(s, 0)))), _x61)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, _x61), _x42))
app#(app(map, app(app(curry, app(curry, app(curry, plus))), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(plus, 0)), _x61))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x61, _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, app(plus, 0)), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, plus)))), app(s, 0)))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, plus))), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, curry), app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, map), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, map), _x61)), app(app(cons, _x63), _x62)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(app(curry, _x51), _x53)))), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, app(plus, 0))))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, map)), _x51))), nil))), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(plus, 0)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, map))), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, app(curry, _x41))))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, map), _x61)))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(plus, app(s, _x52))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, plus)), 0))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, app(plus, app(s, _x52)))))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, map), _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), plus)), 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, map), _x61))), nil))), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(curry, _x41))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, app(s, app(s, 0))))))), _x131)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(s, _x131)))), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, plus), app(s, 0))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(map, _x51))), nil))), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(map, _x51)), nil)))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, plus))), app(s, app(s, _x62)))), app(app(cons, _x61), xs)) → app#(cons, app(s, app(s, app(app(plus, _x62), _x61))))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, plus), app(s, _x62)))), _x61))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, app(s, _x72)))), _x71)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, plus), 0))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))
app#(app(map, app(app(curry, app(app(curry, curry), app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, curry), _x31)))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, app(s, 0)))), _x81))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))app#(app(map, app(app(curry, map), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, app(map, _x51))))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, app(app(curry, _x51), _x53))))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x51)), nil))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(app(curry, _x61), _x63)), _x62)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(curry, _x61)), _x63)))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, plus))), app(s, app(s, 0))))), app(app(cons, _x71), xs)) → app#(cons, app(s, app(s, _x71)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, app(plus, 0)), _x71)), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, map), _x31)))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, 0))), app(map, _x41)))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, 0))), app(app(curry, _x41), _x43)))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, curry), _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(curry, _x31)))), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(plus, app(s, _x52))))), _x51))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, 0)))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, plus))), app(s, app(s, app(s, _x72)))))), app(app(cons, _x71), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x72), _x71)))))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(map, _x51)))), app(app(cons, _x53), _x52)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(map, _x51)))), nil))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(curry, _x31))), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, app(curry, _x61)), _x63)), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), plus))), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, plus))), app(s, 0)))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), plus))), app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(plus, app(s, app(s, _x72)))), _x71)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(s, app(app(plus, _x72), _x71))), _x52), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, plus))), 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(map, _x51))))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(map, _x51)))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(map, _x61)), app(app(cons, _x63), _x62))), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x52), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, app(map, _x61)), app(app(cons, _x63), _x62)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(map, _x71)))), app(app(cons, _x73), _x72))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, plus), app(s, 0)))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))
app#(app(map, app(app(curry, app(curry, app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(map, _x51))))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(plus, app(s, _x72))))), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, plus)), app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(map, _x51))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, 0))), _x61)))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, _x61), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, _x51), _x53)), _x52)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, map), _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(plus, 0)))), _x51))), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), app(map, _x41)))), app(app(cons, _x43), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), map)), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, 0)))), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(app(curry, app(curry, plus)), 0)), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(app(curry, _x51), _x53))))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, app(s, 0)))), _x91)))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(s, _x91)), _x42))app#(app(map, app(app(curry, app(curry, plus)), app(s, 0))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72)))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x62), _x32))app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))
app#(app(map, app(plus, app(s, 0))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, 0))))), _x91)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, _x91)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, plus)), app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(map, _x71))), app(app(cons, _x73), _x72))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, plus), app(s, _x62))), _x61))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, 0))), app(app(curry, _x31), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, map))), _x31))), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, 0))), app(plus, app(s, _x42))))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, app(curry, app(curry, app(plus, app(s, _x52))))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, app(plus, app(s, _x52))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, app(s, app(s, app(s, _x102))))), _x101))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(s, app(s, app(app(plus, _x102), _x101)))), _x52), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), map))), _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, app(s, 0)))))), _x121)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, _x121))), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(curry, app(app(curry, map), _x41))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(plus, 0)), _x51))), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, map)), _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(plus, app(s, _x52)))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(curry, _x51))), _x53))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(curry, _x41)), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, plus), app(s, app(s, 0)))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, _x81)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, map), _x41))), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(app(curry, plus), app(s, app(s, _x72)))), _x71)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x72), _x71))), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(curry, _x31)), _x33)))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, app(app(curry, _x51), _x53))))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(plus, app(s, _x72))), _x71))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, map), _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, app(s, _x62)))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))
app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(map, _x41))), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(map, _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, app(s, app(s, _x92))))), _x91)))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(s, app(s, app(app(plus, _x92), _x91)))), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, plus)), app(s, app(s, app(s, app(s, _x122))))))), _x121))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(s, app(app(plus, _x122), _x121))))), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(plus, 0)), _x71)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, plus)))), 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(map, _x51))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, map))), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(curry, app(app(curry, app(curry, _x41)), _x43))), _x42)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, map), _x41)), nil))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, app(s, _x72))), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, map), _x61)), nil))), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(app(curry, _x71), _x73))), _x72))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(plus, 0)), _x51)))), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, plus), 0))), _x61))), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(plus, 0)))), app(app(curry, _x31), _x33)))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, app(app(curry, _x51), _x53)), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(map, _x61)), nil))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(nil, _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), 0))), app(map, _x41))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(curry, app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, map)))), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, 0)))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(map, _x61)), app(app(cons, _x63), _x62))))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, map)))), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(curry, _x31))))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, _x71), _x73)), _x72))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x62), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(plus, 0)))), app(map, _x31)))), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(app(curry, curry), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, app(s, app(s, _x82))))), _x81))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x82), _x81))), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, _x72))), _x71))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x62), _x32))app#(app(map, app(app(curry, app(curry, app(curry, app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), app(plus, app(s, app(s, _x62))))), _x61)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x62), _x61))), _x42))app#(app(map, app(app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, curry), _x41))), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, plus))), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(plus, app(s, _x52))))), _x51))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, app(s, app(s, app(s, _x102)))))), _x101))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(s, app(s, app(s, app(app(plus, _x102), _x101))))), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, plus), app(s, _x42))), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(plus, app(s, app(s, _x102)))), _x101)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(s, app(app(plus, _x102), _x101))), _x52), _x32))
app#(app(map, app(app(curry, app(curry, app(curry, app(app(curry, _x51), _x53)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, 0)))), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, plus))), app(s, 0))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, curry), _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, app(s, app(s, _x82))))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x82), _x81)))))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, map), _x41))), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, plus), 0)), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, 0))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))app#(app(map, app(plus, app(s, app(s, _x62)))), app(app(cons, _x61), xs)) → app#(cons, app(s, app(s, app(app(plus, _x62), _x61))))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(app(curry, _x71), _x73)))), _x72)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, plus), app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, 0)))), _x81)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, map))), _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43))), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, plus))), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(curry, app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, map)))), _x41))), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(curry, app(app(curry, plus), app(s, _x42)))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(plus, 0)), _x71))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, app(map, _x71)), nil)), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x52), _x32))
app#(app(map, app(app(curry, app(curry, app(app(curry, app(app(curry, _x61), _x63)), _x62))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), 0))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(map, _x51)))), nil))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(map, _x61)), nil)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(nil, _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(app(curry, _x61), _x63)), _x62))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(plus, 0)), _x61)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x61, _x52), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(map, _x51))), app(app(cons, _x53), _x52)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, map))), _x61)), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, app(map, _x51))))), app(app(cons, _x53), _x52)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72)), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, plus), app(s, app(s, app(s, _x102))))))), _x101)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(app(plus, _x102), _x101)))), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(curry, _x41)), _x43)), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(plus, 0)))), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, map))), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, app(curry, _x41))))), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, app(s, 0)))), _x91))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(s, _x91)), _x42))app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)
app#(app(map, app(app(curry, plus), app(s, app(s, app(s, _x82))))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x82), _x81)))))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, plus)))), app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x71)), nil))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x62), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(map, _x71))), app(app(cons, _x73), _x72)))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), 0))), app(plus, app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, map), _x41)))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), map)), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(plus, 0))), _x71))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(curry, _x51)), _x53))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, _x32))))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, map))), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, plus), app(s, app(s, 0)))))), _x101)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, _x101)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, 0))), app(map, _x41)))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), app(curry, _x31)))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), map)), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, curry), _x41)), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(plus, app(s, _x62))), _x61))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(app(plus, _x62), _x61)), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, app(curry, _x41)), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, curry), _x41)))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(curry, _x31)))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(plus, 0)))), app(map, _x31)))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), map))), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, app(s, app(s, app(s, 0)))))))), _x161)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(s, app(s, _x161))))), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, 0))), app(plus, app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72)))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, map))), _x61)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(plus, app(s, 0))), _x71)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, _x71), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, map), _x31)))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, app(plus, 0))))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, plus), app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), plus))), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(plus, app(s, _x72)))), _x71))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, app(s, _x52))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, map), _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(curry, plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), map)), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(app(curry, app(curry, app(app(curry, _x71), _x73))), _x72)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(map, _x51))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, plus)), app(s, app(s, 0))))), _x91))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, _x91)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, app(s, _x52))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, plus), 0)))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, app(s, app(s, app(s, app(s, _x162))))))))), _x161)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x162), _x161))))))), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, app(curry, app(map, _x71))), nil)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x62), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(plus, 0)), _x71))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, map)), _x51))), app(app(cons, _x53), _x52)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(plus, 0))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32)) is 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
app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32)) 
app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42))) 
app#(cons, app(app(_x41, _x43), _x42)) 
app#(cons, _x41) 
app#(cons, app(s, app(app(plus, _x42), _x41))) 
app#(cons, app(_x51, _x32)) 
app#(cons, app(app(app(_x51, _x53), _x52), _x32)) 
app#(cons, nil) 
app#(cons, app(nil, _x32)) 
app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32)) 
Thus, the rule app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32)) is replaced by the following rules:
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, app(plus, app(s, _x52))))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, map))), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, map))), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, app(map, _x51)))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, app(curry, _x41)))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, app(app(curry, _x51), _x53)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, plus))), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, app(plus, 0)))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, plus))), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))

Problem 25: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

app#(app(map, app(app(curry, app(curry, app(curry, app(curry, app(map, _x51))))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(map, _x71))))), app(app(cons, _x73), _x72))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, map), _x61))))), app(app(cons, _x63), _x62))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, f), app(app(cons, x), xs)) → app#(app(map, f), xs)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, map), _x41))), app(app(cons, _x43), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, map), _x41)))), app(app(cons, _x43), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, map)))), _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(map, _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(curry, _x41)), _x43)))), _x42)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(curry, _x41)), _x43))), _x42)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, map), _x61))), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))app#(app(map, app(app(curry, app(curry, app(curry, map))), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(curry, map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(app(curry, app(map, _x91)), app(app(cons, _x93), _x92))), _x72)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(app(cons, app(_x91, _x93)), app(app(map, _x91), _x92)), _x72), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, map), _x41))), app(app(cons, _x43), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, curry), app(map, _x51))), app(app(cons, _x53), _x52)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, 0))), app(map, _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), 0))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, map), _x61)), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), app(s, _x42))))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, plus))), 0)), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(app(curry, g), x), y) → app#(app(g, x), y)
app#(app(map, f), app(app(cons, x), xs)) → app#(app(cons, app(f, x)), app(app(map, f), xs))app#(app(map, app(app(curry, app(curry, app(app(curry, plus), 0))), app(map, _x31))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, curry)))), _x41)), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(curry, app(curry, plus))), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, plus)))), app(s, app(s, app(s, app(s, app(s, _x122))))))), app(app(cons, _x121), xs)) → app#(cons, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x122), _x121)))))))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(plus, 0)), _x61))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x61, _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, plus), app(s, _x62)))))), _x61)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x62), _x61)), _x62), _x32))
app#(app(map, app(app(curry, app(curry, app(app(curry, plus), 0))), app(plus, app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(app(curry, _x51), _x53)))), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, app(plus, 0))))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, curry), _x51))))), _x53)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, app(plus, app(s, 0))), _x101)), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, _x101), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, app(plus, app(s, _x52))))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(plus, app(s, _x52))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(map, _x81)), app(app(cons, _x83), _x82)))))), _x72)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(app(cons, app(_x81, _x83)), app(app(map, _x81), _x82)), _x72), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, map), _x61)))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, app(plus, app(s, _x52)))))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, map), _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), plus)), 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(app(curry, plus), app(s, _x42))))), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, app(s, app(s, 0))))))), _x131)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(s, _x131)))), _x32))app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, plus), app(s, 0))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(map, _x51)), nil)))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(app(curry, app(map, _x91)), nil)), _x72)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(nil, _x72), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(app(curry, _x61), _x63)))))), _x62)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(curry, _x61)), _x63))))), _x62)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x62), _x32))app#(app(map, app(app(curry, app(curry, plus)), app(s, app(s, app(s, app(s, _x102)))))), app(app(cons, _x101), xs)) → app#(cons, app(s, app(s, app(s, app(s, app(app(plus, _x102), _x101))))))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, app(s, 0)))), _x81))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, curry), _x31)))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, app(s, app(s, _x62)))))), app(app(cons, _x61), xs)) → app#(cons, app(s, app(s, app(app(plus, _x62), _x61))))app#(app(map, app(app(curry, app(curry, app(app(curry, plus), 0))), app(map, _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, plus)))), app(s, app(s, 0)))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, _x81)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, app(plus, 0)), _x71)), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), plus)), app(s, app(s, 0)))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, _x81)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, 0)))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(plus, app(s, _x52))))), _x51))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(map, _x51)))), nil))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, plus))), app(s, app(s, app(s, _x72)))))), app(app(cons, _x71), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x72), _x71)))))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(app(curry, app(plus, app(s, _x92))), _x91)), _x72)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(s, app(app(plus, _x92), _x91)), _x72), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, map))), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, app(s, app(s, 0)))), _x91)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, _x91)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, app(plus, app(s, app(s, app(s, _x92)))))))), _x91)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(app(plus, _x92), _x91)))), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), map))))), _x51)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, plus))), 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(map, _x51))))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(map, _x61)), app(app(cons, _x63), _x62))), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x52), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(plus, 0)), _x61)))), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x61, _x52), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, app(map, _x61)), app(app(cons, _x63), _x62)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x52), _x42))
app#(app(map, app(app(curry, app(curry, app(app(curry, plus), 0))), app(plus, 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(curry, app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, plus)), app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(map, _x51))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, _x51), _x53)), _x52)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(plus, 0)))), _x51))), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, plus))), 0)), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), map)), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, 0)))), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(app(curry, _x51), _x53))))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(app(curry, _x61), _x63)), _x62)))), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, 0))))), _x91)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, _x91)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, plus)), app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, plus), app(s, _x62))), _x61))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))
app#(app(map, app(map, _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, app(s, app(s, app(s, _x102))))), _x101))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(s, app(s, app(app(plus, _x102), _x101)))), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, app(s, 0)))))), _x121)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, _x121))), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(map, _x81)), nil))))), _x72)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(nil, _x72), _x62), _x32))
app#(app(plus, app(s, app(s, app(s, app(s, app(s, app(s, _x112))))))), _x111) → app#(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x112), _x111)))))))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(plus, app(s, _x52)))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, plus), app(s, app(s, 0)))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, _x81)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(curry, _x41)), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, map), _x41))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, app(app(curry, _x51), _x53))))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(curry, _x31)), _x33)))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(app(curry, plus), app(s, app(s, _x72)))), _x71)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x72), _x71))), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))))), app(plus, 0))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, map), _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(plus, app(s, _x72))), _x71))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, app(s, _x62)))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))app#(app(map, app(plus, 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(map, _x41))), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(map, _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, app(s, app(s, _x92))))), _x91)))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(s, app(s, app(app(plus, _x92), _x91)))), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, plus)), app(s, app(s, app(s, app(s, _x122))))))), _x121))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(s, app(app(plus, _x122), _x121))))), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, map))), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(curry, app(app(curry, app(curry, _x41)), _x43))), _x42)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, map), _x41)), nil))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, map), _x61)), nil))), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(app(curry, _x71), _x73))), _x72))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), plus)), app(s, app(s, app(s, _x82))))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x82), _x81)))))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), 0))), app(map, _x41))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, 0)))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), plus)), app(s, 0))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, map)))), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(curry, _x31))))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, map)))), _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, _x72))), _x71))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x62), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, app(s, app(s, _x82))))), _x81))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x82), _x81))), _x32))app#(app(map, app(app(curry, app(app(curry, curry), app(plus, app(s, app(s, _x62))))), _x61)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x62), _x61))), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, plus)))), app(s, app(s, app(s, app(s, 0)))))), app(app(cons, _x121), xs)) → app#(cons, app(s, app(s, app(s, app(s, _x121)))))app#(app(map, app(app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(plus, app(s, _x52))))), _x51))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, plus))), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, app(s, app(s, app(s, _x102)))))), _x101))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(s, app(s, app(s, app(app(plus, _x102), _x101))))), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(plus, app(s, app(s, _x102)))), _x101)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(s, app(app(plus, _x102), _x101))), _x52), _x32))
app#(app(map, app(app(curry, app(curry, app(curry, app(app(curry, _x51), _x53)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, app(plus, app(s, 0)))))), _x81)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, curry), _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, map), _x41))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, 0))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, plus), 0)), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))
app#(app(map, app(app(curry, app(curry, app(curry, app(curry, map)))), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, plus), app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, 0)))), _x81)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, map))), _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(curry, _x51))))), _x53)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, plus))), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43))), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))
app#(app(map, app(app(curry, app(curry, app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, curry), plus)), app(s, 0)))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))
app#(app(map, app(app(curry, app(curry, app(app(curry, plus), app(s, _x42)))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(plus, 0)), _x71))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, app(map, _x71)), nil)), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(map, _x51)))), nil))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), 0))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(map, _x61)), nil)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(nil, _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, map))), _x61)), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(map, _x51))), app(app(cons, _x53), _x52)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(curry, _x41)), _x43)), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))app#(app(map, app(app(curry, app(curry, app(curry, app(curry, map)))), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(plus, 0)))), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(app(curry, map), _x41)))), app(app(cons, _x43), _x42)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, curry), map)), _x41))), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, _x51), _x53))))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(plus, app(s, x)), y) → app#(app(plus, x), y)app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))))), app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x71)), nil))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x62), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(map, _x71))), app(app(cons, _x73), _x72)))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), 0))), app(plus, app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, map), _x41)))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), map)), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(map, _x61)), nil)))), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(nil, _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, map))), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(map, _x61)), app(app(cons, _x63), _x62))))), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, plus), app(s, app(s, 0)))))), _x101)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, _x101)), _x32))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), app(curry, _x31)))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, app(plus, 0)), _x71))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, curry), _x41)), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(plus, app(s, _x62))), _x61))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(app(plus, _x62), _x61)), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, curry), _x41)))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, app(curry, _x41)))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(curry, _x31)))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(plus, 0)))), app(map, _x31)))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), map))), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(app(curry, map), _x81)), app(app(cons, _x83), _x82))))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x81, _x83)), app(app(map, _x81), _x82)), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, app(s, 0))))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72)))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(plus, app(s, 0))), _x71)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, _x71), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(app(curry, app(app(curry, _x91), _x93)), _x92)), _x72)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(app(_x91, _x93), _x92), _x72), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, map), _x31)))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, app(plus, 0))))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, curry), _x41))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, map), _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(curry, plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, app(curry, app(app(curry, _x71), _x73))), _x72)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, app(s, _x52))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), plus)), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, app(curry, app(map, _x71))), nil)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x62), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(plus, 0)), _x71))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, curry), plus)), app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, curry), app(plus, 0))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))), app(plus, 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, curry), app(app(curry, _x51), _x53))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, app(plus, app(s, app(s, _x102)))), _x101)), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(s, app(app(plus, _x102), _x101))), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, plus), app(s, _x42)))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, app(s, _x42))))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(map, _x61))), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), plus))))), app(s, 0))), _x81)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, map), _x41)), app(app(cons, _x43), _x42)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(map, _x51)))), app(app(cons, _x53), _x52)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))))), app(map, _x51))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(map, _x61)), app(app(cons, _x63), _x62)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), plus))))), 0)), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, app(plus, app(s, app(s, 0))))))), _x91)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, _x91)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(map, _x71))))), nil)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x62), _x32))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), app(app(curry, _x41), _x43)))), _x42)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))
app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))), app(plus, app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, map), _x61)))), app(app(cons, _x63), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(app(curry, app(curry, _x81)), _x83)), _x82)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x81, _x83), _x82), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))))), plus)), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, plus)))), app(s, app(s, _x62)))), app(app(cons, _x61), xs)) → app#(cons, app(s, app(s, app(app(plus, _x62), _x61))))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, app(map, _x71)), nil))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), plus))))), app(s, app(s, _x82)))), _x81)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x82), _x81))), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(plus, app(s, _x62))), _x61)))), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(app(plus, _x62), _x61)), _x52), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(map, _x41))), app(app(cons, _x43), _x42)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, app(s, _x82))), _x81))))), _x72)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(s, app(app(plus, _x82), _x81)), _x72), _x62), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, curry), plus)), 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), map)), _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), map))), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), map))), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, plus), app(s, 0))))), _x71)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x71), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(map, _x41)))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(curry, app(curry, app(map, _x51)))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, plus), 0)), _x61))), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, plus))), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, plus)))), app(s, _x52))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(plus, app(s, app(s, app(s, _x72)))))), app(app(cons, _x71), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x72), _x71)))))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(plus, app(s, app(s, 0))))), app(app(cons, _x71), xs)) → app#(cons, app(s, app(s, _x71)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, app(map, _x51)))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(map, _x51)))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, app(s, 0)))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, _x81)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(app(curry, _x51), _x53)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), map))))), _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, plus)))), app(s, 0))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), plus))), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, plus)), app(s, 0)))), _x81))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), curry))))), _x41)), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, 0))), _x61))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, _x61), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72))))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(plus, app(s, app(s, _x52)))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), plus))), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(app(curry, app(curry, map)), _x51)), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, plus), 0))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(map, _x61)), nil)), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(nil, _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, map), _x41))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(plus, 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))))), map)), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, plus))), app(s, app(s, _x72)))), _x71)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(app(plus, _x72), _x71))), _x32))app#(app(map, app(app(curry, app(app(curry, plus), 0)), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))
app#(app(map, app(app(curry, app(curry, app(app(curry, app(map, _x61)), nil))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(nil, _x52), _x42))app#(app(map, app(app(curry, app(curry, app(curry, map))), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, app(s, app(s, 0)))), _x101))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(s, _x101)), _x52), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(curry, plus)), app(s, app(s, app(s, 0))))), app(app(cons, _x101), xs)) → app#(cons, app(s, app(s, app(s, _x101))))app#(app(map, app(app(curry, app(app(curry, curry), app(app(curry, _x51), _x53))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, plus), app(s, _x62)))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, plus)), 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(plus, 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(app(curry, _x61), _x63)), _x62)), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, 0)))), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(plus, app(s, _x72)))))), _x71)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x62), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, app(s, _x62))), _x61)), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(app(plus, _x62), _x61)), _x52), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(map, _x71))), nil))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x62), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(curry, _x41)), _x43)))), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(_x41, _x43), _x42), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), plus))), 0))), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(plus, app(s, 0)))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(plus, app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, map), _x61))), app(app(cons, _x63), _x62)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))app#(app(map, app(app(curry, app(app(curry, curry), app(plus, app(s, 0)))), _x61)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, _x61), _x42))
app#(app(map, app(app(curry, app(curry, app(curry, app(curry, app(plus, 0))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, app(app(curry, curry), app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, plus))), app(s, _x42))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, plus)))), app(s, 0)))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, app(plus, 0)), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, plus)))), 0)), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))
app#(app(map, app(app(curry, map), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, map), _x61)), app(app(cons, _x63), _x62)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, map)), _x51))), nil))), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, curry), app(plus, app(s, _x52)))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(plus, 0)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, app(s, app(s, 0)))))), _x91)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, _x91)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(app(curry, curry), _x61)), _x63)))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(plus, app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, map))), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, plus))), 0)), app(plus, app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, app(curry, _x41))))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, plus)), 0))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(map, app(app(curry, app(app(curry, curry), map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, map), _x61))), nil))), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(curry, _x41))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, plus))), 0)), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(app(curry, curry), _x31)))), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(map, _x51))), nil))), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, app(curry, _x61)), _x63))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, plus))), app(s, app(s, _x62)))), app(app(cons, _x61), xs)) → app#(cons, app(s, app(s, app(app(plus, _x62), _x61))))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, plus), app(s, _x62)))), _x61))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x62), _x61)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))))), app(curry, _x41))), _x43)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, app(s, _x72)))), _x71)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, curry), app(curry, _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, plus), 0))), _x41)), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))app#(app(map, app(app(curry, map), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(curry, app(map, _x51))))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, curry), map)), _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x51)), nil))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, app(app(curry, _x51), _x53))))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(app(curry, _x61), _x63)), _x62)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(curry, _x61)), _x63)))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, plus))), app(s, app(s, 0))))), app(app(cons, _x71), xs)) → app#(cons, app(s, app(s, _x71)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, map), _x31)))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(app(curry, plus), 0)), _x81)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x81, _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, 0))), app(map, _x41)))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, 0))), app(app(curry, _x41), _x43)))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(curry, app(app(curry, curry), _x31))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(curry, _x31)))), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(curry, _x31))), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(map, _x51)))), app(app(cons, _x53), _x52)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, app(plus, app(s, _x72))), _x71))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), app(map, _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, app(curry, _x61)), _x63)), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x61, _x63), _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), plus))), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(plus, 0))))), _x71)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x62), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, plus))), app(s, 0)))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), map)), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), plus))), app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(plus, app(s, app(s, _x72)))), _x71)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(s, app(s, app(app(plus, _x72), _x71))), _x52), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(app(curry, plus), app(s, _x82))), _x81)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x82), _x81)), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(map, _x51)))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(map, _x71)))), app(app(cons, _x73), _x72))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, plus), app(s, 0)))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(map, _x51))))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(plus, app(s, _x72))))), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, 0))), _x61)))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, _x61), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, map), _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), app(map, _x41)))), app(app(cons, _x43), _x42))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, app(s, 0)))), _x91)))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(s, _x91)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, plus)), 0)), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72)))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x62), _x32))
app#(app(map, app(app(curry, app(curry, plus)), app(s, 0))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))app#(app(map, app(plus, app(s, 0))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))
app#(app(map, app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(curry, _x51)))))), _x53)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(map, _x71))), app(app(cons, _x73), _x72))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x62), _x32))app#(app(map, app(app(curry, app(plus, app(s, app(s, app(s, _x92))))), _x91)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(app(plus, _x92), _x91)))), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), app(app(curry, _x41), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, 0))), app(app(curry, _x31), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, map))), _x31))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(app(curry, map), _x81)), nil)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), map))), _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, app(plus, app(s, _x52))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(curry, app(curry, app(plus, app(s, _x52))))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, 0))), app(plus, app(s, _x42))))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, app(app(curry, _x71), _x73)), _x72))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, curry), plus)), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))app#(app(map, app(app(curry, app(curry, app(app(curry, map), _x41))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(plus, 0)), _x51))), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, map)), _x41))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(curry, _x51))), _x53))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, curry), app(curry, _x41))), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(app(curry, map), _x41)))), nil))), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, plus)))), app(s, 0))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), app(plus, app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))))), plus)), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, curry)), app(app(curry, plus), 0)))), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(plus, 0)), _x71)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), app(plus, 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, plus)))), 0))), app(app(cons, _x41), xs)) → app#(cons, _x41)app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(map, _x51))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, map), _x61))))), nil)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(nil, _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, app(s, _x72))), _x71)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, app(s, _x62))))))), _x61)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x62), _x61)), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, plus), 0))))), _x61)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x61, _x62), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, app(plus, 0)), _x51)))), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, plus), 0))), _x61))), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, app(s, 0))))), _x81)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, app(app(curry, _x51), _x53)), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(plus, 0)))), app(app(curry, _x31), _x33)))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(map, _x61)), nil))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(nil, _x52), _x42))
app#(app(map, app(app(curry, app(curry, app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, map)))), _x31)), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))))), map)), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(map, _x61)), app(app(cons, _x63), _x62))))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x52), _x42))
app#(app(map, app(app(curry, app(curry, app(curry, app(curry, app(plus, app(s, _x52)))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(plus, 0)))), app(map, _x31)))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, _x71), _x73)), _x72))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, curry), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(plus, app(s, app(s, app(s, _x92))))))), _x91)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(app(plus, _x92), _x91)))), _x32))app#(app(map, app(app(curry, app(curry, app(curry, app(map, _x51)))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(app(curry, _x81), _x83)), _x82))))), _x72)), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(app(_x81, _x83), _x82), _x72), _x62), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, curry), _x41))), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, plus), app(s, _x42))), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x42), _x41)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))))), app(map, _x51))), app(app(cons, _x53), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(plus, 0)))), app(plus, 0)))), app(app(cons, _x31), xs)) → app#(cons, _x31)app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(plus, 0))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, plus))), app(s, 0))), app(app(cons, _x61), xs)) → app#(cons, app(s, _x61))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), plus)), app(s, app(s, app(s, _x82))))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x82), _x81)))))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, map)))), _x51)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(plus, app(s, app(s, _x62)))), app(app(cons, _x61), xs)) → app#(cons, app(s, app(s, app(app(plus, _x62), _x61))))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, plus))), 0)), app(map, _x41))), app(app(cons, nil), xs)) → app#(cons, nil)app#(app(map, app(app(curry, app(curry, app(curry, app(curry, plus)))), app(s, _x32))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(map, _x61)))))), app(app(cons, _x63), _x62))), _x62)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x61, _x63)), app(app(map, _x61), _x62)), _x62), _x32))app#(app(map, app(app(curry, app(curry, app(curry, app(curry, app(map, _x51))))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(app(curry, _x71), _x73)))), _x72)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, map)))), _x41))), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(curry, app(app(curry, app(app(curry, _x61), _x63)), _x62))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x52), _x42))app#(app(map, app(app(curry, app(plus, app(s, 0))), _x81)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, _x81), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(app(curry, app(app(curry, _x61), _x63)), _x62))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(app(app(_x61, _x63), _x62), _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, app(map, _x71)), app(app(cons, _x73), _x72))), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(cons, app(_x71, _x73)), app(app(map, _x71), _x72)), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, app(plus, 0)), _x61)))), _x52)), app(app(cons, _x42), xs)) → app#(cons, app(app(_x61, _x52), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72)), _x52))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, plus), app(s, app(s, app(s, _x102))))))), _x101)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(app(plus, _x102), _x101)))), _x32))app#(app(map, app(app(curry, app(curry, app(app(curry, plus), 0))), app(app(curry, _x31), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, app(map, _x51))))), app(app(cons, _x53), _x52)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, map))), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(plus, app(s, app(s, 0)))), _x91))), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(s, _x91)), _x42))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, app(curry, _x41))))), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, plus))), 0)), app(plus, app(s, 0)))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))app#(app(map, app(app(curry, plus), app(s, app(s, app(s, _x82))))), app(app(cons, _x81), xs)) → app#(cons, app(s, app(s, app(s, app(app(plus, _x82), _x81)))))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(curry, app(curry, plus)))), app(s, app(s, _x52))))), app(app(cons, _x51), xs)) → app#(cons, app(s, app(s, app(app(plus, _x52), _x51))))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, app(app(curry, app(plus, 0)), _x91)), _x72)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x91, _x72), _x52), _x32))
app#(app(map, f), app(app(cons, x), xs)) → app#(f, x)app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, app(plus, 0)), app(plus, 0))), _x41))), app(app(cons, _x42), xs)) → app#(cons, app(_x41, _x42))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(plus, 0))), _x71))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x71, _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, _x32))))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, app(curry, _x51)), _x53))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))), app(app(curry, _x31), _x33))), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(plus, 0))), app(map, _x41)))), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), map)), _x41)), app(app(cons, app(app(cons, _x43), _x42)), xs)) → app#(cons, app(app(cons, app(_x41, _x43)), app(app(map, _x41), _x42)))
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(curry, app(plus, 0)))), app(app(curry, app(curry, _x41)), _x43))), app(app(cons, _x42), xs)) → app#(cons, app(app(_x41, _x43), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), map)), _x31)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(app(curry, app(app(curry, _x71), _x73)), _x72)), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(app(_x71, _x73), _x72), _x52), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, plus))), 0)), app(app(cons, _x41), xs)) → app#(cons, _x41)
app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, app(s, app(s, app(s, 0)))))))), _x161)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(s, app(s, _x161))))), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(plus, 0))), app(plus, app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))))), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, _x32)))), app(app(cons, _x31), xs)) → app#(cons, app(s, app(app(plus, _x32), _x31)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, map))), _x61)), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(app(curry, g), x), y) → app#(g, x)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(app(curry, curry), app(map, _x51))), nil))), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, plus), app(s, _x42)))), app(app(cons, _x41), xs)) → app#(cons, app(s, app(app(plus, _x42), _x41)))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(plus, 0))), app(plus, app(s, 0)))), app(app(cons, _x51), xs)) → app#(cons, app(s, _x51))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), plus))), 0)), app(app(cons, _x31), xs)) → app#(cons, _x31)
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(plus, app(s, _x52)))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x42))app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, app(plus, 0)))), _x51)), app(app(cons, _x32), xs)) → app#(cons, app(_x51, _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, app(plus, app(s, _x72)))), _x71))), _x62))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(s, app(app(plus, _x72), _x71)), _x62), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, curry), app(app(curry, plus), 0)))), app(app(curry, app(plus, app(s, _x52))), _x51))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(app(plus, _x52), _x51)), _x32))
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(map, _x51)), app(app(cons, _x53), _x52)))), app(app(cons, _x42), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x42))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), map)), _x41)), app(app(cons, nil), xs)) → app#(cons, nil)
app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, plus)), app(s, app(s, 0))))), _x91))), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, _x91)), _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(map, _x51))), nil)), app(app(cons, _x42), xs)) → app#(cons, app(nil, _x42))
app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(app(curry, plus), 0)))), _x61)), app(app(cons, _x32), xs)) → app#(cons, app(_x61, _x32))app#(app(map, app(app(curry, app(curry, app(app(curry, app(plus, 0)), app(plus, 0)))), app(map, _x31))), app(app(cons, app(app(cons, _x33), _x32)), xs)) → app#(cons, app(app(cons, app(_x31, _x33)), app(app(map, _x31), _x32)))
app#(app(map, app(app(curry, app(curry, app(curry, app(curry, app(curry, _x31))))), _x33)), app(app(cons, _x32), xs)) → app#(cons, app(app(_x31, _x33), _x32))app#(app(map, app(app(curry, app(app(curry, app(plus, 0)), app(app(curry, plus), app(s, app(s, app(s, app(s, app(s, app(s, _x162))))))))), _x161)), app(app(cons, _x32), xs)) → app#(cons, app(app(s, app(s, app(s, app(s, app(s, app(s, app(app(plus, _x162), _x161))))))), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(curry, curry))), app(curry, app(app(curry, _x51), _x53)))), _x52)), app(app(cons, _x32), xs)) → app#(cons, app(app(app(_x51, _x53), _x52), _x32))app#(app(map, app(app(curry, app(plus, 0)), app(app(curry, app(curry, app(app(curry, app(curry, map)), _x51))), app(app(cons, _x53), _x52)))), app(app(cons, _x32), xs)) → app#(cons, app(app(app(cons, app(_x51, _x53)), app(app(map, _x51), _x52)), _x32))
app#(app(map, app(app(curry, app(app(curry, app(curry, app(plus, 0))), app(app(curry, map), _x61))), nil)), app(app(cons, _x32), xs)) → app#(cons, app(nil, _x32))app#(app(map, app(app(curry, app(app(curry, app(curry, curry)), app(curry, app(curry, app(plus, 0))))), _x51)), app(app(cons, _x42), xs)) → app#(cons, app(_x51, _x42))

Rewrite Rules

app(app(plus, 0), y) → yapp(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(map, f), nil) → nilapp(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(curry, g), x), y) → app(app(g, x), y)inc → app(map, app(app(curry, plus), app(s, 0)))

Original Signature

Termination of terms over the following signature is verified: app, plus, 0, s, inc, map, curry, nil, cons

Strategy

The right-hand side of the rule app#(app(map, app(app(curry, app(curry, app(app(curry, plus), 0))), app(map, _x31))), app(app(cons, nil), xs)) → app#(cons, nil) is 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
Thus, the rule app#(app(map, app(app(curry, app(curry, app(app(curry, plus), 0))), app(map, _x31))), app(app(cons, nil), xs)) → app#(cons, nil) is deleted.