YES
The TRS could be proven terminating. The proof took 1144 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (199ms).
| – Problem 2 was processed with processor PolynomialLinearRange4 (170ms).
| | – Problem 5 was processed with processor DependencyGraph (0ms).
| – Problem 3 was processed with processor PolynomialLinearRange4 (240ms).
| | – Problem 6 was processed with processor PolynomialLinearRange4 (80ms).
| | | – Problem 8 was processed with processor DependencyGraph (1ms).
| – Problem 4 was processed with processor PolynomialLinearRange4 (212ms).
| | – Problem 7 was processed with processor DependencyGraph (1ms).
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| isNatIList#(cons(V1, V2)) | → | isNat#(V1) | | U62#(tt, L) | → | T(L) |
| isNat#(s(V1)) | → | U21#(isNat(V1)) | | isNat#(s(V1)) | → | isNat#(V1) |
| length#(cons(N, L)) | → | U61#(isNatList(L), L, N) | | isNatList#(cons(V1, V2)) | → | isNat#(V1) |
| U41#(tt, V2) | → | U42#(isNatIList(V2)) | | U61#(tt, L, N) | → | isNat#(N) |
| U51#(tt, V2) | → | U52#(isNatList(V2)) | | isNatIList#(V) | → | isNatList#(V) |
| isNat#(length(V1)) | → | isNatList#(V1) | | T(zeros) | → | zeros# |
| isNatList#(cons(V1, V2)) | → | U51#(isNat(V1), V2) | | isNat#(length(V1)) | → | U11#(isNatList(V1)) |
| U61#(tt, L, N) | → | U62#(isNat(N), L) | | U51#(tt, V2) | → | isNatList#(V2) |
| isNatIList#(cons(V1, V2)) | → | U41#(isNat(V1), V2) | | isNatIList#(V) | → | U31#(isNatList(V)) |
| U62#(tt, L) | → | length#(L) | | length#(cons(N, L)) | → | isNatList#(L) |
| U41#(tt, V2) | → | isNatIList#(V2) |
Rewrite Rules
| zeros | → | cons(0, zeros) | | U11(tt) | → | tt |
| U21(tt) | → | tt | | U31(tt) | → | tt |
| U41(tt, V2) | → | U42(isNatIList(V2)) | | U42(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatList(V2)) | | U52(tt) | → | tt |
| U61(tt, L, N) | → | U62(isNat(N), L) | | U62(tt, L) | → | s(length(L)) |
| isNat(0) | → | tt | | isNat(length(V1)) | → | U11(isNatList(V1)) |
| isNat(s(V1)) | → | U21(isNat(V1)) | | isNatIList(V) | → | U31(isNatList(V)) |
| isNatIList(zeros) | → | tt | | isNatIList(cons(V1, V2)) | → | U41(isNat(V1), V2) |
| isNatList(nil) | → | tt | | isNatList(cons(V1, V2)) | → | U51(isNat(V1), V2) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U61(isNatList(L), L, N) |
Original Signature
Termination of terms over the following signature is verified: isNatIList, isNat, U62, U61, 0, s, U42, isNatList, U51, zeros, tt, U41, U52, length, U11, U31, U21, cons, nil
Strategy
Context-sensitive strategy:
μ(isNatList#) = μ(zeros#) = μ(isNat) = μ(T) = μ(isNatIList) = μ(isNatIList#) = μ(0) = μ(isNatList) = μ(zeros) = μ(tt) = μ(isNat#) = μ(nil) = ∅
μ(U11#) = μ(U31#) = μ(length#) = μ(U21#) = μ(U62#) = μ(U52#) = μ(U62) = μ(U41#) = μ(U61) = μ(U42) = μ(U41) = μ(length) = μ(U21) = μ(cons) = μ(U61#) = μ(U51#) = μ(U42#) = μ(U51) = μ(s) = μ(U52) = μ(U11) = μ(U31) = {1}
The following SCCs where found
| isNatIList#(cons(V1, V2)) → U41#(isNat(V1), V2) | U41#(tt, V2) → isNatIList#(V2) |
| length#(cons(N, L)) → U61#(isNatList(L), L, N) | U61#(tt, L, N) → U62#(isNat(N), L) |
| U62#(tt, L) → length#(L) |
| isNat#(length(V1)) → isNatList#(V1) | isNat#(s(V1)) → isNat#(V1) |
| isNatList#(cons(V1, V2)) → U51#(isNat(V1), V2) | isNatList#(cons(V1, V2)) → isNat#(V1) |
| U51#(tt, V2) → isNatList#(V2) |
Problem 2: PolynomialLinearRange4
Dependency Pair Problem
Dependency Pairs
| isNatIList#(cons(V1, V2)) | → | U41#(isNat(V1), V2) | | U41#(tt, V2) | → | isNatIList#(V2) |
Rewrite Rules
| zeros | → | cons(0, zeros) | | U11(tt) | → | tt |
| U21(tt) | → | tt | | U31(tt) | → | tt |
| U41(tt, V2) | → | U42(isNatIList(V2)) | | U42(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatList(V2)) | | U52(tt) | → | tt |
| U61(tt, L, N) | → | U62(isNat(N), L) | | U62(tt, L) | → | s(length(L)) |
| isNat(0) | → | tt | | isNat(length(V1)) | → | U11(isNatList(V1)) |
| isNat(s(V1)) | → | U21(isNat(V1)) | | isNatIList(V) | → | U31(isNatList(V)) |
| isNatIList(zeros) | → | tt | | isNatIList(cons(V1, V2)) | → | U41(isNat(V1), V2) |
| isNatList(nil) | → | tt | | isNatList(cons(V1, V2)) | → | U51(isNat(V1), V2) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U61(isNatList(L), L, N) |
Original Signature
Termination of terms over the following signature is verified: isNatIList, isNat, U62, U61, 0, s, U42, isNatList, U51, zeros, tt, U41, U52, length, U11, U31, U21, cons, nil
Strategy
Context-sensitive strategy:
μ(isNatList#) = μ(zeros#) = μ(isNat) = μ(T) = μ(isNatIList) = μ(isNatIList#) = μ(0) = μ(isNatList) = μ(tt) = μ(zeros) = μ(isNat#) = μ(nil) = ∅
μ(U11#) = μ(U31#) = μ(length#) = μ(U21#) = μ(U62#) = μ(U52#) = μ(U41#) = μ(U62) = μ(U61) = μ(U42) = μ(U41) = μ(length) = μ(U21) = μ(cons) = μ(U61#) = μ(U51#) = μ(U42#) = μ(s) = μ(U51) = μ(U52) = μ(U11) = μ(U31) = {1}
Polynomial Interpretation
- 0: 3
- U11(x): 0
- U21(x): 1
- U31(x): 0
- U41(x,y): 0
- U41#(x,y): 2y
- U42(x): 0
- U51(x,y): 0
- U52(x): 0
- U61(x,y,z): 0
- U62(x,y): 0
- cons(x,y): 3y + 3x + 1
- isNat(x): 3
- isNatIList(x): 0
- isNatIList#(x): 2x
- isNatList(x): 2x
- length(x): 3x + 3
- nil: 1
- s(x): 3x + 3
- tt: 0
- zeros: 0
Standard Usable rules
| U11(tt) | → | tt | | isNat(0) | → | tt |
| isNatList(nil) | → | tt | | U51(tt, V2) | → | U52(isNatList(V2)) |
| U21(tt) | → | tt | | isNat(length(V1)) | → | U11(isNatList(V1)) |
| isNatList(cons(V1, V2)) | → | U51(isNat(V1), V2) | | U52(tt) | → | tt |
| isNat(s(V1)) | → | U21(isNat(V1)) |
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| isNatIList#(cons(V1, V2)) | → | U41#(isNat(V1), V2) |
Problem 5: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| U41#(tt, V2) | → | isNatIList#(V2) |
Rewrite Rules
| zeros | → | cons(0, zeros) | | U11(tt) | → | tt |
| U21(tt) | → | tt | | U31(tt) | → | tt |
| U41(tt, V2) | → | U42(isNatIList(V2)) | | U42(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatList(V2)) | | U52(tt) | → | tt |
| U61(tt, L, N) | → | U62(isNat(N), L) | | U62(tt, L) | → | s(length(L)) |
| isNat(0) | → | tt | | isNat(length(V1)) | → | U11(isNatList(V1)) |
| isNat(s(V1)) | → | U21(isNat(V1)) | | isNatIList(V) | → | U31(isNatList(V)) |
| isNatIList(zeros) | → | tt | | isNatIList(cons(V1, V2)) | → | U41(isNat(V1), V2) |
| isNatList(nil) | → | tt | | isNatList(cons(V1, V2)) | → | U51(isNat(V1), V2) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U61(isNatList(L), L, N) |
Original Signature
Termination of terms over the following signature is verified: isNatIList, isNat, U62, U61, 0, s, U42, isNatList, U51, zeros, tt, U41, U52, length, U11, U31, U21, nil, cons
Strategy
Context-sensitive strategy:
μ(isNatList#) = μ(zeros#) = μ(isNat) = μ(T) = μ(isNatIList) = μ(isNatIList#) = μ(0) = μ(isNatList) = μ(zeros) = μ(tt) = μ(isNat#) = μ(nil) = ∅
μ(U11#) = μ(U31#) = μ(length#) = μ(U21#) = μ(U62#) = μ(U52#) = μ(U62) = μ(U41#) = μ(U61) = μ(U42) = μ(U41) = μ(length) = μ(U21) = μ(cons) = μ(U61#) = μ(U51#) = μ(U42#) = μ(U51) = μ(s) = μ(U52) = μ(U11) = μ(U31) = {1}
There are no SCCs!
Problem 3: PolynomialLinearRange4
Dependency Pair Problem
Dependency Pairs
| isNat#(length(V1)) | → | isNatList#(V1) | | isNat#(s(V1)) | → | isNat#(V1) |
| isNatList#(cons(V1, V2)) | → | U51#(isNat(V1), V2) | | isNatList#(cons(V1, V2)) | → | isNat#(V1) |
| U51#(tt, V2) | → | isNatList#(V2) |
Rewrite Rules
| zeros | → | cons(0, zeros) | | U11(tt) | → | tt |
| U21(tt) | → | tt | | U31(tt) | → | tt |
| U41(tt, V2) | → | U42(isNatIList(V2)) | | U42(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatList(V2)) | | U52(tt) | → | tt |
| U61(tt, L, N) | → | U62(isNat(N), L) | | U62(tt, L) | → | s(length(L)) |
| isNat(0) | → | tt | | isNat(length(V1)) | → | U11(isNatList(V1)) |
| isNat(s(V1)) | → | U21(isNat(V1)) | | isNatIList(V) | → | U31(isNatList(V)) |
| isNatIList(zeros) | → | tt | | isNatIList(cons(V1, V2)) | → | U41(isNat(V1), V2) |
| isNatList(nil) | → | tt | | isNatList(cons(V1, V2)) | → | U51(isNat(V1), V2) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U61(isNatList(L), L, N) |
Original Signature
Termination of terms over the following signature is verified: isNatIList, isNat, U62, U61, 0, s, U42, isNatList, U51, zeros, tt, U41, U52, length, U11, U31, U21, cons, nil
Strategy
Context-sensitive strategy:
μ(isNatList#) = μ(zeros#) = μ(isNat) = μ(T) = μ(isNatIList) = μ(isNatIList#) = μ(0) = μ(isNatList) = μ(tt) = μ(zeros) = μ(isNat#) = μ(nil) = ∅
μ(U11#) = μ(U31#) = μ(length#) = μ(U21#) = μ(U62#) = μ(U52#) = μ(U41#) = μ(U62) = μ(U61) = μ(U42) = μ(U41) = μ(length) = μ(U21) = μ(cons) = μ(U61#) = μ(U51#) = μ(U42#) = μ(s) = μ(U51) = μ(U52) = μ(U11) = μ(U31) = {1}
Polynomial Interpretation
- 0: 2
- U11(x): 0
- U21(x): 0
- U31(x): 0
- U41(x,y): 0
- U42(x): 0
- U51(x,y): 0
- U51#(x,y): 3y
- U52(x): 0
- U61(x,y,z): 0
- U62(x,y): 0
- cons(x,y): y + 3x
- isNat(x): 2
- isNat#(x): 3x
- isNatIList(x): 0
- isNatList(x): 0
- isNatList#(x): 3x
- length(x): 3x
- nil: 2
- s(x): x + 1
- tt: 0
- zeros: 0
Standard Usable rules
| U11(tt) | → | tt | | isNat(0) | → | tt |
| isNatList(nil) | → | tt | | U51(tt, V2) | → | U52(isNatList(V2)) |
| U21(tt) | → | tt | | isNat(length(V1)) | → | U11(isNatList(V1)) |
| isNatList(cons(V1, V2)) | → | U51(isNat(V1), V2) | | U52(tt) | → | tt |
| isNat(s(V1)) | → | U21(isNat(V1)) |
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| isNat#(s(V1)) | → | isNat#(V1) |
Problem 6: PolynomialLinearRange4
Dependency Pair Problem
Dependency Pairs
| isNat#(length(V1)) | → | isNatList#(V1) | | isNatList#(cons(V1, V2)) | → | U51#(isNat(V1), V2) |
| isNatList#(cons(V1, V2)) | → | isNat#(V1) | | U51#(tt, V2) | → | isNatList#(V2) |
Rewrite Rules
| zeros | → | cons(0, zeros) | | U11(tt) | → | tt |
| U21(tt) | → | tt | | U31(tt) | → | tt |
| U41(tt, V2) | → | U42(isNatIList(V2)) | | U42(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatList(V2)) | | U52(tt) | → | tt |
| U61(tt, L, N) | → | U62(isNat(N), L) | | U62(tt, L) | → | s(length(L)) |
| isNat(0) | → | tt | | isNat(length(V1)) | → | U11(isNatList(V1)) |
| isNat(s(V1)) | → | U21(isNat(V1)) | | isNatIList(V) | → | U31(isNatList(V)) |
| isNatIList(zeros) | → | tt | | isNatIList(cons(V1, V2)) | → | U41(isNat(V1), V2) |
| isNatList(nil) | → | tt | | isNatList(cons(V1, V2)) | → | U51(isNat(V1), V2) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U61(isNatList(L), L, N) |
Original Signature
Termination of terms over the following signature is verified: isNatIList, isNat, U62, U61, 0, s, U42, isNatList, U51, zeros, tt, U41, U52, length, U11, U31, U21, nil, cons
Strategy
Context-sensitive strategy:
μ(isNatList#) = μ(zeros#) = μ(isNat) = μ(T) = μ(isNatIList) = μ(isNatIList#) = μ(0) = μ(isNatList) = μ(zeros) = μ(tt) = μ(isNat#) = μ(nil) = ∅
μ(U11#) = μ(U31#) = μ(length#) = μ(U21#) = μ(U62#) = μ(U52#) = μ(U62) = μ(U41#) = μ(U61) = μ(U42) = μ(U41) = μ(length) = μ(U21) = μ(cons) = μ(U61#) = μ(U51#) = μ(U42#) = μ(U51) = μ(s) = μ(U52) = μ(U11) = μ(U31) = {1}
Polynomial Interpretation
- 0: 1
- U11(x): x + 1
- U21(x): x + 1
- U31(x): 0
- U41(x,y): 0
- U42(x): 0
- U51(x,y): y
- U51#(x,y): 2y + x + 1
- U52(x): x
- U61(x,y,z): 0
- U62(x,y): 0
- cons(x,y): y + x
- isNat(x): 2x + 1
- isNat#(x): 2x + 1
- isNatIList(x): 0
- isNatList(x): x
- isNatList#(x): 2x + 3
- length(x): 2x + 1
- nil: 3
- s(x): x + 1
- tt: 2
- zeros: 0
Standard Usable rules
| U11(tt) | → | tt | | isNat(0) | → | tt |
| isNatList(nil) | → | tt | | U51(tt, V2) | → | U52(isNatList(V2)) |
| U21(tt) | → | tt | | isNat(length(V1)) | → | U11(isNatList(V1)) |
| isNatList(cons(V1, V2)) | → | U51(isNat(V1), V2) | | U52(tt) | → | tt |
| isNat(s(V1)) | → | U21(isNat(V1)) |
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| isNatList#(cons(V1, V2)) | → | U51#(isNat(V1), V2) | | isNatList#(cons(V1, V2)) | → | isNat#(V1) |
Problem 8: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| isNat#(length(V1)) | → | isNatList#(V1) | | U51#(tt, V2) | → | isNatList#(V2) |
Rewrite Rules
| zeros | → | cons(0, zeros) | | U11(tt) | → | tt |
| U21(tt) | → | tt | | U31(tt) | → | tt |
| U41(tt, V2) | → | U42(isNatIList(V2)) | | U42(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatList(V2)) | | U52(tt) | → | tt |
| U61(tt, L, N) | → | U62(isNat(N), L) | | U62(tt, L) | → | s(length(L)) |
| isNat(0) | → | tt | | isNat(length(V1)) | → | U11(isNatList(V1)) |
| isNat(s(V1)) | → | U21(isNat(V1)) | | isNatIList(V) | → | U31(isNatList(V)) |
| isNatIList(zeros) | → | tt | | isNatIList(cons(V1, V2)) | → | U41(isNat(V1), V2) |
| isNatList(nil) | → | tt | | isNatList(cons(V1, V2)) | → | U51(isNat(V1), V2) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U61(isNatList(L), L, N) |
Original Signature
Termination of terms over the following signature is verified: isNatIList, isNat, U62, U61, 0, s, U42, isNatList, U51, zeros, tt, U41, U52, length, U11, U31, U21, cons, nil
Strategy
Context-sensitive strategy:
μ(isNatList#) = μ(zeros#) = μ(isNat) = μ(T) = μ(isNatIList) = μ(isNatIList#) = μ(0) = μ(isNatList) = μ(tt) = μ(zeros) = μ(isNat#) = μ(nil) = ∅
μ(U11#) = μ(U31#) = μ(length#) = μ(U21#) = μ(U62#) = μ(U52#) = μ(U41#) = μ(U62) = μ(U61) = μ(U42) = μ(U41) = μ(length) = μ(U21) = μ(cons) = μ(U61#) = μ(U51#) = μ(U42#) = μ(s) = μ(U51) = μ(U52) = μ(U11) = μ(U31) = {1}
There are no SCCs!
Problem 4: PolynomialLinearRange4
Dependency Pair Problem
Dependency Pairs
| length#(cons(N, L)) | → | U61#(isNatList(L), L, N) | | U61#(tt, L, N) | → | U62#(isNat(N), L) |
| U62#(tt, L) | → | length#(L) |
Rewrite Rules
| zeros | → | cons(0, zeros) | | U11(tt) | → | tt |
| U21(tt) | → | tt | | U31(tt) | → | tt |
| U41(tt, V2) | → | U42(isNatIList(V2)) | | U42(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatList(V2)) | | U52(tt) | → | tt |
| U61(tt, L, N) | → | U62(isNat(N), L) | | U62(tt, L) | → | s(length(L)) |
| isNat(0) | → | tt | | isNat(length(V1)) | → | U11(isNatList(V1)) |
| isNat(s(V1)) | → | U21(isNat(V1)) | | isNatIList(V) | → | U31(isNatList(V)) |
| isNatIList(zeros) | → | tt | | isNatIList(cons(V1, V2)) | → | U41(isNat(V1), V2) |
| isNatList(nil) | → | tt | | isNatList(cons(V1, V2)) | → | U51(isNat(V1), V2) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U61(isNatList(L), L, N) |
Original Signature
Termination of terms over the following signature is verified: isNatIList, isNat, U62, U61, 0, s, U42, isNatList, U51, zeros, tt, U41, U52, length, U11, U31, U21, cons, nil
Strategy
Context-sensitive strategy:
μ(isNatList#) = μ(zeros#) = μ(isNat) = μ(T) = μ(isNatIList) = μ(isNatIList#) = μ(0) = μ(isNatList) = μ(tt) = μ(zeros) = μ(isNat#) = μ(nil) = ∅
μ(U11#) = μ(U31#) = μ(length#) = μ(U21#) = μ(U62#) = μ(U52#) = μ(U41#) = μ(U62) = μ(U61) = μ(U42) = μ(U41) = μ(length) = μ(U21) = μ(cons) = μ(U61#) = μ(U51#) = μ(U42#) = μ(s) = μ(U51) = μ(U52) = μ(U11) = μ(U31) = {1}
Polynomial Interpretation
- 0: 1
- U11(x): 2
- U21(x): 2
- U31(x): x
- U41(x,y): 3y + 2
- U42(x): x
- U51(x,y): 3y
- U52(x): x
- U61(x,y,z): 1
- U61#(x,y,z): 2y + x
- U62(x,y): 1
- U62#(x,y): 2y
- cons(x,y): 2y
- isNat(x): 2x
- isNatIList(x): 2x + 2
- isNatList(x): 2x
- length(x): 1
- length#(x): 2x
- nil: 1
- s(x): 1
- tt: 2
- zeros: 0
Standard Usable rules
| U11(tt) | → | tt | | isNat(0) | → | tt |
| isNatList(nil) | → | tt | | U51(tt, V2) | → | U52(isNatList(V2)) |
| zeros | → | cons(0, zeros) | | U61(tt, L, N) | → | U62(isNat(N), L) |
| U31(tt) | → | tt | | isNat(length(V1)) | → | U11(isNatList(V1)) |
| U62(tt, L) | → | s(length(L)) | | isNatList(cons(V1, V2)) | → | U51(isNat(V1), V2) |
| isNat(s(V1)) | → | U21(isNat(V1)) | | length(cons(N, L)) | → | U61(isNatList(L), L, N) |
| U42(tt) | → | tt | | isNatIList(cons(V1, V2)) | → | U41(isNat(V1), V2) |
| isNatIList(V) | → | U31(isNatList(V)) | | U21(tt) | → | tt |
| isNatIList(zeros) | → | tt | | U41(tt, V2) | → | U42(isNatIList(V2)) |
| U52(tt) | → | tt | | length(nil) | → | 0 |
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| U61#(tt, L, N) | → | U62#(isNat(N), L) |
Problem 7: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| length#(cons(N, L)) | → | U61#(isNatList(L), L, N) | | U62#(tt, L) | → | length#(L) |
Rewrite Rules
| zeros | → | cons(0, zeros) | | U11(tt) | → | tt |
| U21(tt) | → | tt | | U31(tt) | → | tt |
| U41(tt, V2) | → | U42(isNatIList(V2)) | | U42(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatList(V2)) | | U52(tt) | → | tt |
| U61(tt, L, N) | → | U62(isNat(N), L) | | U62(tt, L) | → | s(length(L)) |
| isNat(0) | → | tt | | isNat(length(V1)) | → | U11(isNatList(V1)) |
| isNat(s(V1)) | → | U21(isNat(V1)) | | isNatIList(V) | → | U31(isNatList(V)) |
| isNatIList(zeros) | → | tt | | isNatIList(cons(V1, V2)) | → | U41(isNat(V1), V2) |
| isNatList(nil) | → | tt | | isNatList(cons(V1, V2)) | → | U51(isNat(V1), V2) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U61(isNatList(L), L, N) |
Original Signature
Termination of terms over the following signature is verified: isNatIList, isNat, U62, U61, 0, s, U42, isNatList, U51, zeros, tt, U41, U52, length, U11, U31, U21, nil, cons
Strategy
Context-sensitive strategy:
μ(isNatList#) = μ(zeros#) = μ(isNat) = μ(T) = μ(isNatIList) = μ(isNatIList#) = μ(0) = μ(isNatList) = μ(zeros) = μ(tt) = μ(isNat#) = μ(nil) = ∅
μ(U11#) = μ(U31#) = μ(length#) = μ(U21#) = μ(U62#) = μ(U52#) = μ(U62) = μ(U41#) = μ(U61) = μ(U42) = μ(U41) = μ(length) = μ(U21) = μ(cons) = μ(U61#) = μ(U51#) = μ(U42#) = μ(U51) = μ(s) = μ(U52) = μ(U11) = μ(U31) = {1}
There are no SCCs!