10.72/3.59 WORST_CASE(NON_POLY, ?) 10.72/3.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 10.72/3.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.72/3.60 10.72/3.60 10.72/3.60 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 10.72/3.60 10.72/3.60 (0) CpxTRS 10.72/3.60 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 10.72/3.60 (2) TRS for Loop Detection 10.72/3.60 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 10.72/3.60 (4) BEST 10.72/3.60 (5) proven lower bound 10.72/3.60 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 10.72/3.60 (7) BOUNDS(n^1, INF) 10.72/3.60 (8) TRS for Loop Detection 10.72/3.60 (9) DecreasingLoopProof [FINISHED, 1585 ms] 10.72/3.60 (10) BOUNDS(EXP, INF) 10.72/3.60 10.72/3.60 10.72/3.60 ---------------------------------------- 10.72/3.60 10.72/3.60 (0) 10.72/3.60 Obligation: 10.72/3.60 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 10.72/3.60 10.72/3.60 10.72/3.60 The TRS R consists of the following rules: 10.72/3.60 10.72/3.60 zeros -> cons(0, n__zeros) 10.72/3.60 U11(tt, V1) -> U12(isNatIListKind(activate(V1)), activate(V1)) 10.72/3.60 U12(tt, V1) -> U13(isNatList(activate(V1))) 10.72/3.60 U13(tt) -> tt 10.72/3.60 U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) 10.72/3.60 U22(tt, V1) -> U23(isNat(activate(V1))) 10.72/3.60 U23(tt) -> tt 10.72/3.60 U31(tt, V) -> U32(isNatIListKind(activate(V)), activate(V)) 10.72/3.60 U32(tt, V) -> U33(isNatList(activate(V))) 10.72/3.60 U33(tt) -> tt 10.72/3.60 U41(tt, V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 U42(tt, V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U43(tt, V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U44(tt, V1, V2) -> U45(isNat(activate(V1)), activate(V2)) 10.72/3.60 U45(tt, V2) -> U46(isNatIList(activate(V2))) 10.72/3.60 U46(tt) -> tt 10.72/3.60 U51(tt, V2) -> U52(isNatIListKind(activate(V2))) 10.72/3.60 U52(tt) -> tt 10.72/3.60 U61(tt) -> tt 10.72/3.60 U71(tt) -> tt 10.72/3.60 U81(tt, V1, V2) -> U82(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 U82(tt, V1, V2) -> U83(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U83(tt, V1, V2) -> U84(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U84(tt, V1, V2) -> U85(isNat(activate(V1)), activate(V2)) 10.72/3.60 U85(tt, V2) -> U86(isNatList(activate(V2))) 10.72/3.60 U86(tt) -> tt 10.72/3.60 U91(tt, L, N) -> U92(isNatIListKind(activate(L)), activate(L), activate(N)) 10.72/3.60 U92(tt, L, N) -> U93(isNat(activate(N)), activate(L), activate(N)) 10.72/3.60 U93(tt, L, N) -> U94(isNatKind(activate(N)), activate(L)) 10.72/3.60 U94(tt, L) -> s(length(activate(L))) 10.72/3.60 isNat(n__0) -> tt 10.72/3.60 isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) 10.72/3.60 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 10.72/3.60 isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 10.72/3.60 isNatIList(n__zeros) -> tt 10.72/3.60 isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 isNatIListKind(n__nil) -> tt 10.72/3.60 isNatIListKind(n__zeros) -> tt 10.72/3.60 isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)) 10.72/3.60 isNatKind(n__0) -> tt 10.72/3.60 isNatKind(n__length(V1)) -> U61(isNatIListKind(activate(V1))) 10.72/3.60 isNatKind(n__s(V1)) -> U71(isNatKind(activate(V1))) 10.72/3.60 isNatList(n__nil) -> tt 10.72/3.60 isNatList(n__cons(V1, V2)) -> U81(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 length(nil) -> 0 10.72/3.60 length(cons(N, L)) -> U91(isNatList(activate(L)), activate(L), N) 10.72/3.60 zeros -> n__zeros 10.72/3.60 0 -> n__0 10.72/3.60 length(X) -> n__length(X) 10.72/3.60 s(X) -> n__s(X) 10.72/3.60 cons(X1, X2) -> n__cons(X1, X2) 10.72/3.60 nil -> n__nil 10.72/3.60 activate(n__zeros) -> zeros 10.72/3.60 activate(n__0) -> 0 10.72/3.60 activate(n__length(X)) -> length(activate(X)) 10.72/3.60 activate(n__s(X)) -> s(activate(X)) 10.72/3.60 activate(n__cons(X1, X2)) -> cons(activate(X1), X2) 10.72/3.60 activate(n__nil) -> nil 10.72/3.60 activate(X) -> X 10.72/3.60 10.72/3.60 S is empty. 10.72/3.60 Rewrite Strategy: FULL 10.72/3.60 ---------------------------------------- 10.72/3.60 10.72/3.60 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 10.72/3.60 Transformed a relative TRS into a decreasing-loop problem. 10.72/3.60 ---------------------------------------- 10.72/3.60 10.72/3.60 (2) 10.72/3.60 Obligation: 10.72/3.60 Analyzing the following TRS for decreasing loops: 10.72/3.60 10.72/3.60 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 10.72/3.60 10.72/3.60 10.72/3.60 The TRS R consists of the following rules: 10.72/3.60 10.72/3.60 zeros -> cons(0, n__zeros) 10.72/3.60 U11(tt, V1) -> U12(isNatIListKind(activate(V1)), activate(V1)) 10.72/3.60 U12(tt, V1) -> U13(isNatList(activate(V1))) 10.72/3.60 U13(tt) -> tt 10.72/3.60 U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) 10.72/3.60 U22(tt, V1) -> U23(isNat(activate(V1))) 10.72/3.60 U23(tt) -> tt 10.72/3.60 U31(tt, V) -> U32(isNatIListKind(activate(V)), activate(V)) 10.72/3.60 U32(tt, V) -> U33(isNatList(activate(V))) 10.72/3.60 U33(tt) -> tt 10.72/3.60 U41(tt, V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 U42(tt, V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U43(tt, V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U44(tt, V1, V2) -> U45(isNat(activate(V1)), activate(V2)) 10.72/3.60 U45(tt, V2) -> U46(isNatIList(activate(V2))) 10.72/3.60 U46(tt) -> tt 10.72/3.60 U51(tt, V2) -> U52(isNatIListKind(activate(V2))) 10.72/3.60 U52(tt) -> tt 10.72/3.60 U61(tt) -> tt 10.72/3.60 U71(tt) -> tt 10.72/3.60 U81(tt, V1, V2) -> U82(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 U82(tt, V1, V2) -> U83(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U83(tt, V1, V2) -> U84(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U84(tt, V1, V2) -> U85(isNat(activate(V1)), activate(V2)) 10.72/3.60 U85(tt, V2) -> U86(isNatList(activate(V2))) 10.72/3.60 U86(tt) -> tt 10.72/3.60 U91(tt, L, N) -> U92(isNatIListKind(activate(L)), activate(L), activate(N)) 10.72/3.60 U92(tt, L, N) -> U93(isNat(activate(N)), activate(L), activate(N)) 10.72/3.60 U93(tt, L, N) -> U94(isNatKind(activate(N)), activate(L)) 10.72/3.60 U94(tt, L) -> s(length(activate(L))) 10.72/3.60 isNat(n__0) -> tt 10.72/3.60 isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) 10.72/3.60 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 10.72/3.60 isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 10.72/3.60 isNatIList(n__zeros) -> tt 10.72/3.60 isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 isNatIListKind(n__nil) -> tt 10.72/3.60 isNatIListKind(n__zeros) -> tt 10.72/3.60 isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)) 10.72/3.60 isNatKind(n__0) -> tt 10.72/3.60 isNatKind(n__length(V1)) -> U61(isNatIListKind(activate(V1))) 10.72/3.60 isNatKind(n__s(V1)) -> U71(isNatKind(activate(V1))) 10.72/3.60 isNatList(n__nil) -> tt 10.72/3.60 isNatList(n__cons(V1, V2)) -> U81(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 length(nil) -> 0 10.72/3.60 length(cons(N, L)) -> U91(isNatList(activate(L)), activate(L), N) 10.72/3.60 zeros -> n__zeros 10.72/3.60 0 -> n__0 10.72/3.60 length(X) -> n__length(X) 10.72/3.60 s(X) -> n__s(X) 10.72/3.60 cons(X1, X2) -> n__cons(X1, X2) 10.72/3.60 nil -> n__nil 10.72/3.60 activate(n__zeros) -> zeros 10.72/3.60 activate(n__0) -> 0 10.72/3.60 activate(n__length(X)) -> length(activate(X)) 10.72/3.60 activate(n__s(X)) -> s(activate(X)) 10.72/3.60 activate(n__cons(X1, X2)) -> cons(activate(X1), X2) 10.72/3.60 activate(n__nil) -> nil 10.72/3.60 activate(X) -> X 10.72/3.60 10.72/3.60 S is empty. 10.72/3.60 Rewrite Strategy: FULL 10.72/3.60 ---------------------------------------- 10.72/3.60 10.72/3.60 (3) DecreasingLoopProof (LOWER BOUND(ID)) 10.72/3.60 The following loop(s) give(s) rise to the lower bound Omega(n^1): 10.72/3.60 10.72/3.60 The rewrite sequence 10.72/3.60 10.72/3.60 activate(n__s(X)) ->^+ s(activate(X)) 10.72/3.60 10.72/3.60 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 10.72/3.60 10.72/3.60 The pumping substitution is [X / n__s(X)]. 10.72/3.60 10.72/3.60 The result substitution is [ ]. 10.72/3.60 10.72/3.60 10.72/3.60 10.72/3.60 10.72/3.60 ---------------------------------------- 10.72/3.60 10.72/3.60 (4) 10.72/3.60 Complex Obligation (BEST) 10.72/3.60 10.72/3.60 ---------------------------------------- 10.72/3.60 10.72/3.60 (5) 10.72/3.60 Obligation: 10.72/3.60 Proved the lower bound n^1 for the following obligation: 10.72/3.60 10.72/3.60 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 10.72/3.60 10.72/3.60 10.72/3.60 The TRS R consists of the following rules: 10.72/3.60 10.72/3.60 zeros -> cons(0, n__zeros) 10.72/3.60 U11(tt, V1) -> U12(isNatIListKind(activate(V1)), activate(V1)) 10.72/3.60 U12(tt, V1) -> U13(isNatList(activate(V1))) 10.72/3.60 U13(tt) -> tt 10.72/3.60 U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) 10.72/3.60 U22(tt, V1) -> U23(isNat(activate(V1))) 10.72/3.60 U23(tt) -> tt 10.72/3.60 U31(tt, V) -> U32(isNatIListKind(activate(V)), activate(V)) 10.72/3.60 U32(tt, V) -> U33(isNatList(activate(V))) 10.72/3.60 U33(tt) -> tt 10.72/3.60 U41(tt, V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 U42(tt, V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U43(tt, V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U44(tt, V1, V2) -> U45(isNat(activate(V1)), activate(V2)) 10.72/3.60 U45(tt, V2) -> U46(isNatIList(activate(V2))) 10.72/3.60 U46(tt) -> tt 10.72/3.60 U51(tt, V2) -> U52(isNatIListKind(activate(V2))) 10.72/3.60 U52(tt) -> tt 10.72/3.60 U61(tt) -> tt 10.72/3.60 U71(tt) -> tt 10.72/3.60 U81(tt, V1, V2) -> U82(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 U82(tt, V1, V2) -> U83(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U83(tt, V1, V2) -> U84(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U84(tt, V1, V2) -> U85(isNat(activate(V1)), activate(V2)) 10.72/3.60 U85(tt, V2) -> U86(isNatList(activate(V2))) 10.72/3.60 U86(tt) -> tt 10.72/3.60 U91(tt, L, N) -> U92(isNatIListKind(activate(L)), activate(L), activate(N)) 10.72/3.60 U92(tt, L, N) -> U93(isNat(activate(N)), activate(L), activate(N)) 10.72/3.60 U93(tt, L, N) -> U94(isNatKind(activate(N)), activate(L)) 10.72/3.60 U94(tt, L) -> s(length(activate(L))) 10.72/3.60 isNat(n__0) -> tt 10.72/3.60 isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) 10.72/3.60 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 10.72/3.60 isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 10.72/3.60 isNatIList(n__zeros) -> tt 10.72/3.60 isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 isNatIListKind(n__nil) -> tt 10.72/3.60 isNatIListKind(n__zeros) -> tt 10.72/3.60 isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)) 10.72/3.60 isNatKind(n__0) -> tt 10.72/3.60 isNatKind(n__length(V1)) -> U61(isNatIListKind(activate(V1))) 10.72/3.60 isNatKind(n__s(V1)) -> U71(isNatKind(activate(V1))) 10.72/3.60 isNatList(n__nil) -> tt 10.72/3.60 isNatList(n__cons(V1, V2)) -> U81(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 length(nil) -> 0 10.72/3.60 length(cons(N, L)) -> U91(isNatList(activate(L)), activate(L), N) 10.72/3.60 zeros -> n__zeros 10.72/3.60 0 -> n__0 10.72/3.60 length(X) -> n__length(X) 10.72/3.60 s(X) -> n__s(X) 10.72/3.60 cons(X1, X2) -> n__cons(X1, X2) 10.72/3.60 nil -> n__nil 10.72/3.60 activate(n__zeros) -> zeros 10.72/3.60 activate(n__0) -> 0 10.72/3.60 activate(n__length(X)) -> length(activate(X)) 10.72/3.60 activate(n__s(X)) -> s(activate(X)) 10.72/3.60 activate(n__cons(X1, X2)) -> cons(activate(X1), X2) 10.72/3.60 activate(n__nil) -> nil 10.72/3.60 activate(X) -> X 10.72/3.60 10.72/3.60 S is empty. 10.72/3.60 Rewrite Strategy: FULL 10.72/3.60 ---------------------------------------- 10.72/3.60 10.72/3.60 (6) LowerBoundPropagationProof (FINISHED) 10.72/3.60 Propagated lower bound. 10.72/3.60 ---------------------------------------- 10.72/3.60 10.72/3.60 (7) 10.72/3.60 BOUNDS(n^1, INF) 10.72/3.60 10.72/3.60 ---------------------------------------- 10.72/3.60 10.72/3.60 (8) 10.72/3.60 Obligation: 10.72/3.60 Analyzing the following TRS for decreasing loops: 10.72/3.60 10.72/3.60 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 10.72/3.60 10.72/3.60 10.72/3.60 The TRS R consists of the following rules: 10.72/3.60 10.72/3.60 zeros -> cons(0, n__zeros) 10.72/3.60 U11(tt, V1) -> U12(isNatIListKind(activate(V1)), activate(V1)) 10.72/3.60 U12(tt, V1) -> U13(isNatList(activate(V1))) 10.72/3.60 U13(tt) -> tt 10.72/3.60 U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) 10.72/3.60 U22(tt, V1) -> U23(isNat(activate(V1))) 10.72/3.60 U23(tt) -> tt 10.72/3.60 U31(tt, V) -> U32(isNatIListKind(activate(V)), activate(V)) 10.72/3.60 U32(tt, V) -> U33(isNatList(activate(V))) 10.72/3.60 U33(tt) -> tt 10.72/3.60 U41(tt, V1, V2) -> U42(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 U42(tt, V1, V2) -> U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U43(tt, V1, V2) -> U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U44(tt, V1, V2) -> U45(isNat(activate(V1)), activate(V2)) 10.72/3.60 U45(tt, V2) -> U46(isNatIList(activate(V2))) 10.72/3.60 U46(tt) -> tt 10.72/3.60 U51(tt, V2) -> U52(isNatIListKind(activate(V2))) 10.72/3.60 U52(tt) -> tt 10.72/3.60 U61(tt) -> tt 10.72/3.60 U71(tt) -> tt 10.72/3.60 U81(tt, V1, V2) -> U82(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 U82(tt, V1, V2) -> U83(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U83(tt, V1, V2) -> U84(isNatIListKind(activate(V2)), activate(V1), activate(V2)) 10.72/3.60 U84(tt, V1, V2) -> U85(isNat(activate(V1)), activate(V2)) 10.72/3.60 U85(tt, V2) -> U86(isNatList(activate(V2))) 10.72/3.60 U86(tt) -> tt 10.72/3.60 U91(tt, L, N) -> U92(isNatIListKind(activate(L)), activate(L), activate(N)) 10.72/3.60 U92(tt, L, N) -> U93(isNat(activate(N)), activate(L), activate(N)) 10.72/3.60 U93(tt, L, N) -> U94(isNatKind(activate(N)), activate(L)) 10.72/3.60 U94(tt, L) -> s(length(activate(L))) 10.72/3.60 isNat(n__0) -> tt 10.72/3.60 isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) 10.72/3.60 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 10.72/3.60 isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 10.72/3.60 isNatIList(n__zeros) -> tt 10.72/3.60 isNatIList(n__cons(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 isNatIListKind(n__nil) -> tt 10.72/3.60 isNatIListKind(n__zeros) -> tt 10.72/3.60 isNatIListKind(n__cons(V1, V2)) -> U51(isNatKind(activate(V1)), activate(V2)) 10.72/3.60 isNatKind(n__0) -> tt 10.72/3.60 isNatKind(n__length(V1)) -> U61(isNatIListKind(activate(V1))) 10.72/3.60 isNatKind(n__s(V1)) -> U71(isNatKind(activate(V1))) 10.72/3.60 isNatList(n__nil) -> tt 10.72/3.60 isNatList(n__cons(V1, V2)) -> U81(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.72/3.60 length(nil) -> 0 10.72/3.60 length(cons(N, L)) -> U91(isNatList(activate(L)), activate(L), N) 10.72/3.60 zeros -> n__zeros 10.72/3.60 0 -> n__0 10.72/3.60 length(X) -> n__length(X) 10.72/3.60 s(X) -> n__s(X) 10.72/3.60 cons(X1, X2) -> n__cons(X1, X2) 10.72/3.60 nil -> n__nil 10.72/3.60 activate(n__zeros) -> zeros 10.72/3.60 activate(n__0) -> 0 10.72/3.60 activate(n__length(X)) -> length(activate(X)) 10.72/3.60 activate(n__s(X)) -> s(activate(X)) 10.72/3.60 activate(n__cons(X1, X2)) -> cons(activate(X1), X2) 10.72/3.60 activate(n__nil) -> nil 10.72/3.60 activate(X) -> X 10.72/3.60 10.72/3.60 S is empty. 10.72/3.60 Rewrite Strategy: FULL 10.72/3.60 ---------------------------------------- 10.72/3.60 10.72/3.60 (9) DecreasingLoopProof (FINISHED) 10.72/3.60 The following loop(s) give(s) rise to the lower bound EXP: 10.72/3.60 10.72/3.60 The rewrite sequence 10.72/3.60 10.72/3.60 activate(n__length(n__cons(X11_0, X22_0))) ->^+ U91(isNatList(activate(X22_0)), activate(X22_0), activate(X11_0)) 10.72/3.60 10.72/3.60 gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0]. 10.72/3.60 10.72/3.60 The pumping substitution is [X22_0 / n__length(n__cons(X11_0, X22_0))]. 10.72/3.60 10.72/3.60 The result substitution is [ ]. 10.72/3.60 10.72/3.60 10.72/3.60 10.72/3.60 The rewrite sequence 10.72/3.60 10.72/3.60 activate(n__length(n__cons(X11_0, X22_0))) ->^+ U91(isNatList(activate(X22_0)), activate(X22_0), activate(X11_0)) 10.72/3.60 10.72/3.60 gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. 10.72/3.60 10.72/3.60 The pumping substitution is [X22_0 / n__length(n__cons(X11_0, X22_0))]. 10.72/3.60 10.72/3.60 The result substitution is [ ]. 10.72/3.60 10.72/3.60 10.72/3.60 10.72/3.60 10.72/3.60 ---------------------------------------- 10.72/3.60 10.72/3.60 (10) 10.72/3.60 BOUNDS(EXP, INF) 11.08/3.65 EOF