358.89/291.52 WORST_CASE(Omega(n^1), ?) 359.00/291.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 359.00/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 359.00/291.56 359.00/291.56 359.00/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 359.00/291.56 359.00/291.56 (0) CpxTRS 359.00/291.56 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 359.00/291.56 (2) TRS for Loop Detection 359.00/291.56 (3) DecreasingLoopProof [LOWER BOUND(ID), 190 ms] 359.00/291.56 (4) BEST 359.00/291.56 (5) proven lower bound 359.00/291.56 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 359.00/291.56 (7) BOUNDS(n^1, INF) 359.00/291.56 (8) TRS for Loop Detection 359.00/291.56 359.00/291.56 359.00/291.56 ---------------------------------------- 359.00/291.56 359.00/291.56 (0) 359.00/291.56 Obligation: 359.00/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 359.00/291.56 359.00/291.56 359.00/291.56 The TRS R consists of the following rules: 359.00/291.56 359.00/291.56 zeros -> cons(0, n__zeros) 359.00/291.56 U11(tt, V1) -> U12(isNatList(activate(V1))) 359.00/291.56 U12(tt) -> tt 359.00/291.56 U21(tt, V1) -> U22(isNat(activate(V1))) 359.00/291.56 U22(tt) -> tt 359.00/291.56 U31(tt, V) -> U32(isNatList(activate(V))) 359.00/291.56 U32(tt) -> tt 359.00/291.56 U41(tt, V1, V2) -> U42(isNat(activate(V1)), activate(V2)) 359.00/291.56 U42(tt, V2) -> U43(isNatIList(activate(V2))) 359.00/291.56 U43(tt) -> tt 359.00/291.56 U51(tt, V1, V2) -> U52(isNat(activate(V1)), activate(V2)) 359.00/291.56 U52(tt, V2) -> U53(isNatList(activate(V2))) 359.00/291.56 U53(tt) -> tt 359.00/291.56 U61(tt, V1, V2) -> U62(isNat(activate(V1)), activate(V2)) 359.00/291.56 U62(tt, V2) -> U63(isNatIList(activate(V2))) 359.00/291.56 U63(tt) -> tt 359.00/291.56 U71(tt, L) -> s(length(activate(L))) 359.00/291.56 U81(tt) -> nil 359.00/291.56 U91(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))) 359.00/291.56 and(tt, X) -> activate(X) 359.00/291.56 isNat(n__0) -> tt 359.00/291.56 isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) 359.00/291.56 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 359.00/291.56 isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 359.00/291.56 isNatIList(n__zeros) -> tt 359.00/291.56 isNatIList(n__cons(V1, V2)) -> U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 isNatIListKind(n__nil) -> tt 359.00/291.56 isNatIListKind(n__zeros) -> tt 359.00/291.56 isNatIListKind(n__cons(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 359.00/291.56 isNatIListKind(n__take(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 359.00/291.56 isNatKind(n__0) -> tt 359.00/291.56 isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) 359.00/291.56 isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 359.00/291.56 isNatList(n__nil) -> tt 359.00/291.56 isNatList(n__cons(V1, V2)) -> U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 isNatList(n__take(V1, V2)) -> U61(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 length(nil) -> 0 359.00/291.56 length(cons(N, L)) -> U71(and(and(isNatList(activate(L)), n__isNatIListKind(activate(L))), n__and(isNat(N), n__isNatKind(N))), activate(L)) 359.00/291.56 take(0, IL) -> U81(and(isNatIList(IL), n__isNatIListKind(IL))) 359.00/291.56 take(s(M), cons(N, IL)) -> U91(and(and(isNatIList(activate(IL)), n__isNatIListKind(activate(IL))), n__and(and(isNat(M), n__isNatKind(M)), n__and(isNat(N), n__isNatKind(N)))), activate(IL), M, N) 359.00/291.56 zeros -> n__zeros 359.00/291.56 take(X1, X2) -> n__take(X1, X2) 359.00/291.56 0 -> n__0 359.00/291.56 length(X) -> n__length(X) 359.00/291.56 s(X) -> n__s(X) 359.00/291.56 cons(X1, X2) -> n__cons(X1, X2) 359.00/291.56 isNatIListKind(X) -> n__isNatIListKind(X) 359.00/291.56 nil -> n__nil 359.00/291.56 and(X1, X2) -> n__and(X1, X2) 359.00/291.56 isNatKind(X) -> n__isNatKind(X) 359.00/291.56 activate(n__zeros) -> zeros 359.00/291.56 activate(n__take(X1, X2)) -> take(X1, X2) 359.00/291.56 activate(n__0) -> 0 359.00/291.56 activate(n__length(X)) -> length(X) 359.00/291.56 activate(n__s(X)) -> s(X) 359.00/291.56 activate(n__cons(X1, X2)) -> cons(X1, X2) 359.00/291.56 activate(n__isNatIListKind(X)) -> isNatIListKind(X) 359.00/291.56 activate(n__nil) -> nil 359.00/291.56 activate(n__and(X1, X2)) -> and(X1, X2) 359.00/291.56 activate(n__isNatKind(X)) -> isNatKind(X) 359.00/291.56 activate(X) -> X 359.00/291.56 359.00/291.56 S is empty. 359.00/291.56 Rewrite Strategy: FULL 359.00/291.56 ---------------------------------------- 359.00/291.56 359.00/291.56 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 359.00/291.56 Transformed a relative TRS into a decreasing-loop problem. 359.00/291.56 ---------------------------------------- 359.00/291.56 359.00/291.56 (2) 359.00/291.56 Obligation: 359.00/291.56 Analyzing the following TRS for decreasing loops: 359.00/291.56 359.00/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 359.00/291.56 359.00/291.56 359.00/291.56 The TRS R consists of the following rules: 359.00/291.56 359.00/291.56 zeros -> cons(0, n__zeros) 359.00/291.56 U11(tt, V1) -> U12(isNatList(activate(V1))) 359.00/291.56 U12(tt) -> tt 359.00/291.56 U21(tt, V1) -> U22(isNat(activate(V1))) 359.00/291.56 U22(tt) -> tt 359.00/291.56 U31(tt, V) -> U32(isNatList(activate(V))) 359.00/291.56 U32(tt) -> tt 359.00/291.56 U41(tt, V1, V2) -> U42(isNat(activate(V1)), activate(V2)) 359.00/291.56 U42(tt, V2) -> U43(isNatIList(activate(V2))) 359.00/291.56 U43(tt) -> tt 359.00/291.56 U51(tt, V1, V2) -> U52(isNat(activate(V1)), activate(V2)) 359.00/291.56 U52(tt, V2) -> U53(isNatList(activate(V2))) 359.00/291.56 U53(tt) -> tt 359.00/291.56 U61(tt, V1, V2) -> U62(isNat(activate(V1)), activate(V2)) 359.00/291.56 U62(tt, V2) -> U63(isNatIList(activate(V2))) 359.00/291.56 U63(tt) -> tt 359.00/291.56 U71(tt, L) -> s(length(activate(L))) 359.00/291.56 U81(tt) -> nil 359.00/291.56 U91(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))) 359.00/291.56 and(tt, X) -> activate(X) 359.00/291.56 isNat(n__0) -> tt 359.00/291.56 isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) 359.00/291.56 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 359.00/291.56 isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 359.00/291.56 isNatIList(n__zeros) -> tt 359.00/291.56 isNatIList(n__cons(V1, V2)) -> U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 isNatIListKind(n__nil) -> tt 359.00/291.56 isNatIListKind(n__zeros) -> tt 359.00/291.56 isNatIListKind(n__cons(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 359.00/291.56 isNatIListKind(n__take(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 359.00/291.56 isNatKind(n__0) -> tt 359.00/291.56 isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) 359.00/291.56 isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 359.00/291.56 isNatList(n__nil) -> tt 359.00/291.56 isNatList(n__cons(V1, V2)) -> U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 isNatList(n__take(V1, V2)) -> U61(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 length(nil) -> 0 359.00/291.56 length(cons(N, L)) -> U71(and(and(isNatList(activate(L)), n__isNatIListKind(activate(L))), n__and(isNat(N), n__isNatKind(N))), activate(L)) 359.00/291.56 take(0, IL) -> U81(and(isNatIList(IL), n__isNatIListKind(IL))) 359.00/291.56 take(s(M), cons(N, IL)) -> U91(and(and(isNatIList(activate(IL)), n__isNatIListKind(activate(IL))), n__and(and(isNat(M), n__isNatKind(M)), n__and(isNat(N), n__isNatKind(N)))), activate(IL), M, N) 359.00/291.56 zeros -> n__zeros 359.00/291.56 take(X1, X2) -> n__take(X1, X2) 359.00/291.56 0 -> n__0 359.00/291.56 length(X) -> n__length(X) 359.00/291.56 s(X) -> n__s(X) 359.00/291.56 cons(X1, X2) -> n__cons(X1, X2) 359.00/291.56 isNatIListKind(X) -> n__isNatIListKind(X) 359.00/291.56 nil -> n__nil 359.00/291.56 and(X1, X2) -> n__and(X1, X2) 359.00/291.56 isNatKind(X) -> n__isNatKind(X) 359.00/291.56 activate(n__zeros) -> zeros 359.00/291.56 activate(n__take(X1, X2)) -> take(X1, X2) 359.00/291.56 activate(n__0) -> 0 359.00/291.56 activate(n__length(X)) -> length(X) 359.00/291.56 activate(n__s(X)) -> s(X) 359.00/291.56 activate(n__cons(X1, X2)) -> cons(X1, X2) 359.00/291.56 activate(n__isNatIListKind(X)) -> isNatIListKind(X) 359.00/291.56 activate(n__nil) -> nil 359.00/291.56 activate(n__and(X1, X2)) -> and(X1, X2) 359.00/291.56 activate(n__isNatKind(X)) -> isNatKind(X) 359.00/291.56 activate(X) -> X 359.00/291.56 359.00/291.56 S is empty. 359.00/291.56 Rewrite Strategy: FULL 359.00/291.56 ---------------------------------------- 359.00/291.56 359.00/291.56 (3) DecreasingLoopProof (LOWER BOUND(ID)) 359.00/291.56 The following loop(s) give(s) rise to the lower bound Omega(n^1): 359.00/291.56 359.00/291.56 The rewrite sequence 359.00/291.56 359.00/291.56 activate(n__isNatKind(n__s(V11_0))) ->^+ isNatKind(activate(V11_0)) 359.00/291.56 359.00/291.56 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 359.00/291.56 359.00/291.56 The pumping substitution is [V11_0 / n__isNatKind(n__s(V11_0))]. 359.00/291.56 359.00/291.56 The result substitution is [ ]. 359.00/291.56 359.00/291.56 359.00/291.56 359.00/291.56 359.00/291.56 ---------------------------------------- 359.00/291.56 359.00/291.56 (4) 359.00/291.56 Complex Obligation (BEST) 359.00/291.56 359.00/291.56 ---------------------------------------- 359.00/291.56 359.00/291.56 (5) 359.00/291.56 Obligation: 359.00/291.56 Proved the lower bound n^1 for the following obligation: 359.00/291.56 359.00/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 359.00/291.56 359.00/291.56 359.00/291.56 The TRS R consists of the following rules: 359.00/291.56 359.00/291.56 zeros -> cons(0, n__zeros) 359.00/291.56 U11(tt, V1) -> U12(isNatList(activate(V1))) 359.00/291.56 U12(tt) -> tt 359.00/291.56 U21(tt, V1) -> U22(isNat(activate(V1))) 359.00/291.56 U22(tt) -> tt 359.00/291.56 U31(tt, V) -> U32(isNatList(activate(V))) 359.00/291.56 U32(tt) -> tt 359.00/291.56 U41(tt, V1, V2) -> U42(isNat(activate(V1)), activate(V2)) 359.00/291.56 U42(tt, V2) -> U43(isNatIList(activate(V2))) 359.00/291.56 U43(tt) -> tt 359.00/291.56 U51(tt, V1, V2) -> U52(isNat(activate(V1)), activate(V2)) 359.00/291.56 U52(tt, V2) -> U53(isNatList(activate(V2))) 359.00/291.56 U53(tt) -> tt 359.00/291.56 U61(tt, V1, V2) -> U62(isNat(activate(V1)), activate(V2)) 359.00/291.56 U62(tt, V2) -> U63(isNatIList(activate(V2))) 359.00/291.56 U63(tt) -> tt 359.00/291.56 U71(tt, L) -> s(length(activate(L))) 359.00/291.56 U81(tt) -> nil 359.00/291.56 U91(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))) 359.00/291.56 and(tt, X) -> activate(X) 359.00/291.56 isNat(n__0) -> tt 359.00/291.56 isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) 359.00/291.56 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 359.00/291.56 isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 359.00/291.56 isNatIList(n__zeros) -> tt 359.00/291.56 isNatIList(n__cons(V1, V2)) -> U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 isNatIListKind(n__nil) -> tt 359.00/291.56 isNatIListKind(n__zeros) -> tt 359.00/291.56 isNatIListKind(n__cons(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 359.00/291.56 isNatIListKind(n__take(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 359.00/291.56 isNatKind(n__0) -> tt 359.00/291.56 isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) 359.00/291.56 isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 359.00/291.56 isNatList(n__nil) -> tt 359.00/291.56 isNatList(n__cons(V1, V2)) -> U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 isNatList(n__take(V1, V2)) -> U61(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 length(nil) -> 0 359.00/291.56 length(cons(N, L)) -> U71(and(and(isNatList(activate(L)), n__isNatIListKind(activate(L))), n__and(isNat(N), n__isNatKind(N))), activate(L)) 359.00/291.56 take(0, IL) -> U81(and(isNatIList(IL), n__isNatIListKind(IL))) 359.00/291.56 take(s(M), cons(N, IL)) -> U91(and(and(isNatIList(activate(IL)), n__isNatIListKind(activate(IL))), n__and(and(isNat(M), n__isNatKind(M)), n__and(isNat(N), n__isNatKind(N)))), activate(IL), M, N) 359.00/291.56 zeros -> n__zeros 359.00/291.56 take(X1, X2) -> n__take(X1, X2) 359.00/291.56 0 -> n__0 359.00/291.56 length(X) -> n__length(X) 359.00/291.56 s(X) -> n__s(X) 359.00/291.56 cons(X1, X2) -> n__cons(X1, X2) 359.00/291.56 isNatIListKind(X) -> n__isNatIListKind(X) 359.00/291.56 nil -> n__nil 359.00/291.56 and(X1, X2) -> n__and(X1, X2) 359.00/291.56 isNatKind(X) -> n__isNatKind(X) 359.00/291.56 activate(n__zeros) -> zeros 359.00/291.56 activate(n__take(X1, X2)) -> take(X1, X2) 359.00/291.56 activate(n__0) -> 0 359.00/291.56 activate(n__length(X)) -> length(X) 359.00/291.56 activate(n__s(X)) -> s(X) 359.00/291.56 activate(n__cons(X1, X2)) -> cons(X1, X2) 359.00/291.56 activate(n__isNatIListKind(X)) -> isNatIListKind(X) 359.00/291.56 activate(n__nil) -> nil 359.00/291.56 activate(n__and(X1, X2)) -> and(X1, X2) 359.00/291.56 activate(n__isNatKind(X)) -> isNatKind(X) 359.00/291.56 activate(X) -> X 359.00/291.56 359.00/291.56 S is empty. 359.00/291.56 Rewrite Strategy: FULL 359.00/291.56 ---------------------------------------- 359.00/291.56 359.00/291.56 (6) LowerBoundPropagationProof (FINISHED) 359.00/291.56 Propagated lower bound. 359.00/291.56 ---------------------------------------- 359.00/291.56 359.00/291.56 (7) 359.00/291.56 BOUNDS(n^1, INF) 359.00/291.56 359.00/291.56 ---------------------------------------- 359.00/291.56 359.00/291.56 (8) 359.00/291.56 Obligation: 359.00/291.56 Analyzing the following TRS for decreasing loops: 359.00/291.56 359.00/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 359.00/291.56 359.00/291.56 359.00/291.56 The TRS R consists of the following rules: 359.00/291.56 359.00/291.56 zeros -> cons(0, n__zeros) 359.00/291.56 U11(tt, V1) -> U12(isNatList(activate(V1))) 359.00/291.56 U12(tt) -> tt 359.00/291.56 U21(tt, V1) -> U22(isNat(activate(V1))) 359.00/291.56 U22(tt) -> tt 359.00/291.56 U31(tt, V) -> U32(isNatList(activate(V))) 359.00/291.56 U32(tt) -> tt 359.00/291.56 U41(tt, V1, V2) -> U42(isNat(activate(V1)), activate(V2)) 359.00/291.56 U42(tt, V2) -> U43(isNatIList(activate(V2))) 359.00/291.56 U43(tt) -> tt 359.00/291.56 U51(tt, V1, V2) -> U52(isNat(activate(V1)), activate(V2)) 359.00/291.56 U52(tt, V2) -> U53(isNatList(activate(V2))) 359.00/291.56 U53(tt) -> tt 359.00/291.56 U61(tt, V1, V2) -> U62(isNat(activate(V1)), activate(V2)) 359.00/291.56 U62(tt, V2) -> U63(isNatIList(activate(V2))) 359.00/291.56 U63(tt) -> tt 359.00/291.56 U71(tt, L) -> s(length(activate(L))) 359.00/291.56 U81(tt) -> nil 359.00/291.56 U91(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))) 359.00/291.56 and(tt, X) -> activate(X) 359.00/291.56 isNat(n__0) -> tt 359.00/291.56 isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1)) 359.00/291.56 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 359.00/291.56 isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V)) 359.00/291.56 isNatIList(n__zeros) -> tt 359.00/291.56 isNatIList(n__cons(V1, V2)) -> U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 isNatIListKind(n__nil) -> tt 359.00/291.56 isNatIListKind(n__zeros) -> tt 359.00/291.56 isNatIListKind(n__cons(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 359.00/291.56 isNatIListKind(n__take(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))) 359.00/291.56 isNatKind(n__0) -> tt 359.00/291.56 isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) 359.00/291.56 isNatKind(n__s(V1)) -> isNatKind(activate(V1)) 359.00/291.56 isNatList(n__nil) -> tt 359.00/291.56 isNatList(n__cons(V1, V2)) -> U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 isNatList(n__take(V1, V2)) -> U61(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2)) 359.00/291.56 length(nil) -> 0 359.00/291.56 length(cons(N, L)) -> U71(and(and(isNatList(activate(L)), n__isNatIListKind(activate(L))), n__and(isNat(N), n__isNatKind(N))), activate(L)) 359.00/291.56 take(0, IL) -> U81(and(isNatIList(IL), n__isNatIListKind(IL))) 359.00/291.56 take(s(M), cons(N, IL)) -> U91(and(and(isNatIList(activate(IL)), n__isNatIListKind(activate(IL))), n__and(and(isNat(M), n__isNatKind(M)), n__and(isNat(N), n__isNatKind(N)))), activate(IL), M, N) 359.00/291.56 zeros -> n__zeros 359.00/291.56 take(X1, X2) -> n__take(X1, X2) 359.00/291.56 0 -> n__0 359.00/291.56 length(X) -> n__length(X) 359.00/291.56 s(X) -> n__s(X) 359.00/291.56 cons(X1, X2) -> n__cons(X1, X2) 359.00/291.56 isNatIListKind(X) -> n__isNatIListKind(X) 359.00/291.56 nil -> n__nil 359.00/291.56 and(X1, X2) -> n__and(X1, X2) 359.00/291.56 isNatKind(X) -> n__isNatKind(X) 359.00/291.56 activate(n__zeros) -> zeros 359.00/291.56 activate(n__take(X1, X2)) -> take(X1, X2) 359.00/291.56 activate(n__0) -> 0 359.00/291.56 activate(n__length(X)) -> length(X) 359.00/291.56 activate(n__s(X)) -> s(X) 359.00/291.56 activate(n__cons(X1, X2)) -> cons(X1, X2) 359.00/291.56 activate(n__isNatIListKind(X)) -> isNatIListKind(X) 359.00/291.56 activate(n__nil) -> nil 359.00/291.56 activate(n__and(X1, X2)) -> and(X1, X2) 359.00/291.56 activate(n__isNatKind(X)) -> isNatKind(X) 359.00/291.56 activate(X) -> X 359.00/291.56 359.00/291.56 S is empty. 359.00/291.56 Rewrite Strategy: FULL 359.00/291.59 EOF