619.76/291.50 WORST_CASE(Omega(n^1), ?) 619.76/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 619.76/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 619.76/291.52 619.76/291.52 619.76/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 619.76/291.52 619.76/291.52 (0) CpxTRS 619.76/291.52 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 619.76/291.52 (2) TRS for Loop Detection 619.76/291.52 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 619.76/291.52 (4) BEST 619.76/291.52 (5) proven lower bound 619.76/291.52 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 619.76/291.52 (7) BOUNDS(n^1, INF) 619.76/291.52 (8) TRS for Loop Detection 619.76/291.52 619.76/291.52 619.76/291.52 ---------------------------------------- 619.76/291.52 619.76/291.52 (0) 619.76/291.52 Obligation: 619.76/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 619.76/291.52 619.76/291.52 619.76/291.52 The TRS R consists of the following rules: 619.76/291.52 619.76/291.52 a__zeros -> cons(0, zeros) 619.76/291.52 a__U11(tt) -> tt 619.76/291.52 a__U21(tt) -> tt 619.76/291.52 a__U31(tt) -> tt 619.76/291.52 a__U41(tt, V2) -> a__U42(a__isNatIList(V2)) 619.76/291.52 a__U42(tt) -> tt 619.76/291.52 a__U51(tt, V2) -> a__U52(a__isNatList(V2)) 619.76/291.52 a__U52(tt) -> tt 619.76/291.52 a__U61(tt, V2) -> a__U62(a__isNatIList(V2)) 619.76/291.52 a__U62(tt) -> tt 619.76/291.52 a__U71(tt, L, N) -> a__U72(a__isNat(N), L) 619.76/291.52 a__U72(tt, L) -> s(a__length(mark(L))) 619.76/291.52 a__U81(tt) -> nil 619.76/291.52 a__U91(tt, IL, M, N) -> a__U92(a__isNat(M), IL, M, N) 619.76/291.52 a__U92(tt, IL, M, N) -> a__U93(a__isNat(N), IL, M, N) 619.76/291.52 a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) 619.76/291.52 a__isNat(0) -> tt 619.76/291.52 a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) 619.76/291.52 a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 619.76/291.52 a__isNatIList(V) -> a__U31(a__isNatList(V)) 619.76/291.52 a__isNatIList(zeros) -> tt 619.76/291.52 a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) 619.76/291.52 a__isNatList(nil) -> tt 619.76/291.52 a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) 619.76/291.52 a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) 619.76/291.52 a__length(nil) -> 0 619.76/291.52 a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) 619.76/291.52 a__take(0, IL) -> a__U81(a__isNatIList(IL)) 619.76/291.52 a__take(s(M), cons(N, IL)) -> a__U91(a__isNatIList(IL), IL, M, N) 619.76/291.52 mark(zeros) -> a__zeros 619.76/291.52 mark(U11(X)) -> a__U11(mark(X)) 619.76/291.52 mark(U21(X)) -> a__U21(mark(X)) 619.76/291.52 mark(U31(X)) -> a__U31(mark(X)) 619.76/291.52 mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 619.76/291.52 mark(U42(X)) -> a__U42(mark(X)) 619.76/291.52 mark(isNatIList(X)) -> a__isNatIList(X) 619.76/291.52 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 619.76/291.52 mark(U52(X)) -> a__U52(mark(X)) 619.76/291.52 mark(isNatList(X)) -> a__isNatList(X) 619.76/291.52 mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 619.76/291.52 mark(U62(X)) -> a__U62(mark(X)) 619.76/291.52 mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 619.76/291.52 mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 619.76/291.52 mark(isNat(X)) -> a__isNat(X) 619.76/291.52 mark(length(X)) -> a__length(mark(X)) 619.76/291.52 mark(U81(X)) -> a__U81(mark(X)) 619.76/291.52 mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) 619.76/291.52 mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) 619.76/291.52 mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) 619.76/291.52 mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 619.76/291.52 mark(cons(X1, X2)) -> cons(mark(X1), X2) 619.76/291.52 mark(0) -> 0 619.76/291.52 mark(tt) -> tt 619.76/291.52 mark(s(X)) -> s(mark(X)) 619.76/291.52 mark(nil) -> nil 619.76/291.52 a__zeros -> zeros 619.76/291.52 a__U11(X) -> U11(X) 619.76/291.52 a__U21(X) -> U21(X) 619.76/291.52 a__U31(X) -> U31(X) 619.76/291.52 a__U41(X1, X2) -> U41(X1, X2) 619.76/291.52 a__U42(X) -> U42(X) 619.76/291.52 a__isNatIList(X) -> isNatIList(X) 619.76/291.52 a__U51(X1, X2) -> U51(X1, X2) 619.76/291.52 a__U52(X) -> U52(X) 619.76/291.52 a__isNatList(X) -> isNatList(X) 619.76/291.52 a__U61(X1, X2) -> U61(X1, X2) 619.76/291.52 a__U62(X) -> U62(X) 619.76/291.52 a__U71(X1, X2, X3) -> U71(X1, X2, X3) 619.76/291.52 a__U72(X1, X2) -> U72(X1, X2) 619.76/291.52 a__isNat(X) -> isNat(X) 619.76/291.52 a__length(X) -> length(X) 619.76/291.52 a__U81(X) -> U81(X) 619.76/291.52 a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) 619.76/291.52 a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) 619.76/291.52 a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) 619.76/291.52 a__take(X1, X2) -> take(X1, X2) 619.76/291.52 619.76/291.52 S is empty. 619.76/291.52 Rewrite Strategy: FULL 619.76/291.52 ---------------------------------------- 619.76/291.52 619.76/291.52 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 619.76/291.52 Transformed a relative TRS into a decreasing-loop problem. 619.76/291.52 ---------------------------------------- 619.76/291.52 619.76/291.52 (2) 619.76/291.52 Obligation: 619.76/291.52 Analyzing the following TRS for decreasing loops: 619.76/291.52 619.76/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 619.76/291.52 619.76/291.52 619.76/291.52 The TRS R consists of the following rules: 619.76/291.52 619.76/291.52 a__zeros -> cons(0, zeros) 619.76/291.52 a__U11(tt) -> tt 619.76/291.52 a__U21(tt) -> tt 619.76/291.52 a__U31(tt) -> tt 619.76/291.52 a__U41(tt, V2) -> a__U42(a__isNatIList(V2)) 619.76/291.52 a__U42(tt) -> tt 619.76/291.52 a__U51(tt, V2) -> a__U52(a__isNatList(V2)) 619.76/291.52 a__U52(tt) -> tt 619.76/291.52 a__U61(tt, V2) -> a__U62(a__isNatIList(V2)) 619.76/291.52 a__U62(tt) -> tt 619.76/291.52 a__U71(tt, L, N) -> a__U72(a__isNat(N), L) 619.76/291.52 a__U72(tt, L) -> s(a__length(mark(L))) 619.76/291.52 a__U81(tt) -> nil 619.76/291.52 a__U91(tt, IL, M, N) -> a__U92(a__isNat(M), IL, M, N) 619.76/291.52 a__U92(tt, IL, M, N) -> a__U93(a__isNat(N), IL, M, N) 619.76/291.52 a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) 619.76/291.52 a__isNat(0) -> tt 619.76/291.52 a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) 619.76/291.52 a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 619.76/291.52 a__isNatIList(V) -> a__U31(a__isNatList(V)) 619.76/291.52 a__isNatIList(zeros) -> tt 619.76/291.52 a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) 619.76/291.52 a__isNatList(nil) -> tt 619.76/291.52 a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) 619.76/291.52 a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) 619.76/291.52 a__length(nil) -> 0 619.76/291.52 a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) 619.76/291.52 a__take(0, IL) -> a__U81(a__isNatIList(IL)) 619.76/291.52 a__take(s(M), cons(N, IL)) -> a__U91(a__isNatIList(IL), IL, M, N) 619.76/291.52 mark(zeros) -> a__zeros 619.76/291.52 mark(U11(X)) -> a__U11(mark(X)) 619.76/291.52 mark(U21(X)) -> a__U21(mark(X)) 619.76/291.52 mark(U31(X)) -> a__U31(mark(X)) 619.76/291.52 mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 619.76/291.52 mark(U42(X)) -> a__U42(mark(X)) 619.76/291.52 mark(isNatIList(X)) -> a__isNatIList(X) 619.76/291.52 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 619.76/291.52 mark(U52(X)) -> a__U52(mark(X)) 619.76/291.52 mark(isNatList(X)) -> a__isNatList(X) 619.76/291.52 mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 619.76/291.52 mark(U62(X)) -> a__U62(mark(X)) 619.76/291.52 mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 619.76/291.52 mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 619.76/291.52 mark(isNat(X)) -> a__isNat(X) 619.76/291.52 mark(length(X)) -> a__length(mark(X)) 619.76/291.52 mark(U81(X)) -> a__U81(mark(X)) 619.76/291.52 mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) 619.76/291.52 mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) 619.76/291.52 mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) 619.76/291.52 mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 619.76/291.52 mark(cons(X1, X2)) -> cons(mark(X1), X2) 619.76/291.52 mark(0) -> 0 619.76/291.52 mark(tt) -> tt 619.76/291.52 mark(s(X)) -> s(mark(X)) 619.76/291.52 mark(nil) -> nil 619.76/291.52 a__zeros -> zeros 619.76/291.52 a__U11(X) -> U11(X) 619.76/291.52 a__U21(X) -> U21(X) 619.76/291.52 a__U31(X) -> U31(X) 619.76/291.52 a__U41(X1, X2) -> U41(X1, X2) 619.76/291.52 a__U42(X) -> U42(X) 619.76/291.52 a__isNatIList(X) -> isNatIList(X) 619.76/291.52 a__U51(X1, X2) -> U51(X1, X2) 619.76/291.52 a__U52(X) -> U52(X) 619.76/291.52 a__isNatList(X) -> isNatList(X) 619.76/291.52 a__U61(X1, X2) -> U61(X1, X2) 619.76/291.52 a__U62(X) -> U62(X) 619.76/291.52 a__U71(X1, X2, X3) -> U71(X1, X2, X3) 619.76/291.52 a__U72(X1, X2) -> U72(X1, X2) 619.76/291.52 a__isNat(X) -> isNat(X) 619.76/291.52 a__length(X) -> length(X) 619.76/291.52 a__U81(X) -> U81(X) 619.76/291.52 a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) 619.76/291.52 a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) 619.76/291.52 a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) 619.76/291.52 a__take(X1, X2) -> take(X1, X2) 619.76/291.52 619.76/291.52 S is empty. 619.76/291.52 Rewrite Strategy: FULL 619.76/291.52 ---------------------------------------- 619.76/291.52 619.76/291.52 (3) DecreasingLoopProof (LOWER BOUND(ID)) 619.76/291.52 The following loop(s) give(s) rise to the lower bound Omega(n^1): 619.76/291.52 619.76/291.52 The rewrite sequence 619.76/291.52 619.76/291.52 mark(U93(X1, X2, X3, X4)) ->^+ a__U93(mark(X1), X2, X3, X4) 619.76/291.52 619.76/291.52 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 619.76/291.52 619.76/291.52 The pumping substitution is [X1 / U93(X1, X2, X3, X4)]. 619.76/291.52 619.76/291.52 The result substitution is [ ]. 619.76/291.52 619.76/291.52 619.76/291.52 619.76/291.52 619.76/291.52 ---------------------------------------- 619.76/291.52 619.76/291.52 (4) 619.76/291.52 Complex Obligation (BEST) 619.76/291.52 619.76/291.52 ---------------------------------------- 619.76/291.52 619.76/291.52 (5) 619.76/291.52 Obligation: 619.76/291.52 Proved the lower bound n^1 for the following obligation: 619.76/291.52 619.76/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 619.76/291.52 619.76/291.52 619.76/291.52 The TRS R consists of the following rules: 619.76/291.52 619.76/291.52 a__zeros -> cons(0, zeros) 619.76/291.52 a__U11(tt) -> tt 619.76/291.52 a__U21(tt) -> tt 619.76/291.52 a__U31(tt) -> tt 619.76/291.52 a__U41(tt, V2) -> a__U42(a__isNatIList(V2)) 619.76/291.52 a__U42(tt) -> tt 619.76/291.52 a__U51(tt, V2) -> a__U52(a__isNatList(V2)) 619.76/291.52 a__U52(tt) -> tt 619.76/291.52 a__U61(tt, V2) -> a__U62(a__isNatIList(V2)) 619.76/291.52 a__U62(tt) -> tt 619.76/291.52 a__U71(tt, L, N) -> a__U72(a__isNat(N), L) 619.76/291.52 a__U72(tt, L) -> s(a__length(mark(L))) 619.76/291.52 a__U81(tt) -> nil 619.76/291.52 a__U91(tt, IL, M, N) -> a__U92(a__isNat(M), IL, M, N) 619.76/291.52 a__U92(tt, IL, M, N) -> a__U93(a__isNat(N), IL, M, N) 619.76/291.52 a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) 619.76/291.52 a__isNat(0) -> tt 619.76/291.52 a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) 619.76/291.52 a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 619.76/291.52 a__isNatIList(V) -> a__U31(a__isNatList(V)) 619.76/291.52 a__isNatIList(zeros) -> tt 619.76/291.52 a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) 619.76/291.52 a__isNatList(nil) -> tt 619.76/291.52 a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) 619.76/291.52 a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) 619.76/291.52 a__length(nil) -> 0 619.76/291.52 a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) 619.76/291.52 a__take(0, IL) -> a__U81(a__isNatIList(IL)) 619.76/291.52 a__take(s(M), cons(N, IL)) -> a__U91(a__isNatIList(IL), IL, M, N) 619.76/291.52 mark(zeros) -> a__zeros 619.76/291.52 mark(U11(X)) -> a__U11(mark(X)) 619.76/291.52 mark(U21(X)) -> a__U21(mark(X)) 619.76/291.52 mark(U31(X)) -> a__U31(mark(X)) 619.76/291.52 mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 619.76/291.52 mark(U42(X)) -> a__U42(mark(X)) 619.76/291.52 mark(isNatIList(X)) -> a__isNatIList(X) 619.76/291.52 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 619.76/291.52 mark(U52(X)) -> a__U52(mark(X)) 619.76/291.52 mark(isNatList(X)) -> a__isNatList(X) 619.76/291.52 mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 619.76/291.52 mark(U62(X)) -> a__U62(mark(X)) 619.76/291.52 mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 619.76/291.52 mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 619.76/291.52 mark(isNat(X)) -> a__isNat(X) 619.76/291.52 mark(length(X)) -> a__length(mark(X)) 619.76/291.52 mark(U81(X)) -> a__U81(mark(X)) 619.76/291.52 mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) 619.76/291.52 mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) 619.76/291.52 mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) 619.76/291.52 mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 619.76/291.52 mark(cons(X1, X2)) -> cons(mark(X1), X2) 619.76/291.52 mark(0) -> 0 619.76/291.52 mark(tt) -> tt 619.76/291.52 mark(s(X)) -> s(mark(X)) 619.76/291.52 mark(nil) -> nil 619.76/291.52 a__zeros -> zeros 619.76/291.52 a__U11(X) -> U11(X) 619.76/291.52 a__U21(X) -> U21(X) 619.76/291.52 a__U31(X) -> U31(X) 619.76/291.52 a__U41(X1, X2) -> U41(X1, X2) 619.76/291.52 a__U42(X) -> U42(X) 619.76/291.52 a__isNatIList(X) -> isNatIList(X) 619.76/291.52 a__U51(X1, X2) -> U51(X1, X2) 619.76/291.52 a__U52(X) -> U52(X) 619.76/291.52 a__isNatList(X) -> isNatList(X) 619.76/291.52 a__U61(X1, X2) -> U61(X1, X2) 619.76/291.52 a__U62(X) -> U62(X) 619.76/291.52 a__U71(X1, X2, X3) -> U71(X1, X2, X3) 619.76/291.52 a__U72(X1, X2) -> U72(X1, X2) 619.76/291.52 a__isNat(X) -> isNat(X) 619.76/291.52 a__length(X) -> length(X) 619.76/291.52 a__U81(X) -> U81(X) 619.76/291.52 a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) 619.76/291.52 a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) 619.76/291.52 a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) 619.76/291.52 a__take(X1, X2) -> take(X1, X2) 619.76/291.52 619.76/291.52 S is empty. 619.76/291.52 Rewrite Strategy: FULL 619.76/291.52 ---------------------------------------- 619.76/291.52 619.76/291.52 (6) LowerBoundPropagationProof (FINISHED) 619.76/291.52 Propagated lower bound. 619.76/291.52 ---------------------------------------- 619.76/291.52 619.76/291.52 (7) 619.76/291.52 BOUNDS(n^1, INF) 619.76/291.52 619.76/291.52 ---------------------------------------- 619.76/291.52 619.76/291.52 (8) 619.76/291.52 Obligation: 619.76/291.52 Analyzing the following TRS for decreasing loops: 619.76/291.52 619.76/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 619.76/291.52 619.76/291.52 619.76/291.52 The TRS R consists of the following rules: 619.76/291.52 619.76/291.52 a__zeros -> cons(0, zeros) 619.76/291.52 a__U11(tt) -> tt 619.76/291.52 a__U21(tt) -> tt 619.76/291.52 a__U31(tt) -> tt 619.76/291.52 a__U41(tt, V2) -> a__U42(a__isNatIList(V2)) 619.76/291.52 a__U42(tt) -> tt 619.76/291.52 a__U51(tt, V2) -> a__U52(a__isNatList(V2)) 619.76/291.52 a__U52(tt) -> tt 619.76/291.52 a__U61(tt, V2) -> a__U62(a__isNatIList(V2)) 619.76/291.52 a__U62(tt) -> tt 619.76/291.52 a__U71(tt, L, N) -> a__U72(a__isNat(N), L) 619.76/291.52 a__U72(tt, L) -> s(a__length(mark(L))) 619.76/291.52 a__U81(tt) -> nil 619.76/291.52 a__U91(tt, IL, M, N) -> a__U92(a__isNat(M), IL, M, N) 619.76/291.52 a__U92(tt, IL, M, N) -> a__U93(a__isNat(N), IL, M, N) 619.76/291.52 a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) 619.76/291.52 a__isNat(0) -> tt 619.76/291.52 a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) 619.76/291.52 a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 619.76/291.52 a__isNatIList(V) -> a__U31(a__isNatList(V)) 619.76/291.52 a__isNatIList(zeros) -> tt 619.76/291.52 a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) 619.76/291.52 a__isNatList(nil) -> tt 619.76/291.52 a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) 619.76/291.52 a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) 619.76/291.52 a__length(nil) -> 0 619.76/291.52 a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) 619.76/291.52 a__take(0, IL) -> a__U81(a__isNatIList(IL)) 619.76/291.52 a__take(s(M), cons(N, IL)) -> a__U91(a__isNatIList(IL), IL, M, N) 619.76/291.52 mark(zeros) -> a__zeros 619.76/291.52 mark(U11(X)) -> a__U11(mark(X)) 619.76/291.52 mark(U21(X)) -> a__U21(mark(X)) 619.76/291.52 mark(U31(X)) -> a__U31(mark(X)) 619.76/291.52 mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 619.76/291.52 mark(U42(X)) -> a__U42(mark(X)) 619.76/291.52 mark(isNatIList(X)) -> a__isNatIList(X) 619.76/291.52 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 619.76/291.52 mark(U52(X)) -> a__U52(mark(X)) 619.76/291.52 mark(isNatList(X)) -> a__isNatList(X) 619.76/291.52 mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 619.76/291.52 mark(U62(X)) -> a__U62(mark(X)) 619.76/291.52 mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 619.76/291.52 mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 619.76/291.52 mark(isNat(X)) -> a__isNat(X) 619.76/291.52 mark(length(X)) -> a__length(mark(X)) 619.76/291.52 mark(U81(X)) -> a__U81(mark(X)) 619.76/291.52 mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) 619.76/291.52 mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) 619.76/291.52 mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) 619.76/291.52 mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 619.76/291.52 mark(cons(X1, X2)) -> cons(mark(X1), X2) 619.76/291.52 mark(0) -> 0 619.76/291.52 mark(tt) -> tt 619.76/291.52 mark(s(X)) -> s(mark(X)) 619.76/291.52 mark(nil) -> nil 619.76/291.52 a__zeros -> zeros 619.76/291.52 a__U11(X) -> U11(X) 619.76/291.52 a__U21(X) -> U21(X) 619.76/291.52 a__U31(X) -> U31(X) 619.76/291.52 a__U41(X1, X2) -> U41(X1, X2) 619.76/291.52 a__U42(X) -> U42(X) 619.76/291.52 a__isNatIList(X) -> isNatIList(X) 619.76/291.52 a__U51(X1, X2) -> U51(X1, X2) 619.76/291.52 a__U52(X) -> U52(X) 619.76/291.52 a__isNatList(X) -> isNatList(X) 619.76/291.52 a__U61(X1, X2) -> U61(X1, X2) 619.76/291.52 a__U62(X) -> U62(X) 619.76/291.52 a__U71(X1, X2, X3) -> U71(X1, X2, X3) 619.76/291.52 a__U72(X1, X2) -> U72(X1, X2) 619.76/291.52 a__isNat(X) -> isNat(X) 619.76/291.52 a__length(X) -> length(X) 619.76/291.52 a__U81(X) -> U81(X) 619.76/291.52 a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) 619.76/291.52 a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) 619.76/291.52 a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) 619.76/291.52 a__take(X1, X2) -> take(X1, X2) 619.76/291.52 619.76/291.52 S is empty. 619.76/291.52 Rewrite Strategy: FULL 619.97/291.56 EOF