MAYBE 907.90/297.15 MAYBE 907.90/297.15 907.90/297.15 We are left with following problem, upon which TcT provides the 907.90/297.15 certificate MAYBE. 907.90/297.15 907.90/297.15 Strict Trs: 907.90/297.15 { a__zeros() -> cons(0(), zeros()) 907.90/297.15 , a__zeros() -> zeros() 907.90/297.15 , a__U11(X) -> U11(X) 907.90/297.15 , a__U11(tt()) -> tt() 907.90/297.15 , a__U21(X) -> U21(X) 907.90/297.15 , a__U21(tt()) -> tt() 907.90/297.15 , a__U31(X) -> U31(X) 907.90/297.15 , a__U31(tt()) -> tt() 907.90/297.15 , a__U41(X1, X2) -> U41(X1, X2) 907.90/297.15 , a__U41(tt(), V2) -> a__U42(a__isNatIList(V2)) 907.90/297.15 , a__U42(X) -> U42(X) 907.90/297.15 , a__U42(tt()) -> tt() 907.90/297.15 , a__isNatIList(V) -> a__U31(a__isNatList(V)) 907.90/297.15 , a__isNatIList(X) -> isNatIList(X) 907.90/297.15 , a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) 907.90/297.15 , a__isNatIList(zeros()) -> tt() 907.90/297.15 , a__U51(X1, X2) -> U51(X1, X2) 907.90/297.15 , a__U51(tt(), V2) -> a__U52(a__isNatList(V2)) 907.90/297.15 , a__U52(X) -> U52(X) 907.90/297.15 , a__U52(tt()) -> tt() 907.90/297.15 , a__isNatList(X) -> isNatList(X) 907.90/297.15 , a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) 907.90/297.15 , a__isNatList(nil()) -> tt() 907.90/297.15 , a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) 907.90/297.15 , a__U61(X1, X2) -> U61(X1, X2) 907.90/297.15 , a__U61(tt(), V2) -> a__U62(a__isNatIList(V2)) 907.90/297.15 , a__U62(X) -> U62(X) 907.90/297.15 , a__U62(tt()) -> tt() 907.90/297.15 , a__U71(X1, X2, X3) -> U71(X1, X2, X3) 907.90/297.15 , a__U71(tt(), L, N) -> a__U72(a__isNat(N), L) 907.90/297.15 , a__U72(X1, X2) -> U72(X1, X2) 907.90/297.15 , a__U72(tt(), L) -> s(a__length(mark(L))) 907.90/297.15 , a__isNat(X) -> isNat(X) 907.90/297.15 , a__isNat(0()) -> tt() 907.90/297.15 , a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 907.90/297.15 , a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) 907.90/297.15 , a__length(X) -> length(X) 907.90/297.15 , a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) 907.90/297.15 , a__length(nil()) -> 0() 907.90/297.15 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 907.90/297.15 , mark(0()) -> 0() 907.90/297.15 , mark(zeros()) -> a__zeros() 907.90/297.15 , mark(tt()) -> tt() 907.90/297.15 , mark(s(X)) -> s(mark(X)) 907.90/297.15 , mark(nil()) -> nil() 907.90/297.15 , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 907.90/297.15 , mark(length(X)) -> a__length(mark(X)) 907.90/297.15 , mark(U11(X)) -> a__U11(mark(X)) 907.90/297.15 , mark(U21(X)) -> a__U21(mark(X)) 907.90/297.15 , mark(U31(X)) -> a__U31(mark(X)) 907.90/297.15 , mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 907.90/297.15 , mark(U42(X)) -> a__U42(mark(X)) 907.90/297.15 , mark(isNatIList(X)) -> a__isNatIList(X) 907.90/297.15 , mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 907.90/297.15 , mark(U52(X)) -> a__U52(mark(X)) 907.90/297.15 , mark(isNatList(X)) -> a__isNatList(X) 907.90/297.15 , mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 907.90/297.15 , mark(U62(X)) -> a__U62(mark(X)) 907.90/297.15 , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 907.90/297.15 , mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 907.90/297.15 , mark(isNat(X)) -> a__isNat(X) 907.90/297.15 , mark(U81(X)) -> a__U81(mark(X)) 907.90/297.15 , mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) 907.90/297.15 , mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) 907.90/297.15 , mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) 907.90/297.15 , a__U81(X) -> U81(X) 907.90/297.15 , a__U81(tt()) -> nil() 907.90/297.15 , a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) 907.90/297.15 , a__U91(tt(), IL, M, N) -> a__U92(a__isNat(M), IL, M, N) 907.90/297.15 , a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) 907.90/297.15 , a__U92(tt(), IL, M, N) -> a__U93(a__isNat(N), IL, M, N) 907.90/297.15 , a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) 907.90/297.15 , a__U93(tt(), IL, M, N) -> cons(mark(N), take(M, IL)) 907.90/297.15 , a__take(X1, X2) -> take(X1, X2) 907.90/297.15 , a__take(0(), IL) -> a__U81(a__isNatIList(IL)) 907.90/297.15 , a__take(s(M), cons(N, IL)) -> 907.90/297.15 a__U91(a__isNatIList(IL), IL, M, N) } 907.90/297.15 Obligation: 907.90/297.15 runtime complexity 907.90/297.15 Answer: 907.90/297.15 MAYBE 907.90/297.15 907.90/297.15 None of the processors succeeded. 907.90/297.15 907.90/297.15 Details of failed attempt(s): 907.90/297.15 ----------------------------- 907.90/297.15 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 907.90/297.15 following reason: 907.90/297.15 907.90/297.15 Computation stopped due to timeout after 297.0 seconds. 907.90/297.15 907.90/297.15 2) 'Best' failed due to the following reason: 907.90/297.15 907.90/297.15 None of the processors succeeded. 907.90/297.15 907.90/297.15 Details of failed attempt(s): 907.90/297.15 ----------------------------- 907.90/297.15 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 907.90/297.15 seconds)' failed due to the following reason: 907.90/297.15 907.90/297.15 None of the processors succeeded. 907.90/297.15 907.90/297.15 Details of failed attempt(s): 907.90/297.15 ----------------------------- 907.90/297.15 1) 'empty' failed due to the following reason: 907.90/297.15 907.90/297.15 Empty strict component of the problem is NOT empty. 907.90/297.15 907.90/297.15 2) 'With Problem ...' failed due to the following reason: 907.90/297.15 907.90/297.15 None of the processors succeeded. 907.90/297.15 907.90/297.15 Details of failed attempt(s): 907.90/297.15 ----------------------------- 907.90/297.15 1) 'empty' failed due to the following reason: 907.90/297.15 907.90/297.15 Empty strict component of the problem is NOT empty. 907.90/297.15 907.90/297.15 2) 'Fastest' failed due to the following reason: 907.90/297.15 907.90/297.15 None of the processors succeeded. 907.90/297.15 907.90/297.15 Details of failed attempt(s): 907.90/297.15 ----------------------------- 907.90/297.15 1) 'With Problem ...' failed due to the following reason: 907.90/297.15 907.90/297.15 None of the processors succeeded. 907.90/297.15 907.90/297.15 Details of failed attempt(s): 907.90/297.15 ----------------------------- 907.90/297.15 1) 'empty' failed due to the following reason: 907.90/297.15 907.90/297.15 Empty strict component of the problem is NOT empty. 907.90/297.15 907.90/297.15 2) 'With Problem ...' failed due to the following reason: 907.90/297.15 907.90/297.15 None of the processors succeeded. 907.90/297.15 907.90/297.15 Details of failed attempt(s): 907.90/297.15 ----------------------------- 907.90/297.15 1) 'empty' failed due to the following reason: 907.90/297.15 907.90/297.15 Empty strict component of the problem is NOT empty. 907.90/297.15 907.90/297.15 2) 'With Problem ...' failed due to the following reason: 907.90/297.15 907.90/297.15 None of the processors succeeded. 907.90/297.15 907.90/297.15 Details of failed attempt(s): 907.90/297.15 ----------------------------- 907.90/297.15 1) 'empty' failed due to the following reason: 907.90/297.15 907.90/297.15 Empty strict component of the problem is NOT empty. 907.90/297.15 907.90/297.15 2) 'With Problem ...' failed due to the following reason: 907.90/297.15 907.90/297.15 Empty strict component of the problem is NOT empty. 907.90/297.15 907.90/297.15 907.90/297.15 907.90/297.15 907.90/297.15 2) 'With Problem ...' failed due to the following reason: 907.90/297.15 907.90/297.15 None of the processors succeeded. 907.90/297.15 907.90/297.15 Details of failed attempt(s): 907.90/297.15 ----------------------------- 907.90/297.15 1) 'empty' failed due to the following reason: 907.90/297.15 907.90/297.15 Empty strict component of the problem is NOT empty. 907.90/297.15 907.90/297.15 2) 'With Problem ...' failed due to the following reason: 907.90/297.15 907.90/297.15 Empty strict component of the problem is NOT empty. 907.90/297.15 907.90/297.15 907.90/297.15 907.90/297.15 907.90/297.15 907.90/297.15 2) 'Best' failed due to the following reason: 907.90/297.15 907.90/297.15 None of the processors succeeded. 907.90/297.15 907.90/297.15 Details of failed attempt(s): 907.90/297.15 ----------------------------- 907.90/297.15 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 907.90/297.15 following reason: 907.90/297.15 907.90/297.15 The processor is inapplicable, reason: 907.90/297.15 Processor only applicable for innermost runtime complexity analysis 907.90/297.15 907.90/297.15 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 907.90/297.15 to the following reason: 907.90/297.15 907.90/297.15 The processor is inapplicable, reason: 907.90/297.15 Processor only applicable for innermost runtime complexity analysis 907.90/297.15 907.90/297.15 907.90/297.15 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 907.90/297.15 failed due to the following reason: 907.90/297.15 907.90/297.15 None of the processors succeeded. 907.90/297.15 907.90/297.15 Details of failed attempt(s): 907.90/297.15 ----------------------------- 907.90/297.15 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 907.90/297.15 failed due to the following reason: 907.90/297.15 907.90/297.15 match-boundness of the problem could not be verified. 907.90/297.15 907.90/297.15 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 907.90/297.15 failed due to the following reason: 907.90/297.15 907.90/297.15 match-boundness of the problem could not be verified. 907.90/297.15 907.90/297.15 907.90/297.15 907.90/297.15 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 907.90/297.15 the following reason: 907.90/297.15 907.90/297.15 We add the following weak dependency pairs: 907.90/297.15 907.90/297.15 Strict DPs: 907.90/297.15 { a__zeros^#() -> c_1() 907.90/297.15 , a__zeros^#() -> c_2() 907.90/297.15 , a__U11^#(X) -> c_3(X) 907.90/297.15 , a__U11^#(tt()) -> c_4() 907.90/297.15 , a__U21^#(X) -> c_5(X) 907.90/297.15 , a__U21^#(tt()) -> c_6() 907.90/297.15 , a__U31^#(X) -> c_7(X) 907.90/297.15 , a__U31^#(tt()) -> c_8() 907.90/297.15 , a__U41^#(X1, X2) -> c_9(X1, X2) 907.90/297.15 , a__U41^#(tt(), V2) -> c_10(a__U42^#(a__isNatIList(V2))) 907.90/297.15 , a__U42^#(X) -> c_11(X) 907.90/297.15 , a__U42^#(tt()) -> c_12() 907.90/297.15 , a__isNatIList^#(V) -> c_13(a__U31^#(a__isNatList(V))) 907.90/297.15 , a__isNatIList^#(X) -> c_14(X) 907.90/297.15 , a__isNatIList^#(cons(V1, V2)) -> c_15(a__U41^#(a__isNat(V1), V2)) 907.90/297.15 , a__isNatIList^#(zeros()) -> c_16() 907.90/297.15 , a__U51^#(X1, X2) -> c_17(X1, X2) 907.90/297.15 , a__U51^#(tt(), V2) -> c_18(a__U52^#(a__isNatList(V2))) 907.90/297.15 , a__U52^#(X) -> c_19(X) 907.90/297.15 , a__U52^#(tt()) -> c_20() 907.90/297.15 , a__isNatList^#(X) -> c_21(X) 907.90/297.15 , a__isNatList^#(cons(V1, V2)) -> c_22(a__U51^#(a__isNat(V1), V2)) 907.90/297.15 , a__isNatList^#(nil()) -> c_23() 907.90/297.15 , a__isNatList^#(take(V1, V2)) -> c_24(a__U61^#(a__isNat(V1), V2)) 907.90/297.15 , a__U61^#(X1, X2) -> c_25(X1, X2) 907.90/297.15 , a__U61^#(tt(), V2) -> c_26(a__U62^#(a__isNatIList(V2))) 907.90/297.15 , a__U62^#(X) -> c_27(X) 907.90/297.15 , a__U62^#(tt()) -> c_28() 907.90/297.15 , a__U71^#(X1, X2, X3) -> c_29(X1, X2, X3) 907.90/297.15 , a__U71^#(tt(), L, N) -> c_30(a__U72^#(a__isNat(N), L)) 907.90/297.15 , a__U72^#(X1, X2) -> c_31(X1, X2) 907.90/297.15 , a__U72^#(tt(), L) -> c_32(a__length^#(mark(L))) 907.90/297.15 , a__length^#(X) -> c_37(X) 907.90/297.15 , a__length^#(cons(N, L)) -> c_38(a__U71^#(a__isNatList(L), L, N)) 907.90/297.15 , a__length^#(nil()) -> c_39() 907.90/297.15 , a__isNat^#(X) -> c_33(X) 907.90/297.15 , a__isNat^#(0()) -> c_34() 907.90/297.15 , a__isNat^#(s(V1)) -> c_35(a__U21^#(a__isNat(V1))) 907.90/297.15 , a__isNat^#(length(V1)) -> c_36(a__U11^#(a__isNatList(V1))) 907.90/297.15 , mark^#(cons(X1, X2)) -> c_40(mark^#(X1), X2) 907.90/297.15 , mark^#(0()) -> c_41() 907.90/297.15 , mark^#(zeros()) -> c_42(a__zeros^#()) 907.90/297.15 , mark^#(tt()) -> c_43() 907.90/297.15 , mark^#(s(X)) -> c_44(mark^#(X)) 907.90/297.15 , mark^#(nil()) -> c_45() 907.90/297.15 , mark^#(take(X1, X2)) -> c_46(a__take^#(mark(X1), mark(X2))) 907.90/297.15 , mark^#(length(X)) -> c_47(a__length^#(mark(X))) 907.90/297.15 , mark^#(U11(X)) -> c_48(a__U11^#(mark(X))) 907.90/297.15 , mark^#(U21(X)) -> c_49(a__U21^#(mark(X))) 907.90/297.15 , mark^#(U31(X)) -> c_50(a__U31^#(mark(X))) 907.90/297.15 , mark^#(U41(X1, X2)) -> c_51(a__U41^#(mark(X1), X2)) 907.90/297.15 , mark^#(U42(X)) -> c_52(a__U42^#(mark(X))) 907.90/297.15 , mark^#(isNatIList(X)) -> c_53(a__isNatIList^#(X)) 907.90/297.15 , mark^#(U51(X1, X2)) -> c_54(a__U51^#(mark(X1), X2)) 907.90/297.15 , mark^#(U52(X)) -> c_55(a__U52^#(mark(X))) 907.90/297.15 , mark^#(isNatList(X)) -> c_56(a__isNatList^#(X)) 907.90/297.15 , mark^#(U61(X1, X2)) -> c_57(a__U61^#(mark(X1), X2)) 907.90/297.15 , mark^#(U62(X)) -> c_58(a__U62^#(mark(X))) 907.90/297.15 , mark^#(U71(X1, X2, X3)) -> c_59(a__U71^#(mark(X1), X2, X3)) 907.90/297.15 , mark^#(U72(X1, X2)) -> c_60(a__U72^#(mark(X1), X2)) 907.90/297.15 , mark^#(isNat(X)) -> c_61(a__isNat^#(X)) 907.90/297.15 , mark^#(U81(X)) -> c_62(a__U81^#(mark(X))) 907.90/297.15 , mark^#(U91(X1, X2, X3, X4)) -> 907.90/297.15 c_63(a__U91^#(mark(X1), X2, X3, X4)) 907.90/297.15 , mark^#(U92(X1, X2, X3, X4)) -> 907.90/297.15 c_64(a__U92^#(mark(X1), X2, X3, X4)) 907.90/297.15 , mark^#(U93(X1, X2, X3, X4)) -> 907.90/297.15 c_65(a__U93^#(mark(X1), X2, X3, X4)) 907.90/297.15 , a__take^#(X1, X2) -> c_74(X1, X2) 907.90/297.15 , a__take^#(0(), IL) -> c_75(a__U81^#(a__isNatIList(IL))) 907.90/297.15 , a__take^#(s(M), cons(N, IL)) -> 907.90/297.15 c_76(a__U91^#(a__isNatIList(IL), IL, M, N)) 907.90/297.15 , a__U81^#(X) -> c_66(X) 907.90/297.15 , a__U81^#(tt()) -> c_67() 907.90/297.15 , a__U91^#(X1, X2, X3, X4) -> c_68(X1, X2, X3, X4) 907.90/297.15 , a__U91^#(tt(), IL, M, N) -> c_69(a__U92^#(a__isNat(M), IL, M, N)) 907.90/297.15 , a__U92^#(X1, X2, X3, X4) -> c_70(X1, X2, X3, X4) 907.90/297.15 , a__U92^#(tt(), IL, M, N) -> c_71(a__U93^#(a__isNat(N), IL, M, N)) 907.90/297.15 , a__U93^#(X1, X2, X3, X4) -> c_72(X1, X2, X3, X4) 907.90/297.15 , a__U93^#(tt(), IL, M, N) -> c_73(mark^#(N), M, IL) } 907.90/297.15 907.90/297.15 and mark the set of starting terms. 907.90/297.15 907.90/297.15 We are left with following problem, upon which TcT provides the 907.90/297.15 certificate MAYBE. 907.90/297.15 907.90/297.15 Strict DPs: 907.90/297.15 { a__zeros^#() -> c_1() 907.90/297.15 , a__zeros^#() -> c_2() 907.90/297.15 , a__U11^#(X) -> c_3(X) 907.90/297.15 , a__U11^#(tt()) -> c_4() 907.90/297.15 , a__U21^#(X) -> c_5(X) 907.90/297.15 , a__U21^#(tt()) -> c_6() 907.90/297.15 , a__U31^#(X) -> c_7(X) 907.90/297.15 , a__U31^#(tt()) -> c_8() 907.90/297.15 , a__U41^#(X1, X2) -> c_9(X1, X2) 907.90/297.15 , a__U41^#(tt(), V2) -> c_10(a__U42^#(a__isNatIList(V2))) 907.90/297.15 , a__U42^#(X) -> c_11(X) 907.90/297.15 , a__U42^#(tt()) -> c_12() 907.90/297.15 , a__isNatIList^#(V) -> c_13(a__U31^#(a__isNatList(V))) 907.90/297.15 , a__isNatIList^#(X) -> c_14(X) 907.90/297.15 , a__isNatIList^#(cons(V1, V2)) -> c_15(a__U41^#(a__isNat(V1), V2)) 907.90/297.15 , a__isNatIList^#(zeros()) -> c_16() 907.90/297.15 , a__U51^#(X1, X2) -> c_17(X1, X2) 907.90/297.15 , a__U51^#(tt(), V2) -> c_18(a__U52^#(a__isNatList(V2))) 907.90/297.15 , a__U52^#(X) -> c_19(X) 907.90/297.15 , a__U52^#(tt()) -> c_20() 907.90/297.15 , a__isNatList^#(X) -> c_21(X) 907.90/297.15 , a__isNatList^#(cons(V1, V2)) -> c_22(a__U51^#(a__isNat(V1), V2)) 907.90/297.15 , a__isNatList^#(nil()) -> c_23() 907.90/297.15 , a__isNatList^#(take(V1, V2)) -> c_24(a__U61^#(a__isNat(V1), V2)) 907.90/297.15 , a__U61^#(X1, X2) -> c_25(X1, X2) 907.90/297.15 , a__U61^#(tt(), V2) -> c_26(a__U62^#(a__isNatIList(V2))) 907.90/297.15 , a__U62^#(X) -> c_27(X) 907.90/297.15 , a__U62^#(tt()) -> c_28() 907.90/297.15 , a__U71^#(X1, X2, X3) -> c_29(X1, X2, X3) 907.90/297.15 , a__U71^#(tt(), L, N) -> c_30(a__U72^#(a__isNat(N), L)) 907.90/297.15 , a__U72^#(X1, X2) -> c_31(X1, X2) 907.90/297.15 , a__U72^#(tt(), L) -> c_32(a__length^#(mark(L))) 907.90/297.15 , a__length^#(X) -> c_37(X) 907.90/297.15 , a__length^#(cons(N, L)) -> c_38(a__U71^#(a__isNatList(L), L, N)) 907.90/297.15 , a__length^#(nil()) -> c_39() 907.90/297.15 , a__isNat^#(X) -> c_33(X) 907.90/297.15 , a__isNat^#(0()) -> c_34() 907.90/297.15 , a__isNat^#(s(V1)) -> c_35(a__U21^#(a__isNat(V1))) 907.90/297.15 , a__isNat^#(length(V1)) -> c_36(a__U11^#(a__isNatList(V1))) 907.90/297.15 , mark^#(cons(X1, X2)) -> c_40(mark^#(X1), X2) 907.90/297.15 , mark^#(0()) -> c_41() 907.90/297.15 , mark^#(zeros()) -> c_42(a__zeros^#()) 907.90/297.15 , mark^#(tt()) -> c_43() 907.90/297.15 , mark^#(s(X)) -> c_44(mark^#(X)) 907.90/297.15 , mark^#(nil()) -> c_45() 907.90/297.15 , mark^#(take(X1, X2)) -> c_46(a__take^#(mark(X1), mark(X2))) 907.90/297.15 , mark^#(length(X)) -> c_47(a__length^#(mark(X))) 907.90/297.15 , mark^#(U11(X)) -> c_48(a__U11^#(mark(X))) 907.90/297.15 , mark^#(U21(X)) -> c_49(a__U21^#(mark(X))) 907.90/297.15 , mark^#(U31(X)) -> c_50(a__U31^#(mark(X))) 907.90/297.15 , mark^#(U41(X1, X2)) -> c_51(a__U41^#(mark(X1), X2)) 907.90/297.15 , mark^#(U42(X)) -> c_52(a__U42^#(mark(X))) 907.90/297.15 , mark^#(isNatIList(X)) -> c_53(a__isNatIList^#(X)) 907.90/297.15 , mark^#(U51(X1, X2)) -> c_54(a__U51^#(mark(X1), X2)) 907.90/297.15 , mark^#(U52(X)) -> c_55(a__U52^#(mark(X))) 907.90/297.15 , mark^#(isNatList(X)) -> c_56(a__isNatList^#(X)) 907.90/297.15 , mark^#(U61(X1, X2)) -> c_57(a__U61^#(mark(X1), X2)) 907.90/297.15 , mark^#(U62(X)) -> c_58(a__U62^#(mark(X))) 907.90/297.15 , mark^#(U71(X1, X2, X3)) -> c_59(a__U71^#(mark(X1), X2, X3)) 907.90/297.15 , mark^#(U72(X1, X2)) -> c_60(a__U72^#(mark(X1), X2)) 907.90/297.15 , mark^#(isNat(X)) -> c_61(a__isNat^#(X)) 907.90/297.15 , mark^#(U81(X)) -> c_62(a__U81^#(mark(X))) 907.90/297.15 , mark^#(U91(X1, X2, X3, X4)) -> 907.90/297.15 c_63(a__U91^#(mark(X1), X2, X3, X4)) 907.90/297.15 , mark^#(U92(X1, X2, X3, X4)) -> 907.90/297.15 c_64(a__U92^#(mark(X1), X2, X3, X4)) 907.90/297.15 , mark^#(U93(X1, X2, X3, X4)) -> 907.90/297.15 c_65(a__U93^#(mark(X1), X2, X3, X4)) 907.90/297.15 , a__take^#(X1, X2) -> c_74(X1, X2) 907.90/297.15 , a__take^#(0(), IL) -> c_75(a__U81^#(a__isNatIList(IL))) 907.90/297.15 , a__take^#(s(M), cons(N, IL)) -> 907.90/297.15 c_76(a__U91^#(a__isNatIList(IL), IL, M, N)) 907.90/297.15 , a__U81^#(X) -> c_66(X) 907.90/297.15 , a__U81^#(tt()) -> c_67() 907.90/297.15 , a__U91^#(X1, X2, X3, X4) -> c_68(X1, X2, X3, X4) 907.90/297.15 , a__U91^#(tt(), IL, M, N) -> c_69(a__U92^#(a__isNat(M), IL, M, N)) 907.90/297.15 , a__U92^#(X1, X2, X3, X4) -> c_70(X1, X2, X3, X4) 907.90/297.15 , a__U92^#(tt(), IL, M, N) -> c_71(a__U93^#(a__isNat(N), IL, M, N)) 907.90/297.15 , a__U93^#(X1, X2, X3, X4) -> c_72(X1, X2, X3, X4) 907.90/297.15 , a__U93^#(tt(), IL, M, N) -> c_73(mark^#(N), M, IL) } 907.90/297.15 Strict Trs: 907.90/297.15 { a__zeros() -> cons(0(), zeros()) 907.90/297.15 , a__zeros() -> zeros() 907.90/297.15 , a__U11(X) -> U11(X) 907.90/297.15 , a__U11(tt()) -> tt() 907.90/297.15 , a__U21(X) -> U21(X) 907.90/297.15 , a__U21(tt()) -> tt() 907.90/297.15 , a__U31(X) -> U31(X) 907.90/297.15 , a__U31(tt()) -> tt() 907.90/297.15 , a__U41(X1, X2) -> U41(X1, X2) 907.90/297.15 , a__U41(tt(), V2) -> a__U42(a__isNatIList(V2)) 907.90/297.15 , a__U42(X) -> U42(X) 907.90/297.15 , a__U42(tt()) -> tt() 907.90/297.15 , a__isNatIList(V) -> a__U31(a__isNatList(V)) 907.90/297.15 , a__isNatIList(X) -> isNatIList(X) 907.90/297.15 , a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) 907.90/297.15 , a__isNatIList(zeros()) -> tt() 907.90/297.15 , a__U51(X1, X2) -> U51(X1, X2) 907.90/297.15 , a__U51(tt(), V2) -> a__U52(a__isNatList(V2)) 907.90/297.15 , a__U52(X) -> U52(X) 907.90/297.15 , a__U52(tt()) -> tt() 907.90/297.15 , a__isNatList(X) -> isNatList(X) 907.90/297.15 , a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) 907.90/297.15 , a__isNatList(nil()) -> tt() 907.90/297.15 , a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) 907.90/297.15 , a__U61(X1, X2) -> U61(X1, X2) 907.90/297.15 , a__U61(tt(), V2) -> a__U62(a__isNatIList(V2)) 907.90/297.15 , a__U62(X) -> U62(X) 907.90/297.15 , a__U62(tt()) -> tt() 907.90/297.15 , a__U71(X1, X2, X3) -> U71(X1, X2, X3) 907.90/297.15 , a__U71(tt(), L, N) -> a__U72(a__isNat(N), L) 907.90/297.15 , a__U72(X1, X2) -> U72(X1, X2) 907.90/297.15 , a__U72(tt(), L) -> s(a__length(mark(L))) 907.90/297.15 , a__isNat(X) -> isNat(X) 907.90/297.15 , a__isNat(0()) -> tt() 907.90/297.15 , a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 907.90/297.15 , a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) 907.90/297.15 , a__length(X) -> length(X) 907.90/297.15 , a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) 907.90/297.15 , a__length(nil()) -> 0() 907.90/297.15 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 907.90/297.15 , mark(0()) -> 0() 907.90/297.15 , mark(zeros()) -> a__zeros() 907.90/297.15 , mark(tt()) -> tt() 907.90/297.15 , mark(s(X)) -> s(mark(X)) 907.90/297.15 , mark(nil()) -> nil() 907.90/297.15 , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 907.90/297.15 , mark(length(X)) -> a__length(mark(X)) 907.90/297.15 , mark(U11(X)) -> a__U11(mark(X)) 907.90/297.15 , mark(U21(X)) -> a__U21(mark(X)) 907.90/297.15 , mark(U31(X)) -> a__U31(mark(X)) 907.90/297.15 , mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 907.90/297.15 , mark(U42(X)) -> a__U42(mark(X)) 907.90/297.15 , mark(isNatIList(X)) -> a__isNatIList(X) 907.90/297.15 , mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 907.90/297.15 , mark(U52(X)) -> a__U52(mark(X)) 907.90/297.15 , mark(isNatList(X)) -> a__isNatList(X) 907.90/297.15 , mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 907.90/297.15 , mark(U62(X)) -> a__U62(mark(X)) 907.90/297.15 , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 907.90/297.15 , mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 907.90/297.15 , mark(isNat(X)) -> a__isNat(X) 907.90/297.15 , mark(U81(X)) -> a__U81(mark(X)) 907.90/297.15 , mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) 907.90/297.15 , mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) 907.90/297.15 , mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) 907.90/297.15 , a__U81(X) -> U81(X) 907.90/297.15 , a__U81(tt()) -> nil() 907.90/297.15 , a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) 907.90/297.15 , a__U91(tt(), IL, M, N) -> a__U92(a__isNat(M), IL, M, N) 907.90/297.15 , a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) 907.90/297.15 , a__U92(tt(), IL, M, N) -> a__U93(a__isNat(N), IL, M, N) 907.90/297.15 , a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) 907.90/297.15 , a__U93(tt(), IL, M, N) -> cons(mark(N), take(M, IL)) 907.90/297.15 , a__take(X1, X2) -> take(X1, X2) 907.90/297.15 , a__take(0(), IL) -> a__U81(a__isNatIList(IL)) 907.90/297.15 , a__take(s(M), cons(N, IL)) -> 907.90/297.15 a__U91(a__isNatIList(IL), IL, M, N) } 907.90/297.15 Obligation: 907.90/297.15 runtime complexity 907.90/297.15 Answer: 907.90/297.15 MAYBE 907.90/297.15 907.90/297.15 We estimate the number of application of 907.90/297.15 {1,2,4,6,8,12,16,20,23,28,35,37,41,43,45,70} by applications of 907.90/297.15 Pre({1,2,4,6,8,12,16,20,23,28,35,37,41,43,45,70}) = 907.90/297.15 {3,5,7,9,10,11,13,14,17,18,19,21,25,26,27,29,31,32,33,36,38,39,40,42,44,47,48,49,50,52,53,55,56,58,61,62,66,67,69,71,73,75,76}. 907.90/297.15 Here rules are labeled as follows: 907.90/297.15 907.90/297.15 DPs: 907.90/297.15 { 1: a__zeros^#() -> c_1() 907.90/297.15 , 2: a__zeros^#() -> c_2() 907.90/297.15 , 3: a__U11^#(X) -> c_3(X) 907.90/297.15 , 4: a__U11^#(tt()) -> c_4() 907.90/297.15 , 5: a__U21^#(X) -> c_5(X) 907.90/297.15 , 6: a__U21^#(tt()) -> c_6() 907.90/297.15 , 7: a__U31^#(X) -> c_7(X) 907.90/297.15 , 8: a__U31^#(tt()) -> c_8() 907.90/297.15 , 9: a__U41^#(X1, X2) -> c_9(X1, X2) 907.90/297.15 , 10: a__U41^#(tt(), V2) -> c_10(a__U42^#(a__isNatIList(V2))) 907.90/297.15 , 11: a__U42^#(X) -> c_11(X) 907.90/297.15 , 12: a__U42^#(tt()) -> c_12() 907.90/297.15 , 13: a__isNatIList^#(V) -> c_13(a__U31^#(a__isNatList(V))) 907.90/297.15 , 14: a__isNatIList^#(X) -> c_14(X) 907.90/297.15 , 15: a__isNatIList^#(cons(V1, V2)) -> 907.90/297.15 c_15(a__U41^#(a__isNat(V1), V2)) 907.90/297.15 , 16: a__isNatIList^#(zeros()) -> c_16() 907.90/297.15 , 17: a__U51^#(X1, X2) -> c_17(X1, X2) 907.90/297.15 , 18: a__U51^#(tt(), V2) -> c_18(a__U52^#(a__isNatList(V2))) 907.90/297.15 , 19: a__U52^#(X) -> c_19(X) 907.90/297.15 , 20: a__U52^#(tt()) -> c_20() 907.90/297.15 , 21: a__isNatList^#(X) -> c_21(X) 907.90/297.15 , 22: a__isNatList^#(cons(V1, V2)) -> 907.90/297.15 c_22(a__U51^#(a__isNat(V1), V2)) 907.90/297.15 , 23: a__isNatList^#(nil()) -> c_23() 907.90/297.15 , 24: a__isNatList^#(take(V1, V2)) -> 907.90/297.15 c_24(a__U61^#(a__isNat(V1), V2)) 907.90/297.15 , 25: a__U61^#(X1, X2) -> c_25(X1, X2) 907.90/297.15 , 26: a__U61^#(tt(), V2) -> c_26(a__U62^#(a__isNatIList(V2))) 907.90/297.15 , 27: a__U62^#(X) -> c_27(X) 907.90/297.15 , 28: a__U62^#(tt()) -> c_28() 907.90/297.15 , 29: a__U71^#(X1, X2, X3) -> c_29(X1, X2, X3) 907.90/297.15 , 30: a__U71^#(tt(), L, N) -> c_30(a__U72^#(a__isNat(N), L)) 907.90/297.15 , 31: a__U72^#(X1, X2) -> c_31(X1, X2) 907.90/297.15 , 32: a__U72^#(tt(), L) -> c_32(a__length^#(mark(L))) 907.90/297.15 , 33: a__length^#(X) -> c_37(X) 907.90/297.15 , 34: a__length^#(cons(N, L)) -> 907.90/297.15 c_38(a__U71^#(a__isNatList(L), L, N)) 907.90/297.15 , 35: a__length^#(nil()) -> c_39() 907.90/297.15 , 36: a__isNat^#(X) -> c_33(X) 907.90/297.15 , 37: a__isNat^#(0()) -> c_34() 907.90/297.15 , 38: a__isNat^#(s(V1)) -> c_35(a__U21^#(a__isNat(V1))) 907.90/297.15 , 39: a__isNat^#(length(V1)) -> c_36(a__U11^#(a__isNatList(V1))) 907.90/297.15 , 40: mark^#(cons(X1, X2)) -> c_40(mark^#(X1), X2) 907.90/297.15 , 41: mark^#(0()) -> c_41() 907.90/297.15 , 42: mark^#(zeros()) -> c_42(a__zeros^#()) 907.90/297.15 , 43: mark^#(tt()) -> c_43() 907.90/297.15 , 44: mark^#(s(X)) -> c_44(mark^#(X)) 907.90/297.15 , 45: mark^#(nil()) -> c_45() 907.90/297.15 , 46: mark^#(take(X1, X2)) -> c_46(a__take^#(mark(X1), mark(X2))) 907.90/297.15 , 47: mark^#(length(X)) -> c_47(a__length^#(mark(X))) 907.90/297.15 , 48: mark^#(U11(X)) -> c_48(a__U11^#(mark(X))) 907.90/297.15 , 49: mark^#(U21(X)) -> c_49(a__U21^#(mark(X))) 907.90/297.15 , 50: mark^#(U31(X)) -> c_50(a__U31^#(mark(X))) 907.90/297.15 , 51: mark^#(U41(X1, X2)) -> c_51(a__U41^#(mark(X1), X2)) 907.90/297.15 , 52: mark^#(U42(X)) -> c_52(a__U42^#(mark(X))) 907.90/297.15 , 53: mark^#(isNatIList(X)) -> c_53(a__isNatIList^#(X)) 907.90/297.15 , 54: mark^#(U51(X1, X2)) -> c_54(a__U51^#(mark(X1), X2)) 907.90/297.15 , 55: mark^#(U52(X)) -> c_55(a__U52^#(mark(X))) 907.90/297.15 , 56: mark^#(isNatList(X)) -> c_56(a__isNatList^#(X)) 907.90/297.15 , 57: mark^#(U61(X1, X2)) -> c_57(a__U61^#(mark(X1), X2)) 907.90/297.15 , 58: mark^#(U62(X)) -> c_58(a__U62^#(mark(X))) 907.90/297.15 , 59: mark^#(U71(X1, X2, X3)) -> c_59(a__U71^#(mark(X1), X2, X3)) 907.90/297.15 , 60: mark^#(U72(X1, X2)) -> c_60(a__U72^#(mark(X1), X2)) 907.90/297.15 , 61: mark^#(isNat(X)) -> c_61(a__isNat^#(X)) 907.90/297.15 , 62: mark^#(U81(X)) -> c_62(a__U81^#(mark(X))) 907.90/297.15 , 63: mark^#(U91(X1, X2, X3, X4)) -> 907.90/297.15 c_63(a__U91^#(mark(X1), X2, X3, X4)) 907.90/297.15 , 64: mark^#(U92(X1, X2, X3, X4)) -> 907.90/297.15 c_64(a__U92^#(mark(X1), X2, X3, X4)) 907.90/297.15 , 65: mark^#(U93(X1, X2, X3, X4)) -> 907.90/297.15 c_65(a__U93^#(mark(X1), X2, X3, X4)) 907.90/297.15 , 66: a__take^#(X1, X2) -> c_74(X1, X2) 907.90/297.15 , 67: a__take^#(0(), IL) -> c_75(a__U81^#(a__isNatIList(IL))) 907.90/297.15 , 68: a__take^#(s(M), cons(N, IL)) -> 907.90/297.15 c_76(a__U91^#(a__isNatIList(IL), IL, M, N)) 907.90/297.15 , 69: a__U81^#(X) -> c_66(X) 907.90/297.15 , 70: a__U81^#(tt()) -> c_67() 907.90/297.15 , 71: a__U91^#(X1, X2, X3, X4) -> c_68(X1, X2, X3, X4) 907.90/297.15 , 72: a__U91^#(tt(), IL, M, N) -> 907.90/297.15 c_69(a__U92^#(a__isNat(M), IL, M, N)) 907.90/297.15 , 73: a__U92^#(X1, X2, X3, X4) -> c_70(X1, X2, X3, X4) 907.90/297.15 , 74: a__U92^#(tt(), IL, M, N) -> 907.90/297.15 c_71(a__U93^#(a__isNat(N), IL, M, N)) 907.90/297.15 , 75: a__U93^#(X1, X2, X3, X4) -> c_72(X1, X2, X3, X4) 907.90/297.15 , 76: a__U93^#(tt(), IL, M, N) -> c_73(mark^#(N), M, IL) } 907.90/297.15 907.90/297.15 We are left with following problem, upon which TcT provides the 907.90/297.15 certificate MAYBE. 907.90/297.15 907.90/297.15 Strict DPs: 907.90/297.15 { a__U11^#(X) -> c_3(X) 907.90/297.15 , a__U21^#(X) -> c_5(X) 907.90/297.15 , a__U31^#(X) -> c_7(X) 907.90/297.15 , a__U41^#(X1, X2) -> c_9(X1, X2) 907.90/297.15 , a__U41^#(tt(), V2) -> c_10(a__U42^#(a__isNatIList(V2))) 907.90/297.15 , a__U42^#(X) -> c_11(X) 907.90/297.15 , a__isNatIList^#(V) -> c_13(a__U31^#(a__isNatList(V))) 907.90/297.15 , a__isNatIList^#(X) -> c_14(X) 907.90/297.15 , a__isNatIList^#(cons(V1, V2)) -> c_15(a__U41^#(a__isNat(V1), V2)) 907.90/297.15 , a__U51^#(X1, X2) -> c_17(X1, X2) 907.90/297.15 , a__U51^#(tt(), V2) -> c_18(a__U52^#(a__isNatList(V2))) 907.90/297.16 , a__U52^#(X) -> c_19(X) 907.90/297.16 , a__isNatList^#(X) -> c_21(X) 907.90/297.16 , a__isNatList^#(cons(V1, V2)) -> c_22(a__U51^#(a__isNat(V1), V2)) 907.90/297.16 , a__isNatList^#(take(V1, V2)) -> c_24(a__U61^#(a__isNat(V1), V2)) 907.90/297.16 , a__U61^#(X1, X2) -> c_25(X1, X2) 907.90/297.16 , a__U61^#(tt(), V2) -> c_26(a__U62^#(a__isNatIList(V2))) 907.90/297.16 , a__U62^#(X) -> c_27(X) 907.90/297.16 , a__U71^#(X1, X2, X3) -> c_29(X1, X2, X3) 907.90/297.16 , a__U71^#(tt(), L, N) -> c_30(a__U72^#(a__isNat(N), L)) 907.90/297.16 , a__U72^#(X1, X2) -> c_31(X1, X2) 907.90/297.16 , a__U72^#(tt(), L) -> c_32(a__length^#(mark(L))) 907.90/297.16 , a__length^#(X) -> c_37(X) 907.90/297.16 , a__length^#(cons(N, L)) -> c_38(a__U71^#(a__isNatList(L), L, N)) 907.90/297.16 , a__isNat^#(X) -> c_33(X) 907.90/297.16 , a__isNat^#(s(V1)) -> c_35(a__U21^#(a__isNat(V1))) 907.90/297.16 , a__isNat^#(length(V1)) -> c_36(a__U11^#(a__isNatList(V1))) 907.90/297.16 , mark^#(cons(X1, X2)) -> c_40(mark^#(X1), X2) 907.90/297.16 , mark^#(zeros()) -> c_42(a__zeros^#()) 907.90/297.16 , mark^#(s(X)) -> c_44(mark^#(X)) 907.90/297.16 , mark^#(take(X1, X2)) -> c_46(a__take^#(mark(X1), mark(X2))) 907.90/297.16 , mark^#(length(X)) -> c_47(a__length^#(mark(X))) 907.90/297.16 , mark^#(U11(X)) -> c_48(a__U11^#(mark(X))) 907.90/297.16 , mark^#(U21(X)) -> c_49(a__U21^#(mark(X))) 907.90/297.16 , mark^#(U31(X)) -> c_50(a__U31^#(mark(X))) 907.90/297.16 , mark^#(U41(X1, X2)) -> c_51(a__U41^#(mark(X1), X2)) 907.90/297.16 , mark^#(U42(X)) -> c_52(a__U42^#(mark(X))) 907.90/297.16 , mark^#(isNatIList(X)) -> c_53(a__isNatIList^#(X)) 907.90/297.16 , mark^#(U51(X1, X2)) -> c_54(a__U51^#(mark(X1), X2)) 907.90/297.16 , mark^#(U52(X)) -> c_55(a__U52^#(mark(X))) 907.90/297.16 , mark^#(isNatList(X)) -> c_56(a__isNatList^#(X)) 907.90/297.16 , mark^#(U61(X1, X2)) -> c_57(a__U61^#(mark(X1), X2)) 907.90/297.16 , mark^#(U62(X)) -> c_58(a__U62^#(mark(X))) 907.90/297.16 , mark^#(U71(X1, X2, X3)) -> c_59(a__U71^#(mark(X1), X2, X3)) 907.90/297.16 , mark^#(U72(X1, X2)) -> c_60(a__U72^#(mark(X1), X2)) 907.90/297.16 , mark^#(isNat(X)) -> c_61(a__isNat^#(X)) 907.90/297.16 , mark^#(U81(X)) -> c_62(a__U81^#(mark(X))) 907.90/297.16 , mark^#(U91(X1, X2, X3, X4)) -> 907.90/297.16 c_63(a__U91^#(mark(X1), X2, X3, X4)) 907.90/297.16 , mark^#(U92(X1, X2, X3, X4)) -> 907.90/297.16 c_64(a__U92^#(mark(X1), X2, X3, X4)) 907.90/297.16 , mark^#(U93(X1, X2, X3, X4)) -> 907.90/297.16 c_65(a__U93^#(mark(X1), X2, X3, X4)) 907.90/297.16 , a__take^#(X1, X2) -> c_74(X1, X2) 907.90/297.16 , a__take^#(0(), IL) -> c_75(a__U81^#(a__isNatIList(IL))) 907.90/297.16 , a__take^#(s(M), cons(N, IL)) -> 907.90/297.16 c_76(a__U91^#(a__isNatIList(IL), IL, M, N)) 907.90/297.16 , a__U81^#(X) -> c_66(X) 907.90/297.16 , a__U91^#(X1, X2, X3, X4) -> c_68(X1, X2, X3, X4) 907.90/297.16 , a__U91^#(tt(), IL, M, N) -> c_69(a__U92^#(a__isNat(M), IL, M, N)) 907.90/297.16 , a__U92^#(X1, X2, X3, X4) -> c_70(X1, X2, X3, X4) 907.90/297.16 , a__U92^#(tt(), IL, M, N) -> c_71(a__U93^#(a__isNat(N), IL, M, N)) 907.90/297.16 , a__U93^#(X1, X2, X3, X4) -> c_72(X1, X2, X3, X4) 907.90/297.16 , a__U93^#(tt(), IL, M, N) -> c_73(mark^#(N), M, IL) } 907.90/297.16 Strict Trs: 907.90/297.16 { a__zeros() -> cons(0(), zeros()) 907.90/297.16 , a__zeros() -> zeros() 907.90/297.16 , a__U11(X) -> U11(X) 907.90/297.16 , a__U11(tt()) -> tt() 907.90/297.16 , a__U21(X) -> U21(X) 907.90/297.16 , a__U21(tt()) -> tt() 907.90/297.16 , a__U31(X) -> U31(X) 907.90/297.16 , a__U31(tt()) -> tt() 907.90/297.16 , a__U41(X1, X2) -> U41(X1, X2) 907.90/297.16 , a__U41(tt(), V2) -> a__U42(a__isNatIList(V2)) 907.90/297.16 , a__U42(X) -> U42(X) 907.90/297.16 , a__U42(tt()) -> tt() 907.90/297.16 , a__isNatIList(V) -> a__U31(a__isNatList(V)) 907.90/297.16 , a__isNatIList(X) -> isNatIList(X) 907.90/297.16 , a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) 907.90/297.16 , a__isNatIList(zeros()) -> tt() 907.90/297.16 , a__U51(X1, X2) -> U51(X1, X2) 907.90/297.16 , a__U51(tt(), V2) -> a__U52(a__isNatList(V2)) 907.90/297.16 , a__U52(X) -> U52(X) 907.90/297.16 , a__U52(tt()) -> tt() 907.90/297.16 , a__isNatList(X) -> isNatList(X) 907.90/297.16 , a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) 907.90/297.16 , a__isNatList(nil()) -> tt() 907.90/297.16 , a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) 907.90/297.16 , a__U61(X1, X2) -> U61(X1, X2) 907.90/297.16 , a__U61(tt(), V2) -> a__U62(a__isNatIList(V2)) 907.90/297.16 , a__U62(X) -> U62(X) 907.90/297.16 , a__U62(tt()) -> tt() 907.90/297.16 , a__U71(X1, X2, X3) -> U71(X1, X2, X3) 907.90/297.16 , a__U71(tt(), L, N) -> a__U72(a__isNat(N), L) 907.90/297.16 , a__U72(X1, X2) -> U72(X1, X2) 907.90/297.16 , a__U72(tt(), L) -> s(a__length(mark(L))) 907.90/297.16 , a__isNat(X) -> isNat(X) 907.90/297.16 , a__isNat(0()) -> tt() 907.90/297.16 , a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 907.90/297.16 , a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) 907.90/297.16 , a__length(X) -> length(X) 907.90/297.16 , a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) 907.90/297.16 , a__length(nil()) -> 0() 907.90/297.16 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 907.90/297.16 , mark(0()) -> 0() 907.90/297.16 , mark(zeros()) -> a__zeros() 907.90/297.16 , mark(tt()) -> tt() 907.90/297.16 , mark(s(X)) -> s(mark(X)) 907.90/297.16 , mark(nil()) -> nil() 907.90/297.16 , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 907.90/297.16 , mark(length(X)) -> a__length(mark(X)) 907.90/297.16 , mark(U11(X)) -> a__U11(mark(X)) 907.90/297.16 , mark(U21(X)) -> a__U21(mark(X)) 907.90/297.16 , mark(U31(X)) -> a__U31(mark(X)) 907.90/297.16 , mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 907.90/297.16 , mark(U42(X)) -> a__U42(mark(X)) 907.90/297.16 , mark(isNatIList(X)) -> a__isNatIList(X) 907.90/297.16 , mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 907.90/297.16 , mark(U52(X)) -> a__U52(mark(X)) 907.90/297.16 , mark(isNatList(X)) -> a__isNatList(X) 907.90/297.16 , mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 907.90/297.16 , mark(U62(X)) -> a__U62(mark(X)) 907.90/297.16 , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 907.90/297.16 , mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 907.90/297.16 , mark(isNat(X)) -> a__isNat(X) 907.90/297.16 , mark(U81(X)) -> a__U81(mark(X)) 907.90/297.16 , mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) 907.90/297.16 , mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) 907.90/297.16 , mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) 907.90/297.16 , a__U81(X) -> U81(X) 907.90/297.16 , a__U81(tt()) -> nil() 907.90/297.16 , a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) 907.90/297.16 , a__U91(tt(), IL, M, N) -> a__U92(a__isNat(M), IL, M, N) 907.90/297.16 , a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) 907.90/297.16 , a__U92(tt(), IL, M, N) -> a__U93(a__isNat(N), IL, M, N) 907.90/297.16 , a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) 907.90/297.16 , a__U93(tt(), IL, M, N) -> cons(mark(N), take(M, IL)) 907.90/297.16 , a__take(X1, X2) -> take(X1, X2) 907.90/297.16 , a__take(0(), IL) -> a__U81(a__isNatIList(IL)) 907.90/297.16 , a__take(s(M), cons(N, IL)) -> 907.90/297.16 a__U91(a__isNatIList(IL), IL, M, N) } 907.90/297.16 Weak DPs: 907.90/297.16 { a__zeros^#() -> c_1() 907.90/297.16 , a__zeros^#() -> c_2() 907.90/297.16 , a__U11^#(tt()) -> c_4() 907.90/297.16 , a__U21^#(tt()) -> c_6() 907.90/297.16 , a__U31^#(tt()) -> c_8() 907.90/297.16 , a__U42^#(tt()) -> c_12() 907.90/297.16 , a__isNatIList^#(zeros()) -> c_16() 907.90/297.16 , a__U52^#(tt()) -> c_20() 907.90/297.16 , a__isNatList^#(nil()) -> c_23() 907.90/297.16 , a__U62^#(tt()) -> c_28() 907.90/297.16 , a__length^#(nil()) -> c_39() 907.90/297.16 , a__isNat^#(0()) -> c_34() 907.90/297.16 , mark^#(0()) -> c_41() 907.90/297.16 , mark^#(tt()) -> c_43() 907.90/297.16 , mark^#(nil()) -> c_45() 907.90/297.16 , a__U81^#(tt()) -> c_67() } 907.90/297.16 Obligation: 907.90/297.16 runtime complexity 907.90/297.16 Answer: 907.90/297.16 MAYBE 907.90/297.16 907.90/297.16 We estimate the number of application of {29} by applications of 907.90/297.16 Pre({29}) = 907.90/297.16 {1,2,3,4,6,8,10,12,13,16,18,19,21,23,25,28,30,51,54,55,57,59,60}. 907.90/297.16 Here rules are labeled as follows: 907.90/297.16 907.90/297.16 DPs: 907.90/297.16 { 1: a__U11^#(X) -> c_3(X) 907.90/297.16 , 2: a__U21^#(X) -> c_5(X) 907.90/297.16 , 3: a__U31^#(X) -> c_7(X) 907.90/297.16 , 4: a__U41^#(X1, X2) -> c_9(X1, X2) 907.90/297.16 , 5: a__U41^#(tt(), V2) -> c_10(a__U42^#(a__isNatIList(V2))) 907.90/297.16 , 6: a__U42^#(X) -> c_11(X) 907.90/297.16 , 7: a__isNatIList^#(V) -> c_13(a__U31^#(a__isNatList(V))) 907.90/297.16 , 8: a__isNatIList^#(X) -> c_14(X) 907.90/297.16 , 9: a__isNatIList^#(cons(V1, V2)) -> 907.90/297.16 c_15(a__U41^#(a__isNat(V1), V2)) 907.90/297.16 , 10: a__U51^#(X1, X2) -> c_17(X1, X2) 907.90/297.16 , 11: a__U51^#(tt(), V2) -> c_18(a__U52^#(a__isNatList(V2))) 907.90/297.16 , 12: a__U52^#(X) -> c_19(X) 907.90/297.16 , 13: a__isNatList^#(X) -> c_21(X) 907.90/297.16 , 14: a__isNatList^#(cons(V1, V2)) -> 907.90/297.16 c_22(a__U51^#(a__isNat(V1), V2)) 907.90/297.16 , 15: a__isNatList^#(take(V1, V2)) -> 907.90/297.16 c_24(a__U61^#(a__isNat(V1), V2)) 907.90/297.16 , 16: a__U61^#(X1, X2) -> c_25(X1, X2) 907.90/297.16 , 17: a__U61^#(tt(), V2) -> c_26(a__U62^#(a__isNatIList(V2))) 907.90/297.16 , 18: a__U62^#(X) -> c_27(X) 907.90/297.16 , 19: a__U71^#(X1, X2, X3) -> c_29(X1, X2, X3) 907.90/297.16 , 20: a__U71^#(tt(), L, N) -> c_30(a__U72^#(a__isNat(N), L)) 907.90/297.16 , 21: a__U72^#(X1, X2) -> c_31(X1, X2) 907.90/297.16 , 22: a__U72^#(tt(), L) -> c_32(a__length^#(mark(L))) 907.90/297.16 , 23: a__length^#(X) -> c_37(X) 907.90/297.16 , 24: a__length^#(cons(N, L)) -> 907.90/297.16 c_38(a__U71^#(a__isNatList(L), L, N)) 907.90/297.16 , 25: a__isNat^#(X) -> c_33(X) 907.90/297.16 , 26: a__isNat^#(s(V1)) -> c_35(a__U21^#(a__isNat(V1))) 907.90/297.16 , 27: a__isNat^#(length(V1)) -> c_36(a__U11^#(a__isNatList(V1))) 907.90/297.16 , 28: mark^#(cons(X1, X2)) -> c_40(mark^#(X1), X2) 907.90/297.16 , 29: mark^#(zeros()) -> c_42(a__zeros^#()) 907.90/297.16 , 30: mark^#(s(X)) -> c_44(mark^#(X)) 907.90/297.16 , 31: mark^#(take(X1, X2)) -> c_46(a__take^#(mark(X1), mark(X2))) 907.90/297.16 , 32: mark^#(length(X)) -> c_47(a__length^#(mark(X))) 907.90/297.16 , 33: mark^#(U11(X)) -> c_48(a__U11^#(mark(X))) 907.90/297.16 , 34: mark^#(U21(X)) -> c_49(a__U21^#(mark(X))) 907.90/297.16 , 35: mark^#(U31(X)) -> c_50(a__U31^#(mark(X))) 907.90/297.16 , 36: mark^#(U41(X1, X2)) -> c_51(a__U41^#(mark(X1), X2)) 907.90/297.16 , 37: mark^#(U42(X)) -> c_52(a__U42^#(mark(X))) 907.90/297.16 , 38: mark^#(isNatIList(X)) -> c_53(a__isNatIList^#(X)) 907.90/297.16 , 39: mark^#(U51(X1, X2)) -> c_54(a__U51^#(mark(X1), X2)) 907.90/297.16 , 40: mark^#(U52(X)) -> c_55(a__U52^#(mark(X))) 907.90/297.16 , 41: mark^#(isNatList(X)) -> c_56(a__isNatList^#(X)) 907.90/297.16 , 42: mark^#(U61(X1, X2)) -> c_57(a__U61^#(mark(X1), X2)) 907.90/297.16 , 43: mark^#(U62(X)) -> c_58(a__U62^#(mark(X))) 907.90/297.16 , 44: mark^#(U71(X1, X2, X3)) -> c_59(a__U71^#(mark(X1), X2, X3)) 907.90/297.16 , 45: mark^#(U72(X1, X2)) -> c_60(a__U72^#(mark(X1), X2)) 907.90/297.16 , 46: mark^#(isNat(X)) -> c_61(a__isNat^#(X)) 907.90/297.16 , 47: mark^#(U81(X)) -> c_62(a__U81^#(mark(X))) 907.90/297.16 , 48: mark^#(U91(X1, X2, X3, X4)) -> 907.90/297.16 c_63(a__U91^#(mark(X1), X2, X3, X4)) 907.90/297.16 , 49: mark^#(U92(X1, X2, X3, X4)) -> 907.90/297.16 c_64(a__U92^#(mark(X1), X2, X3, X4)) 907.90/297.16 , 50: mark^#(U93(X1, X2, X3, X4)) -> 907.90/297.16 c_65(a__U93^#(mark(X1), X2, X3, X4)) 907.90/297.16 , 51: a__take^#(X1, X2) -> c_74(X1, X2) 907.90/297.16 , 52: a__take^#(0(), IL) -> c_75(a__U81^#(a__isNatIList(IL))) 907.90/297.16 , 53: a__take^#(s(M), cons(N, IL)) -> 907.90/297.16 c_76(a__U91^#(a__isNatIList(IL), IL, M, N)) 907.90/297.16 , 54: a__U81^#(X) -> c_66(X) 907.90/297.16 , 55: a__U91^#(X1, X2, X3, X4) -> c_68(X1, X2, X3, X4) 907.90/297.16 , 56: a__U91^#(tt(), IL, M, N) -> 907.90/297.16 c_69(a__U92^#(a__isNat(M), IL, M, N)) 907.90/297.16 , 57: a__U92^#(X1, X2, X3, X4) -> c_70(X1, X2, X3, X4) 907.90/297.16 , 58: a__U92^#(tt(), IL, M, N) -> 907.90/297.16 c_71(a__U93^#(a__isNat(N), IL, M, N)) 907.90/297.16 , 59: a__U93^#(X1, X2, X3, X4) -> c_72(X1, X2, X3, X4) 907.90/297.16 , 60: a__U93^#(tt(), IL, M, N) -> c_73(mark^#(N), M, IL) 907.90/297.16 , 61: a__zeros^#() -> c_1() 907.90/297.16 , 62: a__zeros^#() -> c_2() 907.90/297.16 , 63: a__U11^#(tt()) -> c_4() 907.90/297.16 , 64: a__U21^#(tt()) -> c_6() 907.90/297.16 , 65: a__U31^#(tt()) -> c_8() 907.90/297.16 , 66: a__U42^#(tt()) -> c_12() 907.90/297.16 , 67: a__isNatIList^#(zeros()) -> c_16() 907.90/297.16 , 68: a__U52^#(tt()) -> c_20() 907.90/297.16 , 69: a__isNatList^#(nil()) -> c_23() 907.90/297.16 , 70: a__U62^#(tt()) -> c_28() 907.90/297.16 , 71: a__length^#(nil()) -> c_39() 907.90/297.16 , 72: a__isNat^#(0()) -> c_34() 907.90/297.16 , 73: mark^#(0()) -> c_41() 907.90/297.16 , 74: mark^#(tt()) -> c_43() 907.90/297.16 , 75: mark^#(nil()) -> c_45() 907.90/297.16 , 76: a__U81^#(tt()) -> c_67() } 907.90/297.16 907.90/297.16 We are left with following problem, upon which TcT provides the 907.90/297.16 certificate MAYBE. 907.90/297.16 907.90/297.16 Strict DPs: 907.90/297.16 { a__U11^#(X) -> c_3(X) 907.90/297.16 , a__U21^#(X) -> c_5(X) 907.90/297.16 , a__U31^#(X) -> c_7(X) 907.90/297.16 , a__U41^#(X1, X2) -> c_9(X1, X2) 907.90/297.16 , a__U41^#(tt(), V2) -> c_10(a__U42^#(a__isNatIList(V2))) 907.90/297.16 , a__U42^#(X) -> c_11(X) 907.90/297.16 , a__isNatIList^#(V) -> c_13(a__U31^#(a__isNatList(V))) 907.90/297.16 , a__isNatIList^#(X) -> c_14(X) 907.90/297.16 , a__isNatIList^#(cons(V1, V2)) -> c_15(a__U41^#(a__isNat(V1), V2)) 907.90/297.16 , a__U51^#(X1, X2) -> c_17(X1, X2) 907.90/297.16 , a__U51^#(tt(), V2) -> c_18(a__U52^#(a__isNatList(V2))) 907.90/297.16 , a__U52^#(X) -> c_19(X) 907.90/297.16 , a__isNatList^#(X) -> c_21(X) 907.90/297.16 , a__isNatList^#(cons(V1, V2)) -> c_22(a__U51^#(a__isNat(V1), V2)) 907.90/297.16 , a__isNatList^#(take(V1, V2)) -> c_24(a__U61^#(a__isNat(V1), V2)) 907.90/297.16 , a__U61^#(X1, X2) -> c_25(X1, X2) 907.90/297.16 , a__U61^#(tt(), V2) -> c_26(a__U62^#(a__isNatIList(V2))) 907.90/297.16 , a__U62^#(X) -> c_27(X) 907.90/297.16 , a__U71^#(X1, X2, X3) -> c_29(X1, X2, X3) 907.90/297.16 , a__U71^#(tt(), L, N) -> c_30(a__U72^#(a__isNat(N), L)) 907.90/297.16 , a__U72^#(X1, X2) -> c_31(X1, X2) 907.90/297.16 , a__U72^#(tt(), L) -> c_32(a__length^#(mark(L))) 907.90/297.16 , a__length^#(X) -> c_37(X) 907.90/297.16 , a__length^#(cons(N, L)) -> c_38(a__U71^#(a__isNatList(L), L, N)) 907.90/297.16 , a__isNat^#(X) -> c_33(X) 907.90/297.16 , a__isNat^#(s(V1)) -> c_35(a__U21^#(a__isNat(V1))) 907.90/297.16 , a__isNat^#(length(V1)) -> c_36(a__U11^#(a__isNatList(V1))) 907.90/297.16 , mark^#(cons(X1, X2)) -> c_40(mark^#(X1), X2) 907.90/297.16 , mark^#(s(X)) -> c_44(mark^#(X)) 907.90/297.16 , mark^#(take(X1, X2)) -> c_46(a__take^#(mark(X1), mark(X2))) 907.90/297.16 , mark^#(length(X)) -> c_47(a__length^#(mark(X))) 907.90/297.16 , mark^#(U11(X)) -> c_48(a__U11^#(mark(X))) 907.90/297.16 , mark^#(U21(X)) -> c_49(a__U21^#(mark(X))) 907.90/297.16 , mark^#(U31(X)) -> c_50(a__U31^#(mark(X))) 907.90/297.16 , mark^#(U41(X1, X2)) -> c_51(a__U41^#(mark(X1), X2)) 907.90/297.16 , mark^#(U42(X)) -> c_52(a__U42^#(mark(X))) 907.90/297.16 , mark^#(isNatIList(X)) -> c_53(a__isNatIList^#(X)) 907.90/297.16 , mark^#(U51(X1, X2)) -> c_54(a__U51^#(mark(X1), X2)) 907.90/297.16 , mark^#(U52(X)) -> c_55(a__U52^#(mark(X))) 907.90/297.16 , mark^#(isNatList(X)) -> c_56(a__isNatList^#(X)) 907.90/297.16 , mark^#(U61(X1, X2)) -> c_57(a__U61^#(mark(X1), X2)) 907.90/297.16 , mark^#(U62(X)) -> c_58(a__U62^#(mark(X))) 907.90/297.16 , mark^#(U71(X1, X2, X3)) -> c_59(a__U71^#(mark(X1), X2, X3)) 907.90/297.16 , mark^#(U72(X1, X2)) -> c_60(a__U72^#(mark(X1), X2)) 907.90/297.16 , mark^#(isNat(X)) -> c_61(a__isNat^#(X)) 907.90/297.16 , mark^#(U81(X)) -> c_62(a__U81^#(mark(X))) 907.90/297.16 , mark^#(U91(X1, X2, X3, X4)) -> 907.90/297.16 c_63(a__U91^#(mark(X1), X2, X3, X4)) 907.90/297.16 , mark^#(U92(X1, X2, X3, X4)) -> 907.90/297.16 c_64(a__U92^#(mark(X1), X2, X3, X4)) 907.90/297.16 , mark^#(U93(X1, X2, X3, X4)) -> 907.90/297.16 c_65(a__U93^#(mark(X1), X2, X3, X4)) 907.90/297.16 , a__take^#(X1, X2) -> c_74(X1, X2) 907.90/297.16 , a__take^#(0(), IL) -> c_75(a__U81^#(a__isNatIList(IL))) 907.90/297.16 , a__take^#(s(M), cons(N, IL)) -> 907.90/297.16 c_76(a__U91^#(a__isNatIList(IL), IL, M, N)) 907.90/297.16 , a__U81^#(X) -> c_66(X) 907.90/297.16 , a__U91^#(X1, X2, X3, X4) -> c_68(X1, X2, X3, X4) 907.90/297.16 , a__U91^#(tt(), IL, M, N) -> c_69(a__U92^#(a__isNat(M), IL, M, N)) 907.90/297.16 , a__U92^#(X1, X2, X3, X4) -> c_70(X1, X2, X3, X4) 907.90/297.16 , a__U92^#(tt(), IL, M, N) -> c_71(a__U93^#(a__isNat(N), IL, M, N)) 907.90/297.16 , a__U93^#(X1, X2, X3, X4) -> c_72(X1, X2, X3, X4) 907.90/297.16 , a__U93^#(tt(), IL, M, N) -> c_73(mark^#(N), M, IL) } 907.90/297.16 Strict Trs: 907.90/297.16 { a__zeros() -> cons(0(), zeros()) 907.90/297.16 , a__zeros() -> zeros() 907.90/297.16 , a__U11(X) -> U11(X) 907.90/297.16 , a__U11(tt()) -> tt() 907.90/297.16 , a__U21(X) -> U21(X) 907.90/297.16 , a__U21(tt()) -> tt() 907.90/297.16 , a__U31(X) -> U31(X) 907.90/297.16 , a__U31(tt()) -> tt() 907.90/297.16 , a__U41(X1, X2) -> U41(X1, X2) 907.90/297.16 , a__U41(tt(), V2) -> a__U42(a__isNatIList(V2)) 907.90/297.16 , a__U42(X) -> U42(X) 907.90/297.16 , a__U42(tt()) -> tt() 907.90/297.16 , a__isNatIList(V) -> a__U31(a__isNatList(V)) 907.90/297.16 , a__isNatIList(X) -> isNatIList(X) 907.90/297.16 , a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) 907.90/297.16 , a__isNatIList(zeros()) -> tt() 907.90/297.16 , a__U51(X1, X2) -> U51(X1, X2) 907.90/297.16 , a__U51(tt(), V2) -> a__U52(a__isNatList(V2)) 907.90/297.16 , a__U52(X) -> U52(X) 907.90/297.16 , a__U52(tt()) -> tt() 907.90/297.16 , a__isNatList(X) -> isNatList(X) 907.90/297.16 , a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) 907.90/297.16 , a__isNatList(nil()) -> tt() 907.90/297.16 , a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) 907.90/297.16 , a__U61(X1, X2) -> U61(X1, X2) 907.90/297.16 , a__U61(tt(), V2) -> a__U62(a__isNatIList(V2)) 907.90/297.16 , a__U62(X) -> U62(X) 907.90/297.16 , a__U62(tt()) -> tt() 907.90/297.16 , a__U71(X1, X2, X3) -> U71(X1, X2, X3) 907.90/297.16 , a__U71(tt(), L, N) -> a__U72(a__isNat(N), L) 907.90/297.16 , a__U72(X1, X2) -> U72(X1, X2) 907.90/297.16 , a__U72(tt(), L) -> s(a__length(mark(L))) 907.90/297.16 , a__isNat(X) -> isNat(X) 907.90/297.16 , a__isNat(0()) -> tt() 907.90/297.16 , a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 907.90/297.16 , a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) 907.90/297.16 , a__length(X) -> length(X) 907.90/297.16 , a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) 907.90/297.16 , a__length(nil()) -> 0() 907.90/297.16 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 907.90/297.16 , mark(0()) -> 0() 907.90/297.16 , mark(zeros()) -> a__zeros() 907.90/297.16 , mark(tt()) -> tt() 907.90/297.16 , mark(s(X)) -> s(mark(X)) 907.90/297.16 , mark(nil()) -> nil() 907.90/297.16 , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 907.90/297.16 , mark(length(X)) -> a__length(mark(X)) 907.90/297.16 , mark(U11(X)) -> a__U11(mark(X)) 907.90/297.16 , mark(U21(X)) -> a__U21(mark(X)) 907.90/297.16 , mark(U31(X)) -> a__U31(mark(X)) 907.90/297.16 , mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 907.90/297.16 , mark(U42(X)) -> a__U42(mark(X)) 907.90/297.16 , mark(isNatIList(X)) -> a__isNatIList(X) 907.90/297.16 , mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 907.90/297.16 , mark(U52(X)) -> a__U52(mark(X)) 907.90/297.16 , mark(isNatList(X)) -> a__isNatList(X) 907.90/297.16 , mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 907.90/297.16 , mark(U62(X)) -> a__U62(mark(X)) 907.90/297.16 , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 907.90/297.16 , mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 907.90/297.16 , mark(isNat(X)) -> a__isNat(X) 907.90/297.16 , mark(U81(X)) -> a__U81(mark(X)) 907.90/297.16 , mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) 907.90/297.16 , mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) 907.90/297.16 , mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) 907.90/297.16 , a__U81(X) -> U81(X) 907.90/297.16 , a__U81(tt()) -> nil() 907.90/297.16 , a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) 907.90/297.16 , a__U91(tt(), IL, M, N) -> a__U92(a__isNat(M), IL, M, N) 907.90/297.16 , a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) 907.90/297.16 , a__U92(tt(), IL, M, N) -> a__U93(a__isNat(N), IL, M, N) 907.90/297.16 , a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) 907.90/297.16 , a__U93(tt(), IL, M, N) -> cons(mark(N), take(M, IL)) 907.90/297.16 , a__take(X1, X2) -> take(X1, X2) 907.90/297.16 , a__take(0(), IL) -> a__U81(a__isNatIList(IL)) 907.90/297.16 , a__take(s(M), cons(N, IL)) -> 907.90/297.16 a__U91(a__isNatIList(IL), IL, M, N) } 907.90/297.16 Weak DPs: 907.90/297.16 { a__zeros^#() -> c_1() 907.90/297.16 , a__zeros^#() -> c_2() 907.90/297.16 , a__U11^#(tt()) -> c_4() 907.90/297.16 , a__U21^#(tt()) -> c_6() 907.90/297.16 , a__U31^#(tt()) -> c_8() 907.90/297.16 , a__U42^#(tt()) -> c_12() 907.90/297.16 , a__isNatIList^#(zeros()) -> c_16() 907.90/297.16 , a__U52^#(tt()) -> c_20() 907.90/297.16 , a__isNatList^#(nil()) -> c_23() 907.90/297.16 , a__U62^#(tt()) -> c_28() 907.90/297.16 , a__length^#(nil()) -> c_39() 907.90/297.16 , a__isNat^#(0()) -> c_34() 907.90/297.16 , mark^#(0()) -> c_41() 907.90/297.16 , mark^#(zeros()) -> c_42(a__zeros^#()) 907.90/297.16 , mark^#(tt()) -> c_43() 907.90/297.16 , mark^#(nil()) -> c_45() 907.90/297.16 , a__U81^#(tt()) -> c_67() } 907.90/297.16 Obligation: 907.90/297.16 runtime complexity 907.90/297.16 Answer: 907.90/297.16 MAYBE 907.90/297.16 907.90/297.16 Empty strict component of the problem is NOT empty. 907.90/297.16 907.90/297.16 907.90/297.16 Arrrr.. 907.90/297.18 EOF