MAYBE 921.23/297.10 MAYBE 921.23/297.10 921.23/297.10 We are left with following problem, upon which TcT provides the 921.23/297.10 certificate MAYBE. 921.23/297.10 921.23/297.10 Strict Trs: 921.23/297.10 { zeros() -> cons(0(), n__zeros()) 921.23/297.10 , zeros() -> n__zeros() 921.23/297.10 , cons(X1, X2) -> n__cons(X1, X2) 921.23/297.10 , 0() -> n__0() 921.23/297.10 , U11(tt(), L) -> s(length(activate(L))) 921.23/297.10 , s(X) -> n__s(X) 921.23/297.10 , length(X) -> n__length(X) 921.23/297.10 , length(cons(N, L)) -> 921.23/297.10 U11(and(isNatList(activate(L)), n__isNat(N)), activate(L)) 921.23/297.10 , length(nil()) -> 0() 921.23/297.10 , activate(X) -> X 921.23/297.10 , activate(n__zeros()) -> zeros() 921.23/297.10 , activate(n__take(X1, X2)) -> take(X1, X2) 921.23/297.10 , activate(n__0()) -> 0() 921.23/297.10 , activate(n__length(X)) -> length(X) 921.23/297.10 , activate(n__s(X)) -> s(X) 921.23/297.10 , activate(n__cons(X1, X2)) -> cons(X1, X2) 921.23/297.10 , activate(n__isNatIList(X)) -> isNatIList(X) 921.23/297.10 , activate(n__nil()) -> nil() 921.23/297.10 , activate(n__isNatList(X)) -> isNatList(X) 921.23/297.10 , activate(n__isNat(X)) -> isNat(X) 921.23/297.10 , activate(n__and(X1, X2)) -> and(X1, X2) 921.23/297.10 , U21(tt()) -> nil() 921.23/297.10 , nil() -> n__nil() 921.23/297.10 , U31(tt(), IL, M, N) -> 921.23/297.10 cons(activate(N), n__take(activate(M), activate(IL))) 921.23/297.10 , and(X1, X2) -> n__and(X1, X2) 921.23/297.10 , and(tt(), X) -> activate(X) 921.23/297.10 , isNat(X) -> n__isNat(X) 921.23/297.10 , isNat(n__0()) -> tt() 921.23/297.10 , isNat(n__length(V1)) -> isNatList(activate(V1)) 921.23/297.10 , isNat(n__s(V1)) -> isNat(activate(V1)) 921.23/297.10 , isNatList(X) -> n__isNatList(X) 921.23/297.10 , isNatList(n__take(V1, V2)) -> 921.23/297.10 and(isNat(activate(V1)), n__isNatIList(activate(V2))) 921.23/297.10 , isNatList(n__cons(V1, V2)) -> 921.23/297.10 and(isNat(activate(V1)), n__isNatList(activate(V2))) 921.23/297.10 , isNatList(n__nil()) -> tt() 921.23/297.10 , isNatIList(V) -> isNatList(activate(V)) 921.23/297.10 , isNatIList(X) -> n__isNatIList(X) 921.23/297.10 , isNatIList(n__zeros()) -> tt() 921.23/297.10 , isNatIList(n__cons(V1, V2)) -> 921.23/297.10 and(isNat(activate(V1)), n__isNatIList(activate(V2))) 921.23/297.10 , take(X1, X2) -> n__take(X1, X2) 921.23/297.10 , take(0(), IL) -> U21(isNatIList(IL)) 921.23/297.10 , take(s(M), cons(N, IL)) -> 921.23/297.10 U31(and(isNatIList(activate(IL)), n__and(isNat(M), n__isNat(N))), 921.23/297.10 activate(IL), 921.23/297.10 M, 921.23/297.10 N) } 921.23/297.10 Obligation: 921.23/297.10 runtime complexity 921.23/297.10 Answer: 921.23/297.10 MAYBE 921.23/297.10 921.23/297.10 None of the processors succeeded. 921.23/297.10 921.23/297.10 Details of failed attempt(s): 921.23/297.10 ----------------------------- 921.23/297.10 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 921.23/297.10 following reason: 921.23/297.10 921.23/297.10 Computation stopped due to timeout after 297.0 seconds. 921.23/297.10 921.23/297.10 2) 'Best' failed due to the following reason: 921.23/297.10 921.23/297.10 None of the processors succeeded. 921.23/297.10 921.23/297.10 Details of failed attempt(s): 921.23/297.10 ----------------------------- 921.23/297.10 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 921.23/297.10 seconds)' failed due to the following reason: 921.23/297.10 921.23/297.10 Computation stopped due to timeout after 148.0 seconds. 921.23/297.10 921.23/297.10 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 921.23/297.10 failed due to the following reason: 921.23/297.10 921.23/297.10 None of the processors succeeded. 921.23/297.10 921.23/297.10 Details of failed attempt(s): 921.23/297.10 ----------------------------- 921.23/297.10 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 921.23/297.10 failed due to the following reason: 921.23/297.10 921.23/297.10 match-boundness of the problem could not be verified. 921.23/297.10 921.23/297.10 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 921.23/297.10 failed due to the following reason: 921.23/297.10 921.23/297.10 match-boundness of the problem could not be verified. 921.23/297.10 921.23/297.10 921.23/297.10 3) 'Best' failed due to the following reason: 921.23/297.10 921.23/297.10 None of the processors succeeded. 921.23/297.10 921.23/297.10 Details of failed attempt(s): 921.23/297.10 ----------------------------- 921.23/297.10 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 921.23/297.10 following reason: 921.23/297.10 921.23/297.10 The processor is inapplicable, reason: 921.23/297.10 Processor only applicable for innermost runtime complexity analysis 921.23/297.10 921.23/297.10 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 921.23/297.10 to the following reason: 921.23/297.10 921.23/297.10 The processor is inapplicable, reason: 921.23/297.10 Processor only applicable for innermost runtime complexity analysis 921.23/297.10 921.23/297.10 921.23/297.10 921.23/297.10 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 921.23/297.10 the following reason: 921.23/297.10 921.23/297.10 We add the following weak dependency pairs: 921.23/297.10 921.23/297.10 Strict DPs: 921.23/297.10 { zeros^#() -> c_1(cons^#(0(), n__zeros())) 921.23/297.10 , zeros^#() -> c_2() 921.23/297.10 , cons^#(X1, X2) -> c_3(X1, X2) 921.23/297.10 , 0^#() -> c_4() 921.23/297.10 , U11^#(tt(), L) -> c_5(s^#(length(activate(L)))) 921.23/297.10 , s^#(X) -> c_6(X) 921.23/297.10 , length^#(X) -> c_7(X) 921.23/297.10 , length^#(cons(N, L)) -> 921.23/297.10 c_8(U11^#(and(isNatList(activate(L)), n__isNat(N)), activate(L))) 921.23/297.10 , length^#(nil()) -> c_9(0^#()) 921.23/297.10 , activate^#(X) -> c_10(X) 921.23/297.10 , activate^#(n__zeros()) -> c_11(zeros^#()) 921.23/297.10 , activate^#(n__take(X1, X2)) -> c_12(take^#(X1, X2)) 921.23/297.10 , activate^#(n__0()) -> c_13(0^#()) 921.23/297.10 , activate^#(n__length(X)) -> c_14(length^#(X)) 921.23/297.10 , activate^#(n__s(X)) -> c_15(s^#(X)) 921.23/297.10 , activate^#(n__cons(X1, X2)) -> c_16(cons^#(X1, X2)) 921.23/297.10 , activate^#(n__isNatIList(X)) -> c_17(isNatIList^#(X)) 921.23/297.10 , activate^#(n__nil()) -> c_18(nil^#()) 921.23/297.10 , activate^#(n__isNatList(X)) -> c_19(isNatList^#(X)) 921.23/297.10 , activate^#(n__isNat(X)) -> c_20(isNat^#(X)) 921.23/297.10 , activate^#(n__and(X1, X2)) -> c_21(and^#(X1, X2)) 921.23/297.10 , take^#(X1, X2) -> c_39(X1, X2) 921.23/297.10 , take^#(0(), IL) -> c_40(U21^#(isNatIList(IL))) 921.23/297.10 , take^#(s(M), cons(N, IL)) -> 921.23/297.10 c_41(U31^#(and(isNatIList(activate(IL)), 921.23/297.10 n__and(isNat(M), n__isNat(N))), 921.23/297.10 activate(IL), 921.23/297.10 M, 921.23/297.10 N)) 921.23/297.10 , isNatIList^#(V) -> c_35(isNatList^#(activate(V))) 921.23/297.10 , isNatIList^#(X) -> c_36(X) 921.23/297.10 , isNatIList^#(n__zeros()) -> c_37() 921.23/297.10 , isNatIList^#(n__cons(V1, V2)) -> 921.23/297.10 c_38(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.23/297.10 , nil^#() -> c_23() 921.23/297.10 , isNatList^#(X) -> c_31(X) 921.23/297.10 , isNatList^#(n__take(V1, V2)) -> 921.23/297.10 c_32(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.23/297.10 , isNatList^#(n__cons(V1, V2)) -> 921.23/297.10 c_33(and^#(isNat(activate(V1)), n__isNatList(activate(V2)))) 921.23/297.10 , isNatList^#(n__nil()) -> c_34() 921.23/297.10 , isNat^#(X) -> c_27(X) 921.23/297.10 , isNat^#(n__0()) -> c_28() 921.23/297.10 , isNat^#(n__length(V1)) -> c_29(isNatList^#(activate(V1))) 921.23/297.10 , isNat^#(n__s(V1)) -> c_30(isNat^#(activate(V1))) 921.23/297.10 , and^#(X1, X2) -> c_25(X1, X2) 921.23/297.10 , and^#(tt(), X) -> c_26(activate^#(X)) 921.23/297.10 , U21^#(tt()) -> c_22(nil^#()) 921.23/297.10 , U31^#(tt(), IL, M, N) -> 921.23/297.10 c_24(cons^#(activate(N), n__take(activate(M), activate(IL)))) } 921.23/297.10 921.23/297.10 and mark the set of starting terms. 921.23/297.10 921.23/297.10 We are left with following problem, upon which TcT provides the 921.23/297.10 certificate MAYBE. 921.23/297.10 921.23/297.10 Strict DPs: 921.23/297.10 { zeros^#() -> c_1(cons^#(0(), n__zeros())) 921.23/297.10 , zeros^#() -> c_2() 921.23/297.10 , cons^#(X1, X2) -> c_3(X1, X2) 921.23/297.10 , 0^#() -> c_4() 921.23/297.10 , U11^#(tt(), L) -> c_5(s^#(length(activate(L)))) 921.23/297.10 , s^#(X) -> c_6(X) 921.23/297.10 , length^#(X) -> c_7(X) 921.23/297.10 , length^#(cons(N, L)) -> 921.23/297.10 c_8(U11^#(and(isNatList(activate(L)), n__isNat(N)), activate(L))) 921.23/297.10 , length^#(nil()) -> c_9(0^#()) 921.23/297.10 , activate^#(X) -> c_10(X) 921.23/297.10 , activate^#(n__zeros()) -> c_11(zeros^#()) 921.23/297.10 , activate^#(n__take(X1, X2)) -> c_12(take^#(X1, X2)) 921.23/297.10 , activate^#(n__0()) -> c_13(0^#()) 921.23/297.10 , activate^#(n__length(X)) -> c_14(length^#(X)) 921.23/297.10 , activate^#(n__s(X)) -> c_15(s^#(X)) 921.23/297.10 , activate^#(n__cons(X1, X2)) -> c_16(cons^#(X1, X2)) 921.23/297.10 , activate^#(n__isNatIList(X)) -> c_17(isNatIList^#(X)) 921.23/297.10 , activate^#(n__nil()) -> c_18(nil^#()) 921.23/297.10 , activate^#(n__isNatList(X)) -> c_19(isNatList^#(X)) 921.23/297.10 , activate^#(n__isNat(X)) -> c_20(isNat^#(X)) 921.23/297.10 , activate^#(n__and(X1, X2)) -> c_21(and^#(X1, X2)) 921.23/297.10 , take^#(X1, X2) -> c_39(X1, X2) 921.23/297.10 , take^#(0(), IL) -> c_40(U21^#(isNatIList(IL))) 921.23/297.10 , take^#(s(M), cons(N, IL)) -> 921.23/297.10 c_41(U31^#(and(isNatIList(activate(IL)), 921.23/297.10 n__and(isNat(M), n__isNat(N))), 921.23/297.10 activate(IL), 921.23/297.10 M, 921.23/297.10 N)) 921.23/297.10 , isNatIList^#(V) -> c_35(isNatList^#(activate(V))) 921.23/297.10 , isNatIList^#(X) -> c_36(X) 921.23/297.10 , isNatIList^#(n__zeros()) -> c_37() 921.23/297.10 , isNatIList^#(n__cons(V1, V2)) -> 921.23/297.10 c_38(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.23/297.10 , nil^#() -> c_23() 921.23/297.10 , isNatList^#(X) -> c_31(X) 921.23/297.10 , isNatList^#(n__take(V1, V2)) -> 921.23/297.10 c_32(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.23/297.10 , isNatList^#(n__cons(V1, V2)) -> 921.23/297.10 c_33(and^#(isNat(activate(V1)), n__isNatList(activate(V2)))) 921.23/297.10 , isNatList^#(n__nil()) -> c_34() 921.23/297.10 , isNat^#(X) -> c_27(X) 921.23/297.10 , isNat^#(n__0()) -> c_28() 921.23/297.10 , isNat^#(n__length(V1)) -> c_29(isNatList^#(activate(V1))) 921.23/297.10 , isNat^#(n__s(V1)) -> c_30(isNat^#(activate(V1))) 921.23/297.10 , and^#(X1, X2) -> c_25(X1, X2) 921.23/297.10 , and^#(tt(), X) -> c_26(activate^#(X)) 921.23/297.10 , U21^#(tt()) -> c_22(nil^#()) 921.23/297.10 , U31^#(tt(), IL, M, N) -> 921.23/297.10 c_24(cons^#(activate(N), n__take(activate(M), activate(IL)))) } 921.23/297.10 Strict Trs: 921.23/297.10 { zeros() -> cons(0(), n__zeros()) 921.23/297.10 , zeros() -> n__zeros() 921.23/297.10 , cons(X1, X2) -> n__cons(X1, X2) 921.23/297.10 , 0() -> n__0() 921.23/297.10 , U11(tt(), L) -> s(length(activate(L))) 921.23/297.10 , s(X) -> n__s(X) 921.23/297.10 , length(X) -> n__length(X) 921.23/297.10 , length(cons(N, L)) -> 921.23/297.10 U11(and(isNatList(activate(L)), n__isNat(N)), activate(L)) 921.23/297.10 , length(nil()) -> 0() 921.23/297.10 , activate(X) -> X 921.23/297.10 , activate(n__zeros()) -> zeros() 921.23/297.10 , activate(n__take(X1, X2)) -> take(X1, X2) 921.23/297.10 , activate(n__0()) -> 0() 921.23/297.10 , activate(n__length(X)) -> length(X) 921.23/297.10 , activate(n__s(X)) -> s(X) 921.23/297.10 , activate(n__cons(X1, X2)) -> cons(X1, X2) 921.23/297.10 , activate(n__isNatIList(X)) -> isNatIList(X) 921.23/297.10 , activate(n__nil()) -> nil() 921.23/297.10 , activate(n__isNatList(X)) -> isNatList(X) 921.23/297.10 , activate(n__isNat(X)) -> isNat(X) 921.23/297.10 , activate(n__and(X1, X2)) -> and(X1, X2) 921.23/297.10 , U21(tt()) -> nil() 921.23/297.10 , nil() -> n__nil() 921.23/297.10 , U31(tt(), IL, M, N) -> 921.23/297.10 cons(activate(N), n__take(activate(M), activate(IL))) 921.23/297.10 , and(X1, X2) -> n__and(X1, X2) 921.23/297.10 , and(tt(), X) -> activate(X) 921.23/297.10 , isNat(X) -> n__isNat(X) 921.23/297.10 , isNat(n__0()) -> tt() 921.23/297.10 , isNat(n__length(V1)) -> isNatList(activate(V1)) 921.23/297.10 , isNat(n__s(V1)) -> isNat(activate(V1)) 921.23/297.10 , isNatList(X) -> n__isNatList(X) 921.23/297.10 , isNatList(n__take(V1, V2)) -> 921.23/297.10 and(isNat(activate(V1)), n__isNatIList(activate(V2))) 921.23/297.10 , isNatList(n__cons(V1, V2)) -> 921.23/297.10 and(isNat(activate(V1)), n__isNatList(activate(V2))) 921.23/297.10 , isNatList(n__nil()) -> tt() 921.23/297.10 , isNatIList(V) -> isNatList(activate(V)) 921.23/297.10 , isNatIList(X) -> n__isNatIList(X) 921.23/297.10 , isNatIList(n__zeros()) -> tt() 921.23/297.10 , isNatIList(n__cons(V1, V2)) -> 921.23/297.10 and(isNat(activate(V1)), n__isNatIList(activate(V2))) 921.23/297.10 , take(X1, X2) -> n__take(X1, X2) 921.23/297.10 , take(0(), IL) -> U21(isNatIList(IL)) 921.23/297.10 , take(s(M), cons(N, IL)) -> 921.23/297.10 U31(and(isNatIList(activate(IL)), n__and(isNat(M), n__isNat(N))), 921.23/297.10 activate(IL), 921.23/297.10 M, 921.23/297.10 N) } 921.23/297.10 Obligation: 921.23/297.10 runtime complexity 921.23/297.10 Answer: 921.23/297.10 MAYBE 921.23/297.10 921.23/297.10 We estimate the number of application of {2,4,27,29,33,35} by 921.23/297.10 applications of Pre({2,4,27,29,33,35}) = 921.23/297.10 {3,6,7,9,10,11,13,17,18,19,20,22,25,26,30,34,36,37,38,40}. Here 921.23/297.10 rules are labeled as follows: 921.23/297.10 921.23/297.10 DPs: 921.23/297.10 { 1: zeros^#() -> c_1(cons^#(0(), n__zeros())) 921.23/297.10 , 2: zeros^#() -> c_2() 921.23/297.10 , 3: cons^#(X1, X2) -> c_3(X1, X2) 921.23/297.10 , 4: 0^#() -> c_4() 921.23/297.10 , 5: U11^#(tt(), L) -> c_5(s^#(length(activate(L)))) 921.23/297.10 , 6: s^#(X) -> c_6(X) 921.23/297.10 , 7: length^#(X) -> c_7(X) 921.23/297.10 , 8: length^#(cons(N, L)) -> 921.23/297.10 c_8(U11^#(and(isNatList(activate(L)), n__isNat(N)), activate(L))) 921.23/297.10 , 9: length^#(nil()) -> c_9(0^#()) 921.23/297.10 , 10: activate^#(X) -> c_10(X) 921.23/297.10 , 11: activate^#(n__zeros()) -> c_11(zeros^#()) 921.23/297.10 , 12: activate^#(n__take(X1, X2)) -> c_12(take^#(X1, X2)) 921.23/297.10 , 13: activate^#(n__0()) -> c_13(0^#()) 921.23/297.10 , 14: activate^#(n__length(X)) -> c_14(length^#(X)) 921.23/297.10 , 15: activate^#(n__s(X)) -> c_15(s^#(X)) 921.23/297.10 , 16: activate^#(n__cons(X1, X2)) -> c_16(cons^#(X1, X2)) 921.23/297.10 , 17: activate^#(n__isNatIList(X)) -> c_17(isNatIList^#(X)) 921.23/297.10 , 18: activate^#(n__nil()) -> c_18(nil^#()) 921.23/297.10 , 19: activate^#(n__isNatList(X)) -> c_19(isNatList^#(X)) 921.23/297.10 , 20: activate^#(n__isNat(X)) -> c_20(isNat^#(X)) 921.23/297.10 , 21: activate^#(n__and(X1, X2)) -> c_21(and^#(X1, X2)) 921.23/297.10 , 22: take^#(X1, X2) -> c_39(X1, X2) 921.23/297.10 , 23: take^#(0(), IL) -> c_40(U21^#(isNatIList(IL))) 921.23/297.10 , 24: take^#(s(M), cons(N, IL)) -> 921.23/297.10 c_41(U31^#(and(isNatIList(activate(IL)), 921.23/297.10 n__and(isNat(M), n__isNat(N))), 921.23/297.10 activate(IL), 921.23/297.10 M, 921.23/297.10 N)) 921.23/297.10 , 25: isNatIList^#(V) -> c_35(isNatList^#(activate(V))) 921.23/297.10 , 26: isNatIList^#(X) -> c_36(X) 921.23/297.10 , 27: isNatIList^#(n__zeros()) -> c_37() 921.23/297.10 , 28: isNatIList^#(n__cons(V1, V2)) -> 921.23/297.10 c_38(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.23/297.10 , 29: nil^#() -> c_23() 921.23/297.10 , 30: isNatList^#(X) -> c_31(X) 921.23/297.10 , 31: isNatList^#(n__take(V1, V2)) -> 921.23/297.10 c_32(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.23/297.10 , 32: isNatList^#(n__cons(V1, V2)) -> 921.23/297.10 c_33(and^#(isNat(activate(V1)), n__isNatList(activate(V2)))) 921.23/297.10 , 33: isNatList^#(n__nil()) -> c_34() 921.23/297.10 , 34: isNat^#(X) -> c_27(X) 921.23/297.10 , 35: isNat^#(n__0()) -> c_28() 921.23/297.10 , 36: isNat^#(n__length(V1)) -> c_29(isNatList^#(activate(V1))) 921.23/297.10 , 37: isNat^#(n__s(V1)) -> c_30(isNat^#(activate(V1))) 921.23/297.10 , 38: and^#(X1, X2) -> c_25(X1, X2) 921.23/297.10 , 39: and^#(tt(), X) -> c_26(activate^#(X)) 921.23/297.10 , 40: U21^#(tt()) -> c_22(nil^#()) 921.23/297.10 , 41: U31^#(tt(), IL, M, N) -> 921.23/297.10 c_24(cons^#(activate(N), n__take(activate(M), activate(IL)))) } 921.23/297.10 921.23/297.10 We are left with following problem, upon which TcT provides the 921.23/297.10 certificate MAYBE. 921.23/297.10 921.23/297.10 Strict DPs: 921.23/297.10 { zeros^#() -> c_1(cons^#(0(), n__zeros())) 921.23/297.10 , cons^#(X1, X2) -> c_3(X1, X2) 921.23/297.10 , U11^#(tt(), L) -> c_5(s^#(length(activate(L)))) 921.23/297.10 , s^#(X) -> c_6(X) 921.23/297.10 , length^#(X) -> c_7(X) 921.23/297.10 , length^#(cons(N, L)) -> 921.23/297.10 c_8(U11^#(and(isNatList(activate(L)), n__isNat(N)), activate(L))) 921.23/297.10 , length^#(nil()) -> c_9(0^#()) 921.23/297.10 , activate^#(X) -> c_10(X) 921.23/297.10 , activate^#(n__zeros()) -> c_11(zeros^#()) 921.23/297.10 , activate^#(n__take(X1, X2)) -> c_12(take^#(X1, X2)) 921.23/297.10 , activate^#(n__0()) -> c_13(0^#()) 921.23/297.10 , activate^#(n__length(X)) -> c_14(length^#(X)) 921.23/297.10 , activate^#(n__s(X)) -> c_15(s^#(X)) 921.23/297.10 , activate^#(n__cons(X1, X2)) -> c_16(cons^#(X1, X2)) 921.23/297.10 , activate^#(n__isNatIList(X)) -> c_17(isNatIList^#(X)) 921.23/297.10 , activate^#(n__nil()) -> c_18(nil^#()) 921.23/297.10 , activate^#(n__isNatList(X)) -> c_19(isNatList^#(X)) 921.23/297.10 , activate^#(n__isNat(X)) -> c_20(isNat^#(X)) 921.23/297.10 , activate^#(n__and(X1, X2)) -> c_21(and^#(X1, X2)) 921.23/297.10 , take^#(X1, X2) -> c_39(X1, X2) 921.23/297.10 , take^#(0(), IL) -> c_40(U21^#(isNatIList(IL))) 921.23/297.10 , take^#(s(M), cons(N, IL)) -> 921.23/297.10 c_41(U31^#(and(isNatIList(activate(IL)), 921.23/297.10 n__and(isNat(M), n__isNat(N))), 921.23/297.10 activate(IL), 921.23/297.10 M, 921.23/297.10 N)) 921.23/297.10 , isNatIList^#(V) -> c_35(isNatList^#(activate(V))) 921.23/297.10 , isNatIList^#(X) -> c_36(X) 921.23/297.10 , isNatIList^#(n__cons(V1, V2)) -> 921.23/297.10 c_38(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.23/297.10 , isNatList^#(X) -> c_31(X) 921.23/297.10 , isNatList^#(n__take(V1, V2)) -> 921.23/297.10 c_32(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.23/297.10 , isNatList^#(n__cons(V1, V2)) -> 921.23/297.10 c_33(and^#(isNat(activate(V1)), n__isNatList(activate(V2)))) 921.23/297.10 , isNat^#(X) -> c_27(X) 921.23/297.10 , isNat^#(n__length(V1)) -> c_29(isNatList^#(activate(V1))) 921.23/297.10 , isNat^#(n__s(V1)) -> c_30(isNat^#(activate(V1))) 921.23/297.10 , and^#(X1, X2) -> c_25(X1, X2) 921.23/297.10 , and^#(tt(), X) -> c_26(activate^#(X)) 921.23/297.10 , U21^#(tt()) -> c_22(nil^#()) 921.23/297.10 , U31^#(tt(), IL, M, N) -> 921.23/297.10 c_24(cons^#(activate(N), n__take(activate(M), activate(IL)))) } 921.23/297.10 Strict Trs: 921.23/297.10 { zeros() -> cons(0(), n__zeros()) 921.23/297.10 , zeros() -> n__zeros() 921.23/297.10 , cons(X1, X2) -> n__cons(X1, X2) 921.23/297.10 , 0() -> n__0() 921.23/297.10 , U11(tt(), L) -> s(length(activate(L))) 921.23/297.10 , s(X) -> n__s(X) 921.23/297.10 , length(X) -> n__length(X) 921.23/297.10 , length(cons(N, L)) -> 921.23/297.10 U11(and(isNatList(activate(L)), n__isNat(N)), activate(L)) 921.23/297.10 , length(nil()) -> 0() 921.23/297.10 , activate(X) -> X 921.23/297.10 , activate(n__zeros()) -> zeros() 921.23/297.10 , activate(n__take(X1, X2)) -> take(X1, X2) 921.23/297.10 , activate(n__0()) -> 0() 921.23/297.10 , activate(n__length(X)) -> length(X) 921.46/297.10 , activate(n__s(X)) -> s(X) 921.46/297.10 , activate(n__cons(X1, X2)) -> cons(X1, X2) 921.46/297.10 , activate(n__isNatIList(X)) -> isNatIList(X) 921.46/297.10 , activate(n__nil()) -> nil() 921.46/297.10 , activate(n__isNatList(X)) -> isNatList(X) 921.46/297.10 , activate(n__isNat(X)) -> isNat(X) 921.46/297.10 , activate(n__and(X1, X2)) -> and(X1, X2) 921.46/297.10 , U21(tt()) -> nil() 921.46/297.10 , nil() -> n__nil() 921.46/297.10 , U31(tt(), IL, M, N) -> 921.46/297.10 cons(activate(N), n__take(activate(M), activate(IL))) 921.46/297.10 , and(X1, X2) -> n__and(X1, X2) 921.46/297.10 , and(tt(), X) -> activate(X) 921.46/297.10 , isNat(X) -> n__isNat(X) 921.46/297.10 , isNat(n__0()) -> tt() 921.46/297.10 , isNat(n__length(V1)) -> isNatList(activate(V1)) 921.46/297.10 , isNat(n__s(V1)) -> isNat(activate(V1)) 921.46/297.10 , isNatList(X) -> n__isNatList(X) 921.46/297.10 , isNatList(n__take(V1, V2)) -> 921.46/297.10 and(isNat(activate(V1)), n__isNatIList(activate(V2))) 921.46/297.10 , isNatList(n__cons(V1, V2)) -> 921.46/297.10 and(isNat(activate(V1)), n__isNatList(activate(V2))) 921.46/297.10 , isNatList(n__nil()) -> tt() 921.46/297.10 , isNatIList(V) -> isNatList(activate(V)) 921.46/297.10 , isNatIList(X) -> n__isNatIList(X) 921.46/297.10 , isNatIList(n__zeros()) -> tt() 921.46/297.10 , isNatIList(n__cons(V1, V2)) -> 921.46/297.10 and(isNat(activate(V1)), n__isNatIList(activate(V2))) 921.46/297.10 , take(X1, X2) -> n__take(X1, X2) 921.46/297.10 , take(0(), IL) -> U21(isNatIList(IL)) 921.46/297.10 , take(s(M), cons(N, IL)) -> 921.46/297.10 U31(and(isNatIList(activate(IL)), n__and(isNat(M), n__isNat(N))), 921.46/297.10 activate(IL), 921.46/297.10 M, 921.46/297.10 N) } 921.46/297.10 Weak DPs: 921.46/297.10 { zeros^#() -> c_2() 921.46/297.10 , 0^#() -> c_4() 921.46/297.10 , isNatIList^#(n__zeros()) -> c_37() 921.46/297.10 , nil^#() -> c_23() 921.46/297.10 , isNatList^#(n__nil()) -> c_34() 921.46/297.10 , isNat^#(n__0()) -> c_28() } 921.46/297.10 Obligation: 921.46/297.10 runtime complexity 921.46/297.10 Answer: 921.46/297.10 MAYBE 921.46/297.10 921.46/297.10 We estimate the number of application of {7,11,16,34} by 921.46/297.10 applications of Pre({7,11,16,34}) = 921.46/297.10 {2,4,5,8,12,20,21,24,26,29,32,33}. Here rules are labeled as 921.46/297.10 follows: 921.46/297.10 921.46/297.10 DPs: 921.46/297.10 { 1: zeros^#() -> c_1(cons^#(0(), n__zeros())) 921.46/297.10 , 2: cons^#(X1, X2) -> c_3(X1, X2) 921.46/297.10 , 3: U11^#(tt(), L) -> c_5(s^#(length(activate(L)))) 921.46/297.10 , 4: s^#(X) -> c_6(X) 921.46/297.10 , 5: length^#(X) -> c_7(X) 921.46/297.10 , 6: length^#(cons(N, L)) -> 921.46/297.10 c_8(U11^#(and(isNatList(activate(L)), n__isNat(N)), activate(L))) 921.46/297.10 , 7: length^#(nil()) -> c_9(0^#()) 921.46/297.10 , 8: activate^#(X) -> c_10(X) 921.46/297.10 , 9: activate^#(n__zeros()) -> c_11(zeros^#()) 921.46/297.10 , 10: activate^#(n__take(X1, X2)) -> c_12(take^#(X1, X2)) 921.46/297.10 , 11: activate^#(n__0()) -> c_13(0^#()) 921.46/297.10 , 12: activate^#(n__length(X)) -> c_14(length^#(X)) 921.46/297.10 , 13: activate^#(n__s(X)) -> c_15(s^#(X)) 921.46/297.10 , 14: activate^#(n__cons(X1, X2)) -> c_16(cons^#(X1, X2)) 921.46/297.10 , 15: activate^#(n__isNatIList(X)) -> c_17(isNatIList^#(X)) 921.46/297.10 , 16: activate^#(n__nil()) -> c_18(nil^#()) 921.46/297.10 , 17: activate^#(n__isNatList(X)) -> c_19(isNatList^#(X)) 921.46/297.10 , 18: activate^#(n__isNat(X)) -> c_20(isNat^#(X)) 921.46/297.10 , 19: activate^#(n__and(X1, X2)) -> c_21(and^#(X1, X2)) 921.46/297.10 , 20: take^#(X1, X2) -> c_39(X1, X2) 921.46/297.10 , 21: take^#(0(), IL) -> c_40(U21^#(isNatIList(IL))) 921.46/297.10 , 22: take^#(s(M), cons(N, IL)) -> 921.46/297.10 c_41(U31^#(and(isNatIList(activate(IL)), 921.46/297.10 n__and(isNat(M), n__isNat(N))), 921.46/297.10 activate(IL), 921.46/297.10 M, 921.46/297.10 N)) 921.46/297.10 , 23: isNatIList^#(V) -> c_35(isNatList^#(activate(V))) 921.46/297.10 , 24: isNatIList^#(X) -> c_36(X) 921.46/297.10 , 25: isNatIList^#(n__cons(V1, V2)) -> 921.46/297.10 c_38(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.46/297.10 , 26: isNatList^#(X) -> c_31(X) 921.46/297.10 , 27: isNatList^#(n__take(V1, V2)) -> 921.46/297.10 c_32(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.46/297.10 , 28: isNatList^#(n__cons(V1, V2)) -> 921.46/297.10 c_33(and^#(isNat(activate(V1)), n__isNatList(activate(V2)))) 921.46/297.10 , 29: isNat^#(X) -> c_27(X) 921.46/297.10 , 30: isNat^#(n__length(V1)) -> c_29(isNatList^#(activate(V1))) 921.46/297.10 , 31: isNat^#(n__s(V1)) -> c_30(isNat^#(activate(V1))) 921.46/297.10 , 32: and^#(X1, X2) -> c_25(X1, X2) 921.46/297.10 , 33: and^#(tt(), X) -> c_26(activate^#(X)) 921.46/297.10 , 34: U21^#(tt()) -> c_22(nil^#()) 921.46/297.10 , 35: U31^#(tt(), IL, M, N) -> 921.46/297.10 c_24(cons^#(activate(N), n__take(activate(M), activate(IL)))) 921.46/297.10 , 36: zeros^#() -> c_2() 921.46/297.10 , 37: 0^#() -> c_4() 921.46/297.10 , 38: isNatIList^#(n__zeros()) -> c_37() 921.46/297.10 , 39: nil^#() -> c_23() 921.46/297.10 , 40: isNatList^#(n__nil()) -> c_34() 921.46/297.10 , 41: isNat^#(n__0()) -> c_28() } 921.46/297.10 921.46/297.10 We are left with following problem, upon which TcT provides the 921.46/297.10 certificate MAYBE. 921.46/297.10 921.46/297.10 Strict DPs: 921.46/297.10 { zeros^#() -> c_1(cons^#(0(), n__zeros())) 921.46/297.10 , cons^#(X1, X2) -> c_3(X1, X2) 921.46/297.10 , U11^#(tt(), L) -> c_5(s^#(length(activate(L)))) 921.46/297.10 , s^#(X) -> c_6(X) 921.46/297.10 , length^#(X) -> c_7(X) 921.46/297.10 , length^#(cons(N, L)) -> 921.46/297.10 c_8(U11^#(and(isNatList(activate(L)), n__isNat(N)), activate(L))) 921.46/297.10 , activate^#(X) -> c_10(X) 921.46/297.10 , activate^#(n__zeros()) -> c_11(zeros^#()) 921.46/297.10 , activate^#(n__take(X1, X2)) -> c_12(take^#(X1, X2)) 921.46/297.10 , activate^#(n__length(X)) -> c_14(length^#(X)) 921.46/297.10 , activate^#(n__s(X)) -> c_15(s^#(X)) 921.46/297.10 , activate^#(n__cons(X1, X2)) -> c_16(cons^#(X1, X2)) 921.46/297.11 , activate^#(n__isNatIList(X)) -> c_17(isNatIList^#(X)) 921.46/297.11 , activate^#(n__isNatList(X)) -> c_19(isNatList^#(X)) 921.46/297.11 , activate^#(n__isNat(X)) -> c_20(isNat^#(X)) 921.46/297.11 , activate^#(n__and(X1, X2)) -> c_21(and^#(X1, X2)) 921.46/297.11 , take^#(X1, X2) -> c_39(X1, X2) 921.46/297.11 , take^#(0(), IL) -> c_40(U21^#(isNatIList(IL))) 921.46/297.11 , take^#(s(M), cons(N, IL)) -> 921.46/297.11 c_41(U31^#(and(isNatIList(activate(IL)), 921.46/297.11 n__and(isNat(M), n__isNat(N))), 921.46/297.11 activate(IL), 921.46/297.11 M, 921.46/297.11 N)) 921.46/297.11 , isNatIList^#(V) -> c_35(isNatList^#(activate(V))) 921.46/297.11 , isNatIList^#(X) -> c_36(X) 921.46/297.11 , isNatIList^#(n__cons(V1, V2)) -> 921.46/297.11 c_38(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.46/297.11 , isNatList^#(X) -> c_31(X) 921.46/297.11 , isNatList^#(n__take(V1, V2)) -> 921.46/297.11 c_32(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.46/297.11 , isNatList^#(n__cons(V1, V2)) -> 921.46/297.11 c_33(and^#(isNat(activate(V1)), n__isNatList(activate(V2)))) 921.46/297.11 , isNat^#(X) -> c_27(X) 921.46/297.11 , isNat^#(n__length(V1)) -> c_29(isNatList^#(activate(V1))) 921.46/297.11 , isNat^#(n__s(V1)) -> c_30(isNat^#(activate(V1))) 921.46/297.11 , and^#(X1, X2) -> c_25(X1, X2) 921.46/297.11 , and^#(tt(), X) -> c_26(activate^#(X)) 921.46/297.11 , U31^#(tt(), IL, M, N) -> 921.46/297.11 c_24(cons^#(activate(N), n__take(activate(M), activate(IL)))) } 921.46/297.11 Strict Trs: 921.46/297.11 { zeros() -> cons(0(), n__zeros()) 921.46/297.11 , zeros() -> n__zeros() 921.46/297.11 , cons(X1, X2) -> n__cons(X1, X2) 921.46/297.11 , 0() -> n__0() 921.46/297.11 , U11(tt(), L) -> s(length(activate(L))) 921.46/297.11 , s(X) -> n__s(X) 921.46/297.11 , length(X) -> n__length(X) 921.46/297.11 , length(cons(N, L)) -> 921.46/297.11 U11(and(isNatList(activate(L)), n__isNat(N)), activate(L)) 921.46/297.11 , length(nil()) -> 0() 921.46/297.11 , activate(X) -> X 921.46/297.11 , activate(n__zeros()) -> zeros() 921.46/297.11 , activate(n__take(X1, X2)) -> take(X1, X2) 921.46/297.11 , activate(n__0()) -> 0() 921.46/297.11 , activate(n__length(X)) -> length(X) 921.46/297.11 , activate(n__s(X)) -> s(X) 921.46/297.11 , activate(n__cons(X1, X2)) -> cons(X1, X2) 921.46/297.11 , activate(n__isNatIList(X)) -> isNatIList(X) 921.46/297.11 , activate(n__nil()) -> nil() 921.46/297.11 , activate(n__isNatList(X)) -> isNatList(X) 921.46/297.11 , activate(n__isNat(X)) -> isNat(X) 921.46/297.11 , activate(n__and(X1, X2)) -> and(X1, X2) 921.46/297.11 , U21(tt()) -> nil() 921.46/297.11 , nil() -> n__nil() 921.46/297.11 , U31(tt(), IL, M, N) -> 921.46/297.11 cons(activate(N), n__take(activate(M), activate(IL))) 921.46/297.11 , and(X1, X2) -> n__and(X1, X2) 921.46/297.11 , and(tt(), X) -> activate(X) 921.46/297.11 , isNat(X) -> n__isNat(X) 921.46/297.11 , isNat(n__0()) -> tt() 921.46/297.11 , isNat(n__length(V1)) -> isNatList(activate(V1)) 921.46/297.11 , isNat(n__s(V1)) -> isNat(activate(V1)) 921.46/297.11 , isNatList(X) -> n__isNatList(X) 921.46/297.11 , isNatList(n__take(V1, V2)) -> 921.46/297.11 and(isNat(activate(V1)), n__isNatIList(activate(V2))) 921.46/297.11 , isNatList(n__cons(V1, V2)) -> 921.46/297.11 and(isNat(activate(V1)), n__isNatList(activate(V2))) 921.46/297.11 , isNatList(n__nil()) -> tt() 921.46/297.11 , isNatIList(V) -> isNatList(activate(V)) 921.46/297.11 , isNatIList(X) -> n__isNatIList(X) 921.46/297.11 , isNatIList(n__zeros()) -> tt() 921.46/297.11 , isNatIList(n__cons(V1, V2)) -> 921.46/297.11 and(isNat(activate(V1)), n__isNatIList(activate(V2))) 921.46/297.11 , take(X1, X2) -> n__take(X1, X2) 921.46/297.11 , take(0(), IL) -> U21(isNatIList(IL)) 921.46/297.11 , take(s(M), cons(N, IL)) -> 921.46/297.11 U31(and(isNatIList(activate(IL)), n__and(isNat(M), n__isNat(N))), 921.46/297.11 activate(IL), 921.46/297.11 M, 921.46/297.11 N) } 921.46/297.11 Weak DPs: 921.46/297.11 { zeros^#() -> c_2() 921.46/297.11 , 0^#() -> c_4() 921.46/297.11 , length^#(nil()) -> c_9(0^#()) 921.46/297.11 , activate^#(n__0()) -> c_13(0^#()) 921.46/297.11 , activate^#(n__nil()) -> c_18(nil^#()) 921.46/297.11 , isNatIList^#(n__zeros()) -> c_37() 921.46/297.11 , nil^#() -> c_23() 921.46/297.11 , isNatList^#(n__nil()) -> c_34() 921.46/297.11 , isNat^#(n__0()) -> c_28() 921.46/297.11 , U21^#(tt()) -> c_22(nil^#()) } 921.46/297.11 Obligation: 921.46/297.11 runtime complexity 921.46/297.11 Answer: 921.46/297.11 MAYBE 921.46/297.11 921.46/297.11 We estimate the number of application of {18} by applications of 921.46/297.11 Pre({18}) = {2,4,5,7,9,17,21,23,26,29}. Here rules are labeled as 921.46/297.11 follows: 921.46/297.11 921.46/297.11 DPs: 921.46/297.11 { 1: zeros^#() -> c_1(cons^#(0(), n__zeros())) 921.46/297.11 , 2: cons^#(X1, X2) -> c_3(X1, X2) 921.46/297.11 , 3: U11^#(tt(), L) -> c_5(s^#(length(activate(L)))) 921.46/297.11 , 4: s^#(X) -> c_6(X) 921.46/297.11 , 5: length^#(X) -> c_7(X) 921.46/297.11 , 6: length^#(cons(N, L)) -> 921.46/297.11 c_8(U11^#(and(isNatList(activate(L)), n__isNat(N)), activate(L))) 921.46/297.11 , 7: activate^#(X) -> c_10(X) 921.46/297.11 , 8: activate^#(n__zeros()) -> c_11(zeros^#()) 921.46/297.11 , 9: activate^#(n__take(X1, X2)) -> c_12(take^#(X1, X2)) 921.46/297.11 , 10: activate^#(n__length(X)) -> c_14(length^#(X)) 921.46/297.11 , 11: activate^#(n__s(X)) -> c_15(s^#(X)) 921.46/297.11 , 12: activate^#(n__cons(X1, X2)) -> c_16(cons^#(X1, X2)) 921.46/297.11 , 13: activate^#(n__isNatIList(X)) -> c_17(isNatIList^#(X)) 921.46/297.11 , 14: activate^#(n__isNatList(X)) -> c_19(isNatList^#(X)) 921.46/297.11 , 15: activate^#(n__isNat(X)) -> c_20(isNat^#(X)) 921.46/297.11 , 16: activate^#(n__and(X1, X2)) -> c_21(and^#(X1, X2)) 921.46/297.11 , 17: take^#(X1, X2) -> c_39(X1, X2) 921.46/297.11 , 18: take^#(0(), IL) -> c_40(U21^#(isNatIList(IL))) 921.46/297.11 , 19: take^#(s(M), cons(N, IL)) -> 921.46/297.11 c_41(U31^#(and(isNatIList(activate(IL)), 921.46/297.11 n__and(isNat(M), n__isNat(N))), 921.46/297.11 activate(IL), 921.46/297.11 M, 921.46/297.11 N)) 921.46/297.11 , 20: isNatIList^#(V) -> c_35(isNatList^#(activate(V))) 921.46/297.11 , 21: isNatIList^#(X) -> c_36(X) 921.46/297.11 , 22: isNatIList^#(n__cons(V1, V2)) -> 921.46/297.11 c_38(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.46/297.11 , 23: isNatList^#(X) -> c_31(X) 921.46/297.11 , 24: isNatList^#(n__take(V1, V2)) -> 921.46/297.11 c_32(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.46/297.11 , 25: isNatList^#(n__cons(V1, V2)) -> 921.46/297.11 c_33(and^#(isNat(activate(V1)), n__isNatList(activate(V2)))) 921.46/297.11 , 26: isNat^#(X) -> c_27(X) 921.46/297.11 , 27: isNat^#(n__length(V1)) -> c_29(isNatList^#(activate(V1))) 921.46/297.11 , 28: isNat^#(n__s(V1)) -> c_30(isNat^#(activate(V1))) 921.46/297.11 , 29: and^#(X1, X2) -> c_25(X1, X2) 921.46/297.11 , 30: and^#(tt(), X) -> c_26(activate^#(X)) 921.46/297.11 , 31: U31^#(tt(), IL, M, N) -> 921.46/297.11 c_24(cons^#(activate(N), n__take(activate(M), activate(IL)))) 921.46/297.11 , 32: zeros^#() -> c_2() 921.46/297.11 , 33: 0^#() -> c_4() 921.46/297.11 , 34: length^#(nil()) -> c_9(0^#()) 921.46/297.11 , 35: activate^#(n__0()) -> c_13(0^#()) 921.46/297.11 , 36: activate^#(n__nil()) -> c_18(nil^#()) 921.46/297.11 , 37: isNatIList^#(n__zeros()) -> c_37() 921.46/297.11 , 38: nil^#() -> c_23() 921.46/297.11 , 39: isNatList^#(n__nil()) -> c_34() 921.46/297.11 , 40: isNat^#(n__0()) -> c_28() 921.46/297.11 , 41: U21^#(tt()) -> c_22(nil^#()) } 921.46/297.11 921.46/297.11 We are left with following problem, upon which TcT provides the 921.46/297.11 certificate MAYBE. 921.46/297.11 921.46/297.11 Strict DPs: 921.46/297.11 { zeros^#() -> c_1(cons^#(0(), n__zeros())) 921.46/297.11 , cons^#(X1, X2) -> c_3(X1, X2) 921.46/297.11 , U11^#(tt(), L) -> c_5(s^#(length(activate(L)))) 921.46/297.11 , s^#(X) -> c_6(X) 921.46/297.11 , length^#(X) -> c_7(X) 921.46/297.11 , length^#(cons(N, L)) -> 921.46/297.11 c_8(U11^#(and(isNatList(activate(L)), n__isNat(N)), activate(L))) 921.46/297.11 , activate^#(X) -> c_10(X) 921.46/297.11 , activate^#(n__zeros()) -> c_11(zeros^#()) 921.46/297.11 , activate^#(n__take(X1, X2)) -> c_12(take^#(X1, X2)) 921.46/297.11 , activate^#(n__length(X)) -> c_14(length^#(X)) 921.46/297.11 , activate^#(n__s(X)) -> c_15(s^#(X)) 921.46/297.11 , activate^#(n__cons(X1, X2)) -> c_16(cons^#(X1, X2)) 921.46/297.11 , activate^#(n__isNatIList(X)) -> c_17(isNatIList^#(X)) 921.46/297.11 , activate^#(n__isNatList(X)) -> c_19(isNatList^#(X)) 921.46/297.11 , activate^#(n__isNat(X)) -> c_20(isNat^#(X)) 921.46/297.11 , activate^#(n__and(X1, X2)) -> c_21(and^#(X1, X2)) 921.46/297.11 , take^#(X1, X2) -> c_39(X1, X2) 921.46/297.11 , take^#(s(M), cons(N, IL)) -> 921.46/297.11 c_41(U31^#(and(isNatIList(activate(IL)), 921.46/297.11 n__and(isNat(M), n__isNat(N))), 921.46/297.11 activate(IL), 921.46/297.11 M, 921.46/297.11 N)) 921.46/297.11 , isNatIList^#(V) -> c_35(isNatList^#(activate(V))) 921.46/297.11 , isNatIList^#(X) -> c_36(X) 921.46/297.11 , isNatIList^#(n__cons(V1, V2)) -> 921.46/297.11 c_38(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.46/297.11 , isNatList^#(X) -> c_31(X) 921.46/297.11 , isNatList^#(n__take(V1, V2)) -> 921.46/297.11 c_32(and^#(isNat(activate(V1)), n__isNatIList(activate(V2)))) 921.46/297.11 , isNatList^#(n__cons(V1, V2)) -> 921.46/297.11 c_33(and^#(isNat(activate(V1)), n__isNatList(activate(V2)))) 921.46/297.11 , isNat^#(X) -> c_27(X) 921.46/297.11 , isNat^#(n__length(V1)) -> c_29(isNatList^#(activate(V1))) 921.46/297.11 , isNat^#(n__s(V1)) -> c_30(isNat^#(activate(V1))) 921.46/297.11 , and^#(X1, X2) -> c_25(X1, X2) 921.46/297.11 , and^#(tt(), X) -> c_26(activate^#(X)) 921.46/297.11 , U31^#(tt(), IL, M, N) -> 921.46/297.11 c_24(cons^#(activate(N), n__take(activate(M), activate(IL)))) } 921.46/297.11 Strict Trs: 921.46/297.11 { zeros() -> cons(0(), n__zeros()) 921.46/297.11 , zeros() -> n__zeros() 921.46/297.11 , cons(X1, X2) -> n__cons(X1, X2) 921.46/297.11 , 0() -> n__0() 921.46/297.11 , U11(tt(), L) -> s(length(activate(L))) 921.46/297.11 , s(X) -> n__s(X) 921.46/297.11 , length(X) -> n__length(X) 921.46/297.11 , length(cons(N, L)) -> 921.46/297.11 U11(and(isNatList(activate(L)), n__isNat(N)), activate(L)) 921.46/297.11 , length(nil()) -> 0() 921.46/297.11 , activate(X) -> X 921.46/297.11 , activate(n__zeros()) -> zeros() 921.46/297.11 , activate(n__take(X1, X2)) -> take(X1, X2) 921.46/297.11 , activate(n__0()) -> 0() 921.46/297.11 , activate(n__length(X)) -> length(X) 921.46/297.11 , activate(n__s(X)) -> s(X) 921.46/297.11 , activate(n__cons(X1, X2)) -> cons(X1, X2) 921.46/297.11 , activate(n__isNatIList(X)) -> isNatIList(X) 921.46/297.11 , activate(n__nil()) -> nil() 921.46/297.11 , activate(n__isNatList(X)) -> isNatList(X) 921.46/297.11 , activate(n__isNat(X)) -> isNat(X) 921.46/297.11 , activate(n__and(X1, X2)) -> and(X1, X2) 921.46/297.11 , U21(tt()) -> nil() 921.46/297.11 , nil() -> n__nil() 921.46/297.11 , U31(tt(), IL, M, N) -> 921.46/297.11 cons(activate(N), n__take(activate(M), activate(IL))) 921.46/297.11 , and(X1, X2) -> n__and(X1, X2) 921.46/297.11 , and(tt(), X) -> activate(X) 921.46/297.11 , isNat(X) -> n__isNat(X) 921.46/297.11 , isNat(n__0()) -> tt() 921.46/297.11 , isNat(n__length(V1)) -> isNatList(activate(V1)) 921.46/297.11 , isNat(n__s(V1)) -> isNat(activate(V1)) 921.46/297.11 , isNatList(X) -> n__isNatList(X) 921.46/297.11 , isNatList(n__take(V1, V2)) -> 921.46/297.11 and(isNat(activate(V1)), n__isNatIList(activate(V2))) 921.46/297.11 , isNatList(n__cons(V1, V2)) -> 921.46/297.11 and(isNat(activate(V1)), n__isNatList(activate(V2))) 921.46/297.11 , isNatList(n__nil()) -> tt() 921.46/297.11 , isNatIList(V) -> isNatList(activate(V)) 921.46/297.11 , isNatIList(X) -> n__isNatIList(X) 921.46/297.11 , isNatIList(n__zeros()) -> tt() 921.46/297.11 , isNatIList(n__cons(V1, V2)) -> 921.46/297.11 and(isNat(activate(V1)), n__isNatIList(activate(V2))) 921.46/297.11 , take(X1, X2) -> n__take(X1, X2) 921.46/297.11 , take(0(), IL) -> U21(isNatIList(IL)) 921.46/297.11 , take(s(M), cons(N, IL)) -> 921.46/297.11 U31(and(isNatIList(activate(IL)), n__and(isNat(M), n__isNat(N))), 921.46/297.11 activate(IL), 921.46/297.11 M, 921.46/297.11 N) } 921.46/297.11 Weak DPs: 921.46/297.11 { zeros^#() -> c_2() 921.46/297.11 , 0^#() -> c_4() 921.46/297.11 , length^#(nil()) -> c_9(0^#()) 921.46/297.11 , activate^#(n__0()) -> c_13(0^#()) 921.46/297.11 , activate^#(n__nil()) -> c_18(nil^#()) 921.46/297.11 , take^#(0(), IL) -> c_40(U21^#(isNatIList(IL))) 921.46/297.11 , isNatIList^#(n__zeros()) -> c_37() 921.46/297.11 , nil^#() -> c_23() 921.46/297.11 , isNatList^#(n__nil()) -> c_34() 921.46/297.11 , isNat^#(n__0()) -> c_28() 921.46/297.11 , U21^#(tt()) -> c_22(nil^#()) } 921.46/297.11 Obligation: 921.46/297.11 runtime complexity 921.46/297.11 Answer: 921.46/297.11 MAYBE 921.46/297.11 921.46/297.11 Empty strict component of the problem is NOT empty. 921.46/297.11 921.46/297.11 921.46/297.11 Arrrr.. 921.46/297.16 EOF