MAYBE 970.99/297.15 MAYBE 970.99/297.15 970.99/297.15 We are left with following problem, upon which TcT provides the 970.99/297.15 certificate MAYBE. 970.99/297.15 970.99/297.15 Strict Trs: 970.99/297.15 { a__zeros() -> cons(0(), zeros()) 970.99/297.15 , a__zeros() -> zeros() 970.99/297.15 , a__U11(X1, X2) -> U11(X1, X2) 970.99/297.15 , a__U11(tt(), V1) -> a__U12(a__isNatList(V1)) 970.99/297.15 , a__U12(X) -> U12(X) 970.99/297.15 , a__U12(tt()) -> tt() 970.99/297.15 , a__isNatList(X) -> isNatList(X) 970.99/297.15 , a__isNatList(cons(V1, V2)) -> 970.99/297.15 a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 970.99/297.15 , a__isNatList(nil()) -> tt() 970.99/297.15 , a__U21(X1, X2) -> U21(X1, X2) 970.99/297.15 , a__U21(tt(), V1) -> a__U22(a__isNat(V1)) 970.99/297.15 , a__U22(X) -> U22(X) 970.99/297.15 , a__U22(tt()) -> tt() 970.99/297.15 , a__isNat(X) -> isNat(X) 970.99/297.15 , a__isNat(0()) -> tt() 970.99/297.15 , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 970.99/297.15 , a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) 970.99/297.15 , a__U31(X1, X2) -> U31(X1, X2) 970.99/297.15 , a__U31(tt(), V) -> a__U32(a__isNatList(V)) 970.99/297.15 , a__U32(X) -> U32(X) 970.99/297.15 , a__U32(tt()) -> tt() 970.99/297.15 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 970.99/297.15 , a__U41(tt(), V1, V2) -> a__U42(a__isNat(V1), V2) 970.99/297.15 , a__U42(X1, X2) -> U42(X1, X2) 970.99/297.15 , a__U42(tt(), V2) -> a__U43(a__isNatIList(V2)) 970.99/297.15 , a__U43(X) -> U43(X) 970.99/297.15 , a__U43(tt()) -> tt() 970.99/297.15 , a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) 970.99/297.15 , a__isNatIList(X) -> isNatIList(X) 970.99/297.15 , a__isNatIList(cons(V1, V2)) -> 970.99/297.15 a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 970.99/297.15 , a__isNatIList(zeros()) -> tt() 970.99/297.15 , a__U51(X1, X2, X3) -> U51(X1, X2, X3) 970.99/297.15 , a__U51(tt(), V1, V2) -> a__U52(a__isNat(V1), V2) 970.99/297.15 , a__U52(X1, X2) -> U52(X1, X2) 970.99/297.15 , a__U52(tt(), V2) -> a__U53(a__isNatList(V2)) 970.99/297.15 , a__U53(X) -> U53(X) 970.99/297.15 , a__U53(tt()) -> tt() 970.99/297.15 , a__U61(X1, X2) -> U61(X1, X2) 970.99/297.15 , a__U61(tt(), L) -> s(a__length(mark(L))) 970.99/297.15 , a__length(X) -> length(X) 970.99/297.15 , a__length(cons(N, L)) -> 970.99/297.15 a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), 970.99/297.15 and(isNat(N), isNatKind(N))), 970.99/297.15 L) 970.99/297.15 , a__length(nil()) -> 0() 970.99/297.15 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 970.99/297.15 , mark(0()) -> 0() 970.99/297.15 , mark(zeros()) -> a__zeros() 970.99/297.15 , mark(tt()) -> tt() 970.99/297.15 , mark(s(X)) -> s(mark(X)) 970.99/297.15 , mark(length(X)) -> a__length(mark(X)) 970.99/297.15 , mark(isNatIListKind(X)) -> a__isNatIListKind(X) 970.99/297.15 , mark(nil()) -> nil() 970.99/297.15 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 970.99/297.15 , mark(isNat(X)) -> a__isNat(X) 970.99/297.15 , mark(isNatKind(X)) -> a__isNatKind(X) 970.99/297.15 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 970.99/297.15 , mark(U12(X)) -> a__U12(mark(X)) 970.99/297.15 , mark(isNatList(X)) -> a__isNatList(X) 970.99/297.15 , mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 970.99/297.15 , mark(U22(X)) -> a__U22(mark(X)) 970.99/297.15 , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 970.99/297.15 , mark(U32(X)) -> a__U32(mark(X)) 970.99/297.15 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 970.99/297.15 , mark(U42(X1, X2)) -> a__U42(mark(X1), X2) 970.99/297.15 , mark(U43(X)) -> a__U43(mark(X)) 970.99/297.15 , mark(isNatIList(X)) -> a__isNatIList(X) 970.99/297.15 , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) 970.99/297.15 , mark(U52(X1, X2)) -> a__U52(mark(X1), X2) 970.99/297.15 , mark(U53(X)) -> a__U53(mark(X)) 970.99/297.15 , mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 970.99/297.15 , a__and(X1, X2) -> and(X1, X2) 970.99/297.15 , a__and(tt(), X) -> mark(X) 970.99/297.15 , a__isNatIListKind(X) -> isNatIListKind(X) 970.99/297.15 , a__isNatIListKind(cons(V1, V2)) -> 970.99/297.15 a__and(a__isNatKind(V1), isNatIListKind(V2)) 970.99/297.15 , a__isNatIListKind(zeros()) -> tt() 970.99/297.15 , a__isNatIListKind(nil()) -> tt() 970.99/297.15 , a__isNatKind(X) -> isNatKind(X) 970.99/297.15 , a__isNatKind(0()) -> tt() 970.99/297.15 , a__isNatKind(s(V1)) -> a__isNatKind(V1) 970.99/297.15 , a__isNatKind(length(V1)) -> a__isNatIListKind(V1) } 970.99/297.15 Obligation: 970.99/297.15 runtime complexity 970.99/297.15 Answer: 970.99/297.15 MAYBE 970.99/297.15 970.99/297.15 None of the processors succeeded. 970.99/297.15 970.99/297.15 Details of failed attempt(s): 970.99/297.15 ----------------------------- 970.99/297.15 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 970.99/297.15 following reason: 970.99/297.15 970.99/297.15 Computation stopped due to timeout after 297.0 seconds. 970.99/297.15 970.99/297.15 2) 'Best' failed due to the following reason: 970.99/297.15 970.99/297.15 None of the processors succeeded. 970.99/297.15 970.99/297.15 Details of failed attempt(s): 970.99/297.15 ----------------------------- 970.99/297.15 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 970.99/297.15 seconds)' failed due to the following reason: 970.99/297.15 970.99/297.15 Computation stopped due to timeout after 148.0 seconds. 970.99/297.15 970.99/297.15 2) 'Best' failed due to the following reason: 970.99/297.15 970.99/297.15 None of the processors succeeded. 970.99/297.15 970.99/297.15 Details of failed attempt(s): 970.99/297.15 ----------------------------- 970.99/297.15 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 970.99/297.15 following reason: 970.99/297.15 970.99/297.15 The processor is inapplicable, reason: 970.99/297.15 Processor only applicable for innermost runtime complexity analysis 970.99/297.15 970.99/297.15 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 970.99/297.15 to the following reason: 970.99/297.15 970.99/297.15 The processor is inapplicable, reason: 970.99/297.15 Processor only applicable for innermost runtime complexity analysis 970.99/297.15 970.99/297.15 970.99/297.15 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 970.99/297.15 failed due to the following reason: 970.99/297.15 970.99/297.15 None of the processors succeeded. 970.99/297.15 970.99/297.15 Details of failed attempt(s): 970.99/297.15 ----------------------------- 970.99/297.15 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 970.99/297.15 failed due to the following reason: 970.99/297.15 970.99/297.15 match-boundness of the problem could not be verified. 970.99/297.15 970.99/297.15 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 970.99/297.15 failed due to the following reason: 970.99/297.15 970.99/297.15 match-boundness of the problem could not be verified. 970.99/297.15 970.99/297.15 970.99/297.15 970.99/297.15 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 970.99/297.15 the following reason: 970.99/297.15 970.99/297.15 We add the following weak dependency pairs: 970.99/297.15 970.99/297.15 Strict DPs: 970.99/297.15 { a__zeros^#() -> c_1() 970.99/297.15 , a__zeros^#() -> c_2() 970.99/297.15 , a__U11^#(X1, X2) -> c_3(X1, X2) 970.99/297.15 , a__U11^#(tt(), V1) -> c_4(a__U12^#(a__isNatList(V1))) 970.99/297.15 , a__U12^#(X) -> c_5(X) 970.99/297.15 , a__U12^#(tt()) -> c_6() 970.99/297.15 , a__isNatList^#(X) -> c_7(X) 970.99/297.15 , a__isNatList^#(cons(V1, V2)) -> 970.99/297.15 c_8(a__U51^#(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)) 970.99/297.15 , a__isNatList^#(nil()) -> c_9() 970.99/297.15 , a__U51^#(X1, X2, X3) -> c_32(X1, X2, X3) 970.99/297.15 , a__U51^#(tt(), V1, V2) -> c_33(a__U52^#(a__isNat(V1), V2)) 970.99/297.15 , a__U21^#(X1, X2) -> c_10(X1, X2) 970.99/297.15 , a__U21^#(tt(), V1) -> c_11(a__U22^#(a__isNat(V1))) 970.99/297.15 , a__U22^#(X) -> c_12(X) 970.99/297.15 , a__U22^#(tt()) -> c_13() 970.99/297.15 , a__isNat^#(X) -> c_14(X) 970.99/297.15 , a__isNat^#(0()) -> c_15() 970.99/297.15 , a__isNat^#(s(V1)) -> c_16(a__U21^#(a__isNatKind(V1), V1)) 970.99/297.15 , a__isNat^#(length(V1)) -> 970.99/297.15 c_17(a__U11^#(a__isNatIListKind(V1), V1)) 970.99/297.15 , a__U31^#(X1, X2) -> c_18(X1, X2) 970.99/297.15 , a__U31^#(tt(), V) -> c_19(a__U32^#(a__isNatList(V))) 970.99/297.15 , a__U32^#(X) -> c_20(X) 970.99/297.15 , a__U32^#(tt()) -> c_21() 970.99/297.15 , a__U41^#(X1, X2, X3) -> c_22(X1, X2, X3) 970.99/297.15 , a__U41^#(tt(), V1, V2) -> c_23(a__U42^#(a__isNat(V1), V2)) 970.99/297.15 , a__U42^#(X1, X2) -> c_24(X1, X2) 970.99/297.15 , a__U42^#(tt(), V2) -> c_25(a__U43^#(a__isNatIList(V2))) 970.99/297.15 , a__U43^#(X) -> c_26(X) 970.99/297.15 , a__U43^#(tt()) -> c_27() 970.99/297.15 , a__isNatIList^#(V) -> c_28(a__U31^#(a__isNatIListKind(V), V)) 970.99/297.15 , a__isNatIList^#(X) -> c_29(X) 970.99/297.15 , a__isNatIList^#(cons(V1, V2)) -> 970.99/297.15 c_30(a__U41^#(a__and(a__isNatKind(V1), isNatIListKind(V2)), 970.99/297.15 V1, 970.99/297.15 V2)) 970.99/297.15 , a__isNatIList^#(zeros()) -> c_31() 970.99/297.15 , a__U52^#(X1, X2) -> c_34(X1, X2) 970.99/297.15 , a__U52^#(tt(), V2) -> c_35(a__U53^#(a__isNatList(V2))) 970.99/297.15 , a__U53^#(X) -> c_36(X) 970.99/297.15 , a__U53^#(tt()) -> c_37() 970.99/297.15 , a__U61^#(X1, X2) -> c_38(X1, X2) 970.99/297.15 , a__U61^#(tt(), L) -> c_39(a__length^#(mark(L))) 970.99/297.15 , a__length^#(X) -> c_40(X) 970.99/297.15 , a__length^#(cons(N, L)) -> 970.99/297.15 c_41(a__U61^#(a__and(a__and(a__isNatList(L), isNatIListKind(L)), 970.99/297.15 and(isNat(N), isNatKind(N))), 970.99/297.15 L)) 970.99/297.15 , a__length^#(nil()) -> c_42() 970.99/297.15 , mark^#(cons(X1, X2)) -> c_43(mark^#(X1), X2) 970.99/297.15 , mark^#(0()) -> c_44() 970.99/297.15 , mark^#(zeros()) -> c_45(a__zeros^#()) 970.99/297.15 , mark^#(tt()) -> c_46() 970.99/297.15 , mark^#(s(X)) -> c_47(mark^#(X)) 970.99/297.15 , mark^#(length(X)) -> c_48(a__length^#(mark(X))) 970.99/297.15 , mark^#(isNatIListKind(X)) -> c_49(a__isNatIListKind^#(X)) 970.99/297.15 , mark^#(nil()) -> c_50() 970.99/297.15 , mark^#(and(X1, X2)) -> c_51(a__and^#(mark(X1), X2)) 970.99/297.15 , mark^#(isNat(X)) -> c_52(a__isNat^#(X)) 970.99/297.15 , mark^#(isNatKind(X)) -> c_53(a__isNatKind^#(X)) 970.99/297.15 , mark^#(U11(X1, X2)) -> c_54(a__U11^#(mark(X1), X2)) 970.99/297.15 , mark^#(U12(X)) -> c_55(a__U12^#(mark(X))) 970.99/297.15 , mark^#(isNatList(X)) -> c_56(a__isNatList^#(X)) 970.99/297.15 , mark^#(U21(X1, X2)) -> c_57(a__U21^#(mark(X1), X2)) 970.99/297.15 , mark^#(U22(X)) -> c_58(a__U22^#(mark(X))) 970.99/297.15 , mark^#(U31(X1, X2)) -> c_59(a__U31^#(mark(X1), X2)) 970.99/297.15 , mark^#(U32(X)) -> c_60(a__U32^#(mark(X))) 970.99/297.15 , mark^#(U41(X1, X2, X3)) -> c_61(a__U41^#(mark(X1), X2, X3)) 970.99/297.15 , mark^#(U42(X1, X2)) -> c_62(a__U42^#(mark(X1), X2)) 970.99/297.15 , mark^#(U43(X)) -> c_63(a__U43^#(mark(X))) 970.99/297.15 , mark^#(isNatIList(X)) -> c_64(a__isNatIList^#(X)) 970.99/297.15 , mark^#(U51(X1, X2, X3)) -> c_65(a__U51^#(mark(X1), X2, X3)) 970.99/297.15 , mark^#(U52(X1, X2)) -> c_66(a__U52^#(mark(X1), X2)) 970.99/297.15 , mark^#(U53(X)) -> c_67(a__U53^#(mark(X))) 970.99/297.15 , mark^#(U61(X1, X2)) -> c_68(a__U61^#(mark(X1), X2)) 970.99/297.15 , a__isNatIListKind^#(X) -> c_71(X) 970.99/297.15 , a__isNatIListKind^#(cons(V1, V2)) -> 970.99/297.15 c_72(a__and^#(a__isNatKind(V1), isNatIListKind(V2))) 970.99/297.15 , a__isNatIListKind^#(zeros()) -> c_73() 970.99/297.15 , a__isNatIListKind^#(nil()) -> c_74() 970.99/297.15 , a__and^#(X1, X2) -> c_69(X1, X2) 970.99/297.15 , a__and^#(tt(), X) -> c_70(mark^#(X)) 970.99/297.15 , a__isNatKind^#(X) -> c_75(X) 970.99/297.15 , a__isNatKind^#(0()) -> c_76() 970.99/297.15 , a__isNatKind^#(s(V1)) -> c_77(a__isNatKind^#(V1)) 970.99/297.15 , a__isNatKind^#(length(V1)) -> c_78(a__isNatIListKind^#(V1)) } 970.99/297.15 970.99/297.15 and mark the set of starting terms. 970.99/297.15 970.99/297.15 We are left with following problem, upon which TcT provides the 970.99/297.15 certificate MAYBE. 970.99/297.15 970.99/297.15 Strict DPs: 970.99/297.15 { a__zeros^#() -> c_1() 970.99/297.15 , a__zeros^#() -> c_2() 970.99/297.15 , a__U11^#(X1, X2) -> c_3(X1, X2) 970.99/297.15 , a__U11^#(tt(), V1) -> c_4(a__U12^#(a__isNatList(V1))) 970.99/297.15 , a__U12^#(X) -> c_5(X) 970.99/297.15 , a__U12^#(tt()) -> c_6() 970.99/297.15 , a__isNatList^#(X) -> c_7(X) 970.99/297.15 , a__isNatList^#(cons(V1, V2)) -> 970.99/297.15 c_8(a__U51^#(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)) 970.99/297.15 , a__isNatList^#(nil()) -> c_9() 970.99/297.15 , a__U51^#(X1, X2, X3) -> c_32(X1, X2, X3) 970.99/297.15 , a__U51^#(tt(), V1, V2) -> c_33(a__U52^#(a__isNat(V1), V2)) 970.99/297.15 , a__U21^#(X1, X2) -> c_10(X1, X2) 970.99/297.15 , a__U21^#(tt(), V1) -> c_11(a__U22^#(a__isNat(V1))) 970.99/297.15 , a__U22^#(X) -> c_12(X) 970.99/297.15 , a__U22^#(tt()) -> c_13() 970.99/297.15 , a__isNat^#(X) -> c_14(X) 970.99/297.15 , a__isNat^#(0()) -> c_15() 970.99/297.15 , a__isNat^#(s(V1)) -> c_16(a__U21^#(a__isNatKind(V1), V1)) 970.99/297.15 , a__isNat^#(length(V1)) -> 970.99/297.15 c_17(a__U11^#(a__isNatIListKind(V1), V1)) 970.99/297.15 , a__U31^#(X1, X2) -> c_18(X1, X2) 970.99/297.15 , a__U31^#(tt(), V) -> c_19(a__U32^#(a__isNatList(V))) 970.99/297.15 , a__U32^#(X) -> c_20(X) 970.99/297.15 , a__U32^#(tt()) -> c_21() 970.99/297.15 , a__U41^#(X1, X2, X3) -> c_22(X1, X2, X3) 970.99/297.15 , a__U41^#(tt(), V1, V2) -> c_23(a__U42^#(a__isNat(V1), V2)) 970.99/297.15 , a__U42^#(X1, X2) -> c_24(X1, X2) 970.99/297.15 , a__U42^#(tt(), V2) -> c_25(a__U43^#(a__isNatIList(V2))) 970.99/297.15 , a__U43^#(X) -> c_26(X) 970.99/297.15 , a__U43^#(tt()) -> c_27() 970.99/297.15 , a__isNatIList^#(V) -> c_28(a__U31^#(a__isNatIListKind(V), V)) 970.99/297.15 , a__isNatIList^#(X) -> c_29(X) 970.99/297.15 , a__isNatIList^#(cons(V1, V2)) -> 970.99/297.15 c_30(a__U41^#(a__and(a__isNatKind(V1), isNatIListKind(V2)), 970.99/297.15 V1, 970.99/297.15 V2)) 970.99/297.15 , a__isNatIList^#(zeros()) -> c_31() 970.99/297.15 , a__U52^#(X1, X2) -> c_34(X1, X2) 970.99/297.15 , a__U52^#(tt(), V2) -> c_35(a__U53^#(a__isNatList(V2))) 970.99/297.15 , a__U53^#(X) -> c_36(X) 970.99/297.15 , a__U53^#(tt()) -> c_37() 970.99/297.15 , a__U61^#(X1, X2) -> c_38(X1, X2) 970.99/297.15 , a__U61^#(tt(), L) -> c_39(a__length^#(mark(L))) 970.99/297.15 , a__length^#(X) -> c_40(X) 970.99/297.15 , a__length^#(cons(N, L)) -> 970.99/297.15 c_41(a__U61^#(a__and(a__and(a__isNatList(L), isNatIListKind(L)), 970.99/297.15 and(isNat(N), isNatKind(N))), 970.99/297.15 L)) 970.99/297.15 , a__length^#(nil()) -> c_42() 970.99/297.15 , mark^#(cons(X1, X2)) -> c_43(mark^#(X1), X2) 970.99/297.15 , mark^#(0()) -> c_44() 970.99/297.15 , mark^#(zeros()) -> c_45(a__zeros^#()) 970.99/297.15 , mark^#(tt()) -> c_46() 970.99/297.15 , mark^#(s(X)) -> c_47(mark^#(X)) 970.99/297.15 , mark^#(length(X)) -> c_48(a__length^#(mark(X))) 970.99/297.15 , mark^#(isNatIListKind(X)) -> c_49(a__isNatIListKind^#(X)) 970.99/297.15 , mark^#(nil()) -> c_50() 970.99/297.15 , mark^#(and(X1, X2)) -> c_51(a__and^#(mark(X1), X2)) 970.99/297.15 , mark^#(isNat(X)) -> c_52(a__isNat^#(X)) 970.99/297.15 , mark^#(isNatKind(X)) -> c_53(a__isNatKind^#(X)) 970.99/297.15 , mark^#(U11(X1, X2)) -> c_54(a__U11^#(mark(X1), X2)) 970.99/297.15 , mark^#(U12(X)) -> c_55(a__U12^#(mark(X))) 970.99/297.15 , mark^#(isNatList(X)) -> c_56(a__isNatList^#(X)) 970.99/297.15 , mark^#(U21(X1, X2)) -> c_57(a__U21^#(mark(X1), X2)) 970.99/297.15 , mark^#(U22(X)) -> c_58(a__U22^#(mark(X))) 970.99/297.15 , mark^#(U31(X1, X2)) -> c_59(a__U31^#(mark(X1), X2)) 970.99/297.15 , mark^#(U32(X)) -> c_60(a__U32^#(mark(X))) 970.99/297.15 , mark^#(U41(X1, X2, X3)) -> c_61(a__U41^#(mark(X1), X2, X3)) 970.99/297.15 , mark^#(U42(X1, X2)) -> c_62(a__U42^#(mark(X1), X2)) 970.99/297.15 , mark^#(U43(X)) -> c_63(a__U43^#(mark(X))) 970.99/297.15 , mark^#(isNatIList(X)) -> c_64(a__isNatIList^#(X)) 970.99/297.15 , mark^#(U51(X1, X2, X3)) -> c_65(a__U51^#(mark(X1), X2, X3)) 970.99/297.15 , mark^#(U52(X1, X2)) -> c_66(a__U52^#(mark(X1), X2)) 970.99/297.15 , mark^#(U53(X)) -> c_67(a__U53^#(mark(X))) 970.99/297.15 , mark^#(U61(X1, X2)) -> c_68(a__U61^#(mark(X1), X2)) 970.99/297.15 , a__isNatIListKind^#(X) -> c_71(X) 970.99/297.15 , a__isNatIListKind^#(cons(V1, V2)) -> 970.99/297.15 c_72(a__and^#(a__isNatKind(V1), isNatIListKind(V2))) 970.99/297.15 , a__isNatIListKind^#(zeros()) -> c_73() 970.99/297.15 , a__isNatIListKind^#(nil()) -> c_74() 970.99/297.15 , a__and^#(X1, X2) -> c_69(X1, X2) 970.99/297.15 , a__and^#(tt(), X) -> c_70(mark^#(X)) 970.99/297.15 , a__isNatKind^#(X) -> c_75(X) 970.99/297.15 , a__isNatKind^#(0()) -> c_76() 970.99/297.15 , a__isNatKind^#(s(V1)) -> c_77(a__isNatKind^#(V1)) 970.99/297.15 , a__isNatKind^#(length(V1)) -> c_78(a__isNatIListKind^#(V1)) } 970.99/297.15 Strict Trs: 970.99/297.15 { a__zeros() -> cons(0(), zeros()) 970.99/297.15 , a__zeros() -> zeros() 970.99/297.15 , a__U11(X1, X2) -> U11(X1, X2) 970.99/297.15 , a__U11(tt(), V1) -> a__U12(a__isNatList(V1)) 970.99/297.15 , a__U12(X) -> U12(X) 970.99/297.15 , a__U12(tt()) -> tt() 970.99/297.15 , a__isNatList(X) -> isNatList(X) 970.99/297.15 , a__isNatList(cons(V1, V2)) -> 970.99/297.15 a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 970.99/297.15 , a__isNatList(nil()) -> tt() 970.99/297.15 , a__U21(X1, X2) -> U21(X1, X2) 970.99/297.15 , a__U21(tt(), V1) -> a__U22(a__isNat(V1)) 970.99/297.15 , a__U22(X) -> U22(X) 970.99/297.15 , a__U22(tt()) -> tt() 970.99/297.15 , a__isNat(X) -> isNat(X) 970.99/297.15 , a__isNat(0()) -> tt() 970.99/297.15 , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 970.99/297.15 , a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) 970.99/297.15 , a__U31(X1, X2) -> U31(X1, X2) 970.99/297.15 , a__U31(tt(), V) -> a__U32(a__isNatList(V)) 970.99/297.15 , a__U32(X) -> U32(X) 970.99/297.15 , a__U32(tt()) -> tt() 970.99/297.15 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 970.99/297.15 , a__U41(tt(), V1, V2) -> a__U42(a__isNat(V1), V2) 970.99/297.15 , a__U42(X1, X2) -> U42(X1, X2) 970.99/297.15 , a__U42(tt(), V2) -> a__U43(a__isNatIList(V2)) 970.99/297.15 , a__U43(X) -> U43(X) 970.99/297.15 , a__U43(tt()) -> tt() 970.99/297.15 , a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) 970.99/297.15 , a__isNatIList(X) -> isNatIList(X) 970.99/297.15 , a__isNatIList(cons(V1, V2)) -> 970.99/297.15 a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 970.99/297.15 , a__isNatIList(zeros()) -> tt() 970.99/297.15 , a__U51(X1, X2, X3) -> U51(X1, X2, X3) 970.99/297.15 , a__U51(tt(), V1, V2) -> a__U52(a__isNat(V1), V2) 970.99/297.15 , a__U52(X1, X2) -> U52(X1, X2) 970.99/297.15 , a__U52(tt(), V2) -> a__U53(a__isNatList(V2)) 970.99/297.15 , a__U53(X) -> U53(X) 970.99/297.15 , a__U53(tt()) -> tt() 970.99/297.15 , a__U61(X1, X2) -> U61(X1, X2) 970.99/297.15 , a__U61(tt(), L) -> s(a__length(mark(L))) 970.99/297.15 , a__length(X) -> length(X) 970.99/297.15 , a__length(cons(N, L)) -> 970.99/297.15 a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), 970.99/297.15 and(isNat(N), isNatKind(N))), 970.99/297.15 L) 970.99/297.15 , a__length(nil()) -> 0() 970.99/297.15 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 970.99/297.15 , mark(0()) -> 0() 970.99/297.15 , mark(zeros()) -> a__zeros() 970.99/297.15 , mark(tt()) -> tt() 970.99/297.15 , mark(s(X)) -> s(mark(X)) 970.99/297.15 , mark(length(X)) -> a__length(mark(X)) 970.99/297.15 , mark(isNatIListKind(X)) -> a__isNatIListKind(X) 970.99/297.15 , mark(nil()) -> nil() 970.99/297.15 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 970.99/297.15 , mark(isNat(X)) -> a__isNat(X) 970.99/297.15 , mark(isNatKind(X)) -> a__isNatKind(X) 970.99/297.15 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 970.99/297.15 , mark(U12(X)) -> a__U12(mark(X)) 970.99/297.15 , mark(isNatList(X)) -> a__isNatList(X) 970.99/297.15 , mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 970.99/297.15 , mark(U22(X)) -> a__U22(mark(X)) 970.99/297.16 , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 970.99/297.16 , mark(U32(X)) -> a__U32(mark(X)) 970.99/297.16 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 970.99/297.16 , mark(U42(X1, X2)) -> a__U42(mark(X1), X2) 970.99/297.16 , mark(U43(X)) -> a__U43(mark(X)) 970.99/297.16 , mark(isNatIList(X)) -> a__isNatIList(X) 970.99/297.16 , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) 970.99/297.16 , mark(U52(X1, X2)) -> a__U52(mark(X1), X2) 970.99/297.16 , mark(U53(X)) -> a__U53(mark(X)) 970.99/297.16 , mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 970.99/297.16 , a__and(X1, X2) -> and(X1, X2) 970.99/297.16 , a__and(tt(), X) -> mark(X) 970.99/297.16 , a__isNatIListKind(X) -> isNatIListKind(X) 970.99/297.16 , a__isNatIListKind(cons(V1, V2)) -> 970.99/297.16 a__and(a__isNatKind(V1), isNatIListKind(V2)) 970.99/297.16 , a__isNatIListKind(zeros()) -> tt() 970.99/297.16 , a__isNatIListKind(nil()) -> tt() 970.99/297.16 , a__isNatKind(X) -> isNatKind(X) 970.99/297.16 , a__isNatKind(0()) -> tt() 970.99/297.16 , a__isNatKind(s(V1)) -> a__isNatKind(V1) 970.99/297.16 , a__isNatKind(length(V1)) -> a__isNatIListKind(V1) } 970.99/297.16 Obligation: 970.99/297.16 runtime complexity 970.99/297.16 Answer: 970.99/297.16 MAYBE 970.99/297.16 970.99/297.16 We estimate the number of application of 970.99/297.16 {1,2,6,9,15,17,23,29,33,37,42,44,46,50,71,72,76} by applications of 970.99/297.16 Pre({1,2,6,9,15,17,23,29,33,37,42,44,46,50,71,72,76}) = 970.99/297.16 {3,4,5,7,10,12,13,14,16,20,21,22,24,26,27,28,31,34,35,36,38,39,40,43,45,47,48,49,52,53,55,56,58,60,63,64,67,69,73,74,75,77,78}. 970.99/297.16 Here rules are labeled as follows: 970.99/297.16 970.99/297.16 DPs: 970.99/297.16 { 1: a__zeros^#() -> c_1() 970.99/297.16 , 2: a__zeros^#() -> c_2() 970.99/297.16 , 3: a__U11^#(X1, X2) -> c_3(X1, X2) 970.99/297.16 , 4: a__U11^#(tt(), V1) -> c_4(a__U12^#(a__isNatList(V1))) 970.99/297.16 , 5: a__U12^#(X) -> c_5(X) 970.99/297.16 , 6: a__U12^#(tt()) -> c_6() 970.99/297.16 , 7: a__isNatList^#(X) -> c_7(X) 970.99/297.16 , 8: a__isNatList^#(cons(V1, V2)) -> 970.99/297.16 c_8(a__U51^#(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)) 970.99/297.16 , 9: a__isNatList^#(nil()) -> c_9() 970.99/297.16 , 10: a__U51^#(X1, X2, X3) -> c_32(X1, X2, X3) 970.99/297.16 , 11: a__U51^#(tt(), V1, V2) -> c_33(a__U52^#(a__isNat(V1), V2)) 970.99/297.16 , 12: a__U21^#(X1, X2) -> c_10(X1, X2) 970.99/297.16 , 13: a__U21^#(tt(), V1) -> c_11(a__U22^#(a__isNat(V1))) 970.99/297.16 , 14: a__U22^#(X) -> c_12(X) 970.99/297.16 , 15: a__U22^#(tt()) -> c_13() 970.99/297.16 , 16: a__isNat^#(X) -> c_14(X) 970.99/297.16 , 17: a__isNat^#(0()) -> c_15() 970.99/297.16 , 18: a__isNat^#(s(V1)) -> c_16(a__U21^#(a__isNatKind(V1), V1)) 970.99/297.16 , 19: a__isNat^#(length(V1)) -> 970.99/297.16 c_17(a__U11^#(a__isNatIListKind(V1), V1)) 970.99/297.16 , 20: a__U31^#(X1, X2) -> c_18(X1, X2) 970.99/297.16 , 21: a__U31^#(tt(), V) -> c_19(a__U32^#(a__isNatList(V))) 970.99/297.16 , 22: a__U32^#(X) -> c_20(X) 970.99/297.16 , 23: a__U32^#(tt()) -> c_21() 970.99/297.16 , 24: a__U41^#(X1, X2, X3) -> c_22(X1, X2, X3) 970.99/297.16 , 25: a__U41^#(tt(), V1, V2) -> c_23(a__U42^#(a__isNat(V1), V2)) 970.99/297.16 , 26: a__U42^#(X1, X2) -> c_24(X1, X2) 970.99/297.16 , 27: a__U42^#(tt(), V2) -> c_25(a__U43^#(a__isNatIList(V2))) 970.99/297.16 , 28: a__U43^#(X) -> c_26(X) 970.99/297.16 , 29: a__U43^#(tt()) -> c_27() 970.99/297.16 , 30: a__isNatIList^#(V) -> c_28(a__U31^#(a__isNatIListKind(V), V)) 970.99/297.16 , 31: a__isNatIList^#(X) -> c_29(X) 970.99/297.16 , 32: a__isNatIList^#(cons(V1, V2)) -> 970.99/297.16 c_30(a__U41^#(a__and(a__isNatKind(V1), isNatIListKind(V2)), 970.99/297.16 V1, 970.99/297.16 V2)) 970.99/297.16 , 33: a__isNatIList^#(zeros()) -> c_31() 970.99/297.16 , 34: a__U52^#(X1, X2) -> c_34(X1, X2) 970.99/297.16 , 35: a__U52^#(tt(), V2) -> c_35(a__U53^#(a__isNatList(V2))) 970.99/297.16 , 36: a__U53^#(X) -> c_36(X) 970.99/297.16 , 37: a__U53^#(tt()) -> c_37() 970.99/297.16 , 38: a__U61^#(X1, X2) -> c_38(X1, X2) 970.99/297.16 , 39: a__U61^#(tt(), L) -> c_39(a__length^#(mark(L))) 970.99/297.16 , 40: a__length^#(X) -> c_40(X) 970.99/297.16 , 41: a__length^#(cons(N, L)) -> 970.99/297.16 c_41(a__U61^#(a__and(a__and(a__isNatList(L), isNatIListKind(L)), 970.99/297.16 and(isNat(N), isNatKind(N))), 970.99/297.16 L)) 970.99/297.16 , 42: a__length^#(nil()) -> c_42() 970.99/297.16 , 43: mark^#(cons(X1, X2)) -> c_43(mark^#(X1), X2) 970.99/297.16 , 44: mark^#(0()) -> c_44() 970.99/297.16 , 45: mark^#(zeros()) -> c_45(a__zeros^#()) 970.99/297.16 , 46: mark^#(tt()) -> c_46() 970.99/297.16 , 47: mark^#(s(X)) -> c_47(mark^#(X)) 970.99/297.16 , 48: mark^#(length(X)) -> c_48(a__length^#(mark(X))) 970.99/297.16 , 49: mark^#(isNatIListKind(X)) -> c_49(a__isNatIListKind^#(X)) 970.99/297.16 , 50: mark^#(nil()) -> c_50() 970.99/297.16 , 51: mark^#(and(X1, X2)) -> c_51(a__and^#(mark(X1), X2)) 970.99/297.16 , 52: mark^#(isNat(X)) -> c_52(a__isNat^#(X)) 970.99/297.16 , 53: mark^#(isNatKind(X)) -> c_53(a__isNatKind^#(X)) 970.99/297.16 , 54: mark^#(U11(X1, X2)) -> c_54(a__U11^#(mark(X1), X2)) 970.99/297.16 , 55: mark^#(U12(X)) -> c_55(a__U12^#(mark(X))) 970.99/297.16 , 56: mark^#(isNatList(X)) -> c_56(a__isNatList^#(X)) 970.99/297.16 , 57: mark^#(U21(X1, X2)) -> c_57(a__U21^#(mark(X1), X2)) 970.99/297.16 , 58: mark^#(U22(X)) -> c_58(a__U22^#(mark(X))) 970.99/297.16 , 59: mark^#(U31(X1, X2)) -> c_59(a__U31^#(mark(X1), X2)) 970.99/297.16 , 60: mark^#(U32(X)) -> c_60(a__U32^#(mark(X))) 970.99/297.16 , 61: mark^#(U41(X1, X2, X3)) -> c_61(a__U41^#(mark(X1), X2, X3)) 970.99/297.16 , 62: mark^#(U42(X1, X2)) -> c_62(a__U42^#(mark(X1), X2)) 970.99/297.16 , 63: mark^#(U43(X)) -> c_63(a__U43^#(mark(X))) 970.99/297.16 , 64: mark^#(isNatIList(X)) -> c_64(a__isNatIList^#(X)) 970.99/297.16 , 65: mark^#(U51(X1, X2, X3)) -> c_65(a__U51^#(mark(X1), X2, X3)) 970.99/297.16 , 66: mark^#(U52(X1, X2)) -> c_66(a__U52^#(mark(X1), X2)) 970.99/297.16 , 67: mark^#(U53(X)) -> c_67(a__U53^#(mark(X))) 970.99/297.16 , 68: mark^#(U61(X1, X2)) -> c_68(a__U61^#(mark(X1), X2)) 970.99/297.16 , 69: a__isNatIListKind^#(X) -> c_71(X) 970.99/297.16 , 70: a__isNatIListKind^#(cons(V1, V2)) -> 970.99/297.16 c_72(a__and^#(a__isNatKind(V1), isNatIListKind(V2))) 970.99/297.16 , 71: a__isNatIListKind^#(zeros()) -> c_73() 970.99/297.16 , 72: a__isNatIListKind^#(nil()) -> c_74() 970.99/297.16 , 73: a__and^#(X1, X2) -> c_69(X1, X2) 970.99/297.16 , 74: a__and^#(tt(), X) -> c_70(mark^#(X)) 970.99/297.16 , 75: a__isNatKind^#(X) -> c_75(X) 970.99/297.16 , 76: a__isNatKind^#(0()) -> c_76() 970.99/297.16 , 77: a__isNatKind^#(s(V1)) -> c_77(a__isNatKind^#(V1)) 970.99/297.16 , 78: a__isNatKind^#(length(V1)) -> c_78(a__isNatIListKind^#(V1)) } 970.99/297.16 970.99/297.16 We are left with following problem, upon which TcT provides the 970.99/297.16 certificate MAYBE. 970.99/297.16 970.99/297.16 Strict DPs: 970.99/297.16 { a__U11^#(X1, X2) -> c_3(X1, X2) 970.99/297.16 , a__U11^#(tt(), V1) -> c_4(a__U12^#(a__isNatList(V1))) 970.99/297.16 , a__U12^#(X) -> c_5(X) 970.99/297.16 , a__isNatList^#(X) -> c_7(X) 970.99/297.16 , a__isNatList^#(cons(V1, V2)) -> 970.99/297.16 c_8(a__U51^#(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)) 970.99/297.16 , a__U51^#(X1, X2, X3) -> c_32(X1, X2, X3) 970.99/297.16 , a__U51^#(tt(), V1, V2) -> c_33(a__U52^#(a__isNat(V1), V2)) 970.99/297.16 , a__U21^#(X1, X2) -> c_10(X1, X2) 970.99/297.16 , a__U21^#(tt(), V1) -> c_11(a__U22^#(a__isNat(V1))) 970.99/297.16 , a__U22^#(X) -> c_12(X) 970.99/297.16 , a__isNat^#(X) -> c_14(X) 970.99/297.16 , a__isNat^#(s(V1)) -> c_16(a__U21^#(a__isNatKind(V1), V1)) 970.99/297.16 , a__isNat^#(length(V1)) -> 970.99/297.16 c_17(a__U11^#(a__isNatIListKind(V1), V1)) 970.99/297.16 , a__U31^#(X1, X2) -> c_18(X1, X2) 970.99/297.16 , a__U31^#(tt(), V) -> c_19(a__U32^#(a__isNatList(V))) 970.99/297.16 , a__U32^#(X) -> c_20(X) 970.99/297.16 , a__U41^#(X1, X2, X3) -> c_22(X1, X2, X3) 970.99/297.16 , a__U41^#(tt(), V1, V2) -> c_23(a__U42^#(a__isNat(V1), V2)) 970.99/297.16 , a__U42^#(X1, X2) -> c_24(X1, X2) 970.99/297.16 , a__U42^#(tt(), V2) -> c_25(a__U43^#(a__isNatIList(V2))) 970.99/297.16 , a__U43^#(X) -> c_26(X) 970.99/297.16 , a__isNatIList^#(V) -> c_28(a__U31^#(a__isNatIListKind(V), V)) 970.99/297.16 , a__isNatIList^#(X) -> c_29(X) 970.99/297.16 , a__isNatIList^#(cons(V1, V2)) -> 970.99/297.16 c_30(a__U41^#(a__and(a__isNatKind(V1), isNatIListKind(V2)), 970.99/297.16 V1, 970.99/297.16 V2)) 970.99/297.16 , a__U52^#(X1, X2) -> c_34(X1, X2) 970.99/297.16 , a__U52^#(tt(), V2) -> c_35(a__U53^#(a__isNatList(V2))) 970.99/297.16 , a__U53^#(X) -> c_36(X) 970.99/297.16 , a__U61^#(X1, X2) -> c_38(X1, X2) 970.99/297.16 , a__U61^#(tt(), L) -> c_39(a__length^#(mark(L))) 970.99/297.16 , a__length^#(X) -> c_40(X) 970.99/297.16 , a__length^#(cons(N, L)) -> 970.99/297.16 c_41(a__U61^#(a__and(a__and(a__isNatList(L), isNatIListKind(L)), 970.99/297.16 and(isNat(N), isNatKind(N))), 970.99/297.16 L)) 970.99/297.16 , mark^#(cons(X1, X2)) -> c_43(mark^#(X1), X2) 970.99/297.16 , mark^#(zeros()) -> c_45(a__zeros^#()) 970.99/297.16 , mark^#(s(X)) -> c_47(mark^#(X)) 970.99/297.16 , mark^#(length(X)) -> c_48(a__length^#(mark(X))) 970.99/297.16 , mark^#(isNatIListKind(X)) -> c_49(a__isNatIListKind^#(X)) 970.99/297.16 , mark^#(and(X1, X2)) -> c_51(a__and^#(mark(X1), X2)) 970.99/297.16 , mark^#(isNat(X)) -> c_52(a__isNat^#(X)) 970.99/297.16 , mark^#(isNatKind(X)) -> c_53(a__isNatKind^#(X)) 970.99/297.16 , mark^#(U11(X1, X2)) -> c_54(a__U11^#(mark(X1), X2)) 970.99/297.16 , mark^#(U12(X)) -> c_55(a__U12^#(mark(X))) 970.99/297.16 , mark^#(isNatList(X)) -> c_56(a__isNatList^#(X)) 970.99/297.16 , mark^#(U21(X1, X2)) -> c_57(a__U21^#(mark(X1), X2)) 970.99/297.16 , mark^#(U22(X)) -> c_58(a__U22^#(mark(X))) 970.99/297.16 , mark^#(U31(X1, X2)) -> c_59(a__U31^#(mark(X1), X2)) 970.99/297.16 , mark^#(U32(X)) -> c_60(a__U32^#(mark(X))) 970.99/297.16 , mark^#(U41(X1, X2, X3)) -> c_61(a__U41^#(mark(X1), X2, X3)) 970.99/297.16 , mark^#(U42(X1, X2)) -> c_62(a__U42^#(mark(X1), X2)) 970.99/297.16 , mark^#(U43(X)) -> c_63(a__U43^#(mark(X))) 970.99/297.16 , mark^#(isNatIList(X)) -> c_64(a__isNatIList^#(X)) 970.99/297.16 , mark^#(U51(X1, X2, X3)) -> c_65(a__U51^#(mark(X1), X2, X3)) 970.99/297.16 , mark^#(U52(X1, X2)) -> c_66(a__U52^#(mark(X1), X2)) 970.99/297.16 , mark^#(U53(X)) -> c_67(a__U53^#(mark(X))) 970.99/297.16 , mark^#(U61(X1, X2)) -> c_68(a__U61^#(mark(X1), X2)) 970.99/297.16 , a__isNatIListKind^#(X) -> c_71(X) 970.99/297.16 , a__isNatIListKind^#(cons(V1, V2)) -> 970.99/297.16 c_72(a__and^#(a__isNatKind(V1), isNatIListKind(V2))) 970.99/297.16 , a__and^#(X1, X2) -> c_69(X1, X2) 970.99/297.16 , a__and^#(tt(), X) -> c_70(mark^#(X)) 970.99/297.16 , a__isNatKind^#(X) -> c_75(X) 970.99/297.16 , a__isNatKind^#(s(V1)) -> c_77(a__isNatKind^#(V1)) 970.99/297.16 , a__isNatKind^#(length(V1)) -> c_78(a__isNatIListKind^#(V1)) } 970.99/297.16 Strict Trs: 970.99/297.16 { a__zeros() -> cons(0(), zeros()) 970.99/297.16 , a__zeros() -> zeros() 970.99/297.16 , a__U11(X1, X2) -> U11(X1, X2) 970.99/297.16 , a__U11(tt(), V1) -> a__U12(a__isNatList(V1)) 970.99/297.16 , a__U12(X) -> U12(X) 970.99/297.16 , a__U12(tt()) -> tt() 970.99/297.16 , a__isNatList(X) -> isNatList(X) 970.99/297.16 , a__isNatList(cons(V1, V2)) -> 970.99/297.16 a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 970.99/297.16 , a__isNatList(nil()) -> tt() 970.99/297.16 , a__U21(X1, X2) -> U21(X1, X2) 970.99/297.16 , a__U21(tt(), V1) -> a__U22(a__isNat(V1)) 970.99/297.16 , a__U22(X) -> U22(X) 970.99/297.16 , a__U22(tt()) -> tt() 970.99/297.16 , a__isNat(X) -> isNat(X) 970.99/297.16 , a__isNat(0()) -> tt() 970.99/297.16 , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 970.99/297.16 , a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) 970.99/297.16 , a__U31(X1, X2) -> U31(X1, X2) 970.99/297.16 , a__U31(tt(), V) -> a__U32(a__isNatList(V)) 970.99/297.16 , a__U32(X) -> U32(X) 970.99/297.16 , a__U32(tt()) -> tt() 970.99/297.16 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 970.99/297.16 , a__U41(tt(), V1, V2) -> a__U42(a__isNat(V1), V2) 970.99/297.16 , a__U42(X1, X2) -> U42(X1, X2) 970.99/297.16 , a__U42(tt(), V2) -> a__U43(a__isNatIList(V2)) 970.99/297.16 , a__U43(X) -> U43(X) 970.99/297.16 , a__U43(tt()) -> tt() 970.99/297.16 , a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) 970.99/297.16 , a__isNatIList(X) -> isNatIList(X) 970.99/297.16 , a__isNatIList(cons(V1, V2)) -> 970.99/297.16 a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 970.99/297.16 , a__isNatIList(zeros()) -> tt() 970.99/297.16 , a__U51(X1, X2, X3) -> U51(X1, X2, X3) 970.99/297.16 , a__U51(tt(), V1, V2) -> a__U52(a__isNat(V1), V2) 970.99/297.16 , a__U52(X1, X2) -> U52(X1, X2) 970.99/297.16 , a__U52(tt(), V2) -> a__U53(a__isNatList(V2)) 970.99/297.16 , a__U53(X) -> U53(X) 970.99/297.16 , a__U53(tt()) -> tt() 970.99/297.16 , a__U61(X1, X2) -> U61(X1, X2) 970.99/297.16 , a__U61(tt(), L) -> s(a__length(mark(L))) 970.99/297.16 , a__length(X) -> length(X) 970.99/297.16 , a__length(cons(N, L)) -> 970.99/297.16 a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), 970.99/297.16 and(isNat(N), isNatKind(N))), 970.99/297.16 L) 970.99/297.16 , a__length(nil()) -> 0() 970.99/297.16 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 970.99/297.16 , mark(0()) -> 0() 970.99/297.16 , mark(zeros()) -> a__zeros() 970.99/297.16 , mark(tt()) -> tt() 970.99/297.16 , mark(s(X)) -> s(mark(X)) 970.99/297.16 , mark(length(X)) -> a__length(mark(X)) 970.99/297.16 , mark(isNatIListKind(X)) -> a__isNatIListKind(X) 970.99/297.16 , mark(nil()) -> nil() 970.99/297.16 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 970.99/297.16 , mark(isNat(X)) -> a__isNat(X) 970.99/297.16 , mark(isNatKind(X)) -> a__isNatKind(X) 970.99/297.16 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 970.99/297.16 , mark(U12(X)) -> a__U12(mark(X)) 970.99/297.16 , mark(isNatList(X)) -> a__isNatList(X) 970.99/297.16 , mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 970.99/297.16 , mark(U22(X)) -> a__U22(mark(X)) 970.99/297.16 , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 970.99/297.16 , mark(U32(X)) -> a__U32(mark(X)) 970.99/297.16 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 970.99/297.16 , mark(U42(X1, X2)) -> a__U42(mark(X1), X2) 970.99/297.16 , mark(U43(X)) -> a__U43(mark(X)) 970.99/297.16 , mark(isNatIList(X)) -> a__isNatIList(X) 970.99/297.16 , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) 970.99/297.16 , mark(U52(X1, X2)) -> a__U52(mark(X1), X2) 970.99/297.16 , mark(U53(X)) -> a__U53(mark(X)) 970.99/297.16 , mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 970.99/297.16 , a__and(X1, X2) -> and(X1, X2) 970.99/297.16 , a__and(tt(), X) -> mark(X) 970.99/297.16 , a__isNatIListKind(X) -> isNatIListKind(X) 970.99/297.16 , a__isNatIListKind(cons(V1, V2)) -> 970.99/297.16 a__and(a__isNatKind(V1), isNatIListKind(V2)) 970.99/297.16 , a__isNatIListKind(zeros()) -> tt() 970.99/297.16 , a__isNatIListKind(nil()) -> tt() 970.99/297.16 , a__isNatKind(X) -> isNatKind(X) 970.99/297.16 , a__isNatKind(0()) -> tt() 970.99/297.16 , a__isNatKind(s(V1)) -> a__isNatKind(V1) 970.99/297.16 , a__isNatKind(length(V1)) -> a__isNatIListKind(V1) } 970.99/297.16 Weak DPs: 970.99/297.16 { a__zeros^#() -> c_1() 970.99/297.16 , a__zeros^#() -> c_2() 970.99/297.16 , a__U12^#(tt()) -> c_6() 970.99/297.16 , a__isNatList^#(nil()) -> c_9() 970.99/297.16 , a__U22^#(tt()) -> c_13() 970.99/297.16 , a__isNat^#(0()) -> c_15() 970.99/297.16 , a__U32^#(tt()) -> c_21() 970.99/297.16 , a__U43^#(tt()) -> c_27() 970.99/297.16 , a__isNatIList^#(zeros()) -> c_31() 970.99/297.16 , a__U53^#(tt()) -> c_37() 970.99/297.16 , a__length^#(nil()) -> c_42() 970.99/297.16 , mark^#(0()) -> c_44() 970.99/297.16 , mark^#(tt()) -> c_46() 970.99/297.16 , mark^#(nil()) -> c_50() 970.99/297.16 , a__isNatIListKind^#(zeros()) -> c_73() 970.99/297.16 , a__isNatIListKind^#(nil()) -> c_74() 970.99/297.16 , a__isNatKind^#(0()) -> c_76() } 970.99/297.16 Obligation: 970.99/297.16 runtime complexity 970.99/297.16 Answer: 970.99/297.16 MAYBE 970.99/297.16 970.99/297.16 We estimate the number of application of {33} by applications of 970.99/297.16 Pre({33}) = 970.99/297.16 {1,3,4,6,8,10,11,14,16,17,19,21,23,25,27,28,30,32,34,55,57,58,59}. 970.99/297.16 Here rules are labeled as follows: 970.99/297.16 970.99/297.16 DPs: 970.99/297.16 { 1: a__U11^#(X1, X2) -> c_3(X1, X2) 970.99/297.16 , 2: a__U11^#(tt(), V1) -> c_4(a__U12^#(a__isNatList(V1))) 970.99/297.16 , 3: a__U12^#(X) -> c_5(X) 970.99/297.16 , 4: a__isNatList^#(X) -> c_7(X) 970.99/297.16 , 5: a__isNatList^#(cons(V1, V2)) -> 970.99/297.16 c_8(a__U51^#(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)) 970.99/297.16 , 6: a__U51^#(X1, X2, X3) -> c_32(X1, X2, X3) 970.99/297.16 , 7: a__U51^#(tt(), V1, V2) -> c_33(a__U52^#(a__isNat(V1), V2)) 970.99/297.16 , 8: a__U21^#(X1, X2) -> c_10(X1, X2) 970.99/297.16 , 9: a__U21^#(tt(), V1) -> c_11(a__U22^#(a__isNat(V1))) 970.99/297.16 , 10: a__U22^#(X) -> c_12(X) 970.99/297.16 , 11: a__isNat^#(X) -> c_14(X) 970.99/297.16 , 12: a__isNat^#(s(V1)) -> c_16(a__U21^#(a__isNatKind(V1), V1)) 970.99/297.16 , 13: a__isNat^#(length(V1)) -> 970.99/297.16 c_17(a__U11^#(a__isNatIListKind(V1), V1)) 970.99/297.16 , 14: a__U31^#(X1, X2) -> c_18(X1, X2) 970.99/297.16 , 15: a__U31^#(tt(), V) -> c_19(a__U32^#(a__isNatList(V))) 970.99/297.16 , 16: a__U32^#(X) -> c_20(X) 970.99/297.16 , 17: a__U41^#(X1, X2, X3) -> c_22(X1, X2, X3) 970.99/297.16 , 18: a__U41^#(tt(), V1, V2) -> c_23(a__U42^#(a__isNat(V1), V2)) 970.99/297.16 , 19: a__U42^#(X1, X2) -> c_24(X1, X2) 970.99/297.16 , 20: a__U42^#(tt(), V2) -> c_25(a__U43^#(a__isNatIList(V2))) 970.99/297.16 , 21: a__U43^#(X) -> c_26(X) 970.99/297.16 , 22: a__isNatIList^#(V) -> c_28(a__U31^#(a__isNatIListKind(V), V)) 970.99/297.16 , 23: a__isNatIList^#(X) -> c_29(X) 970.99/297.16 , 24: a__isNatIList^#(cons(V1, V2)) -> 970.99/297.16 c_30(a__U41^#(a__and(a__isNatKind(V1), isNatIListKind(V2)), 970.99/297.16 V1, 970.99/297.16 V2)) 970.99/297.16 , 25: a__U52^#(X1, X2) -> c_34(X1, X2) 970.99/297.16 , 26: a__U52^#(tt(), V2) -> c_35(a__U53^#(a__isNatList(V2))) 970.99/297.16 , 27: a__U53^#(X) -> c_36(X) 970.99/297.16 , 28: a__U61^#(X1, X2) -> c_38(X1, X2) 970.99/297.16 , 29: a__U61^#(tt(), L) -> c_39(a__length^#(mark(L))) 970.99/297.16 , 30: a__length^#(X) -> c_40(X) 970.99/297.16 , 31: a__length^#(cons(N, L)) -> 970.99/297.16 c_41(a__U61^#(a__and(a__and(a__isNatList(L), isNatIListKind(L)), 970.99/297.16 and(isNat(N), isNatKind(N))), 970.99/297.16 L)) 970.99/297.16 , 32: mark^#(cons(X1, X2)) -> c_43(mark^#(X1), X2) 970.99/297.16 , 33: mark^#(zeros()) -> c_45(a__zeros^#()) 970.99/297.16 , 34: mark^#(s(X)) -> c_47(mark^#(X)) 970.99/297.16 , 35: mark^#(length(X)) -> c_48(a__length^#(mark(X))) 970.99/297.16 , 36: mark^#(isNatIListKind(X)) -> c_49(a__isNatIListKind^#(X)) 970.99/297.16 , 37: mark^#(and(X1, X2)) -> c_51(a__and^#(mark(X1), X2)) 970.99/297.16 , 38: mark^#(isNat(X)) -> c_52(a__isNat^#(X)) 970.99/297.16 , 39: mark^#(isNatKind(X)) -> c_53(a__isNatKind^#(X)) 970.99/297.16 , 40: mark^#(U11(X1, X2)) -> c_54(a__U11^#(mark(X1), X2)) 970.99/297.16 , 41: mark^#(U12(X)) -> c_55(a__U12^#(mark(X))) 970.99/297.16 , 42: mark^#(isNatList(X)) -> c_56(a__isNatList^#(X)) 970.99/297.16 , 43: mark^#(U21(X1, X2)) -> c_57(a__U21^#(mark(X1), X2)) 970.99/297.16 , 44: mark^#(U22(X)) -> c_58(a__U22^#(mark(X))) 970.99/297.16 , 45: mark^#(U31(X1, X2)) -> c_59(a__U31^#(mark(X1), X2)) 970.99/297.16 , 46: mark^#(U32(X)) -> c_60(a__U32^#(mark(X))) 970.99/297.16 , 47: mark^#(U41(X1, X2, X3)) -> c_61(a__U41^#(mark(X1), X2, X3)) 970.99/297.16 , 48: mark^#(U42(X1, X2)) -> c_62(a__U42^#(mark(X1), X2)) 970.99/297.16 , 49: mark^#(U43(X)) -> c_63(a__U43^#(mark(X))) 970.99/297.16 , 50: mark^#(isNatIList(X)) -> c_64(a__isNatIList^#(X)) 970.99/297.16 , 51: mark^#(U51(X1, X2, X3)) -> c_65(a__U51^#(mark(X1), X2, X3)) 970.99/297.16 , 52: mark^#(U52(X1, X2)) -> c_66(a__U52^#(mark(X1), X2)) 970.99/297.16 , 53: mark^#(U53(X)) -> c_67(a__U53^#(mark(X))) 970.99/297.16 , 54: mark^#(U61(X1, X2)) -> c_68(a__U61^#(mark(X1), X2)) 970.99/297.16 , 55: a__isNatIListKind^#(X) -> c_71(X) 970.99/297.16 , 56: a__isNatIListKind^#(cons(V1, V2)) -> 970.99/297.16 c_72(a__and^#(a__isNatKind(V1), isNatIListKind(V2))) 970.99/297.16 , 57: a__and^#(X1, X2) -> c_69(X1, X2) 970.99/297.16 , 58: a__and^#(tt(), X) -> c_70(mark^#(X)) 970.99/297.16 , 59: a__isNatKind^#(X) -> c_75(X) 970.99/297.16 , 60: a__isNatKind^#(s(V1)) -> c_77(a__isNatKind^#(V1)) 970.99/297.16 , 61: a__isNatKind^#(length(V1)) -> c_78(a__isNatIListKind^#(V1)) 970.99/297.16 , 62: a__zeros^#() -> c_1() 970.99/297.16 , 63: a__zeros^#() -> c_2() 970.99/297.16 , 64: a__U12^#(tt()) -> c_6() 970.99/297.16 , 65: a__isNatList^#(nil()) -> c_9() 970.99/297.16 , 66: a__U22^#(tt()) -> c_13() 970.99/297.16 , 67: a__isNat^#(0()) -> c_15() 970.99/297.16 , 68: a__U32^#(tt()) -> c_21() 970.99/297.16 , 69: a__U43^#(tt()) -> c_27() 970.99/297.16 , 70: a__isNatIList^#(zeros()) -> c_31() 970.99/297.16 , 71: a__U53^#(tt()) -> c_37() 970.99/297.16 , 72: a__length^#(nil()) -> c_42() 970.99/297.16 , 73: mark^#(0()) -> c_44() 970.99/297.16 , 74: mark^#(tt()) -> c_46() 970.99/297.16 , 75: mark^#(nil()) -> c_50() 970.99/297.16 , 76: a__isNatIListKind^#(zeros()) -> c_73() 970.99/297.16 , 77: a__isNatIListKind^#(nil()) -> c_74() 970.99/297.16 , 78: a__isNatKind^#(0()) -> c_76() } 970.99/297.16 970.99/297.16 We are left with following problem, upon which TcT provides the 970.99/297.16 certificate MAYBE. 970.99/297.16 970.99/297.16 Strict DPs: 970.99/297.16 { a__U11^#(X1, X2) -> c_3(X1, X2) 970.99/297.16 , a__U11^#(tt(), V1) -> c_4(a__U12^#(a__isNatList(V1))) 970.99/297.16 , a__U12^#(X) -> c_5(X) 970.99/297.16 , a__isNatList^#(X) -> c_7(X) 970.99/297.16 , a__isNatList^#(cons(V1, V2)) -> 970.99/297.16 c_8(a__U51^#(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)) 970.99/297.16 , a__U51^#(X1, X2, X3) -> c_32(X1, X2, X3) 970.99/297.16 , a__U51^#(tt(), V1, V2) -> c_33(a__U52^#(a__isNat(V1), V2)) 970.99/297.16 , a__U21^#(X1, X2) -> c_10(X1, X2) 970.99/297.16 , a__U21^#(tt(), V1) -> c_11(a__U22^#(a__isNat(V1))) 970.99/297.16 , a__U22^#(X) -> c_12(X) 970.99/297.16 , a__isNat^#(X) -> c_14(X) 970.99/297.16 , a__isNat^#(s(V1)) -> c_16(a__U21^#(a__isNatKind(V1), V1)) 970.99/297.16 , a__isNat^#(length(V1)) -> 970.99/297.16 c_17(a__U11^#(a__isNatIListKind(V1), V1)) 970.99/297.16 , a__U31^#(X1, X2) -> c_18(X1, X2) 970.99/297.16 , a__U31^#(tt(), V) -> c_19(a__U32^#(a__isNatList(V))) 970.99/297.16 , a__U32^#(X) -> c_20(X) 970.99/297.16 , a__U41^#(X1, X2, X3) -> c_22(X1, X2, X3) 970.99/297.16 , a__U41^#(tt(), V1, V2) -> c_23(a__U42^#(a__isNat(V1), V2)) 970.99/297.16 , a__U42^#(X1, X2) -> c_24(X1, X2) 970.99/297.16 , a__U42^#(tt(), V2) -> c_25(a__U43^#(a__isNatIList(V2))) 970.99/297.16 , a__U43^#(X) -> c_26(X) 970.99/297.16 , a__isNatIList^#(V) -> c_28(a__U31^#(a__isNatIListKind(V), V)) 970.99/297.16 , a__isNatIList^#(X) -> c_29(X) 970.99/297.16 , a__isNatIList^#(cons(V1, V2)) -> 970.99/297.16 c_30(a__U41^#(a__and(a__isNatKind(V1), isNatIListKind(V2)), 970.99/297.16 V1, 970.99/297.16 V2)) 970.99/297.16 , a__U52^#(X1, X2) -> c_34(X1, X2) 970.99/297.16 , a__U52^#(tt(), V2) -> c_35(a__U53^#(a__isNatList(V2))) 970.99/297.16 , a__U53^#(X) -> c_36(X) 970.99/297.16 , a__U61^#(X1, X2) -> c_38(X1, X2) 970.99/297.16 , a__U61^#(tt(), L) -> c_39(a__length^#(mark(L))) 970.99/297.16 , a__length^#(X) -> c_40(X) 970.99/297.16 , a__length^#(cons(N, L)) -> 970.99/297.16 c_41(a__U61^#(a__and(a__and(a__isNatList(L), isNatIListKind(L)), 970.99/297.16 and(isNat(N), isNatKind(N))), 970.99/297.16 L)) 970.99/297.16 , mark^#(cons(X1, X2)) -> c_43(mark^#(X1), X2) 970.99/297.16 , mark^#(s(X)) -> c_47(mark^#(X)) 970.99/297.16 , mark^#(length(X)) -> c_48(a__length^#(mark(X))) 970.99/297.16 , mark^#(isNatIListKind(X)) -> c_49(a__isNatIListKind^#(X)) 970.99/297.16 , mark^#(and(X1, X2)) -> c_51(a__and^#(mark(X1), X2)) 970.99/297.16 , mark^#(isNat(X)) -> c_52(a__isNat^#(X)) 970.99/297.16 , mark^#(isNatKind(X)) -> c_53(a__isNatKind^#(X)) 970.99/297.16 , mark^#(U11(X1, X2)) -> c_54(a__U11^#(mark(X1), X2)) 970.99/297.16 , mark^#(U12(X)) -> c_55(a__U12^#(mark(X))) 970.99/297.16 , mark^#(isNatList(X)) -> c_56(a__isNatList^#(X)) 970.99/297.16 , mark^#(U21(X1, X2)) -> c_57(a__U21^#(mark(X1), X2)) 970.99/297.16 , mark^#(U22(X)) -> c_58(a__U22^#(mark(X))) 970.99/297.16 , mark^#(U31(X1, X2)) -> c_59(a__U31^#(mark(X1), X2)) 970.99/297.16 , mark^#(U32(X)) -> c_60(a__U32^#(mark(X))) 970.99/297.16 , mark^#(U41(X1, X2, X3)) -> c_61(a__U41^#(mark(X1), X2, X3)) 970.99/297.16 , mark^#(U42(X1, X2)) -> c_62(a__U42^#(mark(X1), X2)) 970.99/297.16 , mark^#(U43(X)) -> c_63(a__U43^#(mark(X))) 970.99/297.16 , mark^#(isNatIList(X)) -> c_64(a__isNatIList^#(X)) 970.99/297.16 , mark^#(U51(X1, X2, X3)) -> c_65(a__U51^#(mark(X1), X2, X3)) 970.99/297.16 , mark^#(U52(X1, X2)) -> c_66(a__U52^#(mark(X1), X2)) 970.99/297.16 , mark^#(U53(X)) -> c_67(a__U53^#(mark(X))) 970.99/297.16 , mark^#(U61(X1, X2)) -> c_68(a__U61^#(mark(X1), X2)) 970.99/297.16 , a__isNatIListKind^#(X) -> c_71(X) 970.99/297.16 , a__isNatIListKind^#(cons(V1, V2)) -> 970.99/297.16 c_72(a__and^#(a__isNatKind(V1), isNatIListKind(V2))) 970.99/297.16 , a__and^#(X1, X2) -> c_69(X1, X2) 970.99/297.16 , a__and^#(tt(), X) -> c_70(mark^#(X)) 970.99/297.16 , a__isNatKind^#(X) -> c_75(X) 970.99/297.16 , a__isNatKind^#(s(V1)) -> c_77(a__isNatKind^#(V1)) 970.99/297.16 , a__isNatKind^#(length(V1)) -> c_78(a__isNatIListKind^#(V1)) } 970.99/297.16 Strict Trs: 970.99/297.16 { a__zeros() -> cons(0(), zeros()) 970.99/297.16 , a__zeros() -> zeros() 970.99/297.16 , a__U11(X1, X2) -> U11(X1, X2) 970.99/297.16 , a__U11(tt(), V1) -> a__U12(a__isNatList(V1)) 970.99/297.16 , a__U12(X) -> U12(X) 970.99/297.16 , a__U12(tt()) -> tt() 970.99/297.16 , a__isNatList(X) -> isNatList(X) 970.99/297.16 , a__isNatList(cons(V1, V2)) -> 970.99/297.16 a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 970.99/297.16 , a__isNatList(nil()) -> tt() 970.99/297.16 , a__U21(X1, X2) -> U21(X1, X2) 970.99/297.16 , a__U21(tt(), V1) -> a__U22(a__isNat(V1)) 970.99/297.16 , a__U22(X) -> U22(X) 970.99/297.16 , a__U22(tt()) -> tt() 970.99/297.16 , a__isNat(X) -> isNat(X) 970.99/297.16 , a__isNat(0()) -> tt() 970.99/297.16 , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) 970.99/297.16 , a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) 970.99/297.16 , a__U31(X1, X2) -> U31(X1, X2) 970.99/297.16 , a__U31(tt(), V) -> a__U32(a__isNatList(V)) 970.99/297.16 , a__U32(X) -> U32(X) 970.99/297.16 , a__U32(tt()) -> tt() 970.99/297.16 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 970.99/297.16 , a__U41(tt(), V1, V2) -> a__U42(a__isNat(V1), V2) 970.99/297.16 , a__U42(X1, X2) -> U42(X1, X2) 970.99/297.16 , a__U42(tt(), V2) -> a__U43(a__isNatIList(V2)) 970.99/297.16 , a__U43(X) -> U43(X) 970.99/297.16 , a__U43(tt()) -> tt() 970.99/297.16 , a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) 970.99/297.16 , a__isNatIList(X) -> isNatIList(X) 970.99/297.16 , a__isNatIList(cons(V1, V2)) -> 970.99/297.16 a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) 970.99/297.16 , a__isNatIList(zeros()) -> tt() 970.99/297.16 , a__U51(X1, X2, X3) -> U51(X1, X2, X3) 970.99/297.16 , a__U51(tt(), V1, V2) -> a__U52(a__isNat(V1), V2) 970.99/297.16 , a__U52(X1, X2) -> U52(X1, X2) 970.99/297.16 , a__U52(tt(), V2) -> a__U53(a__isNatList(V2)) 970.99/297.16 , a__U53(X) -> U53(X) 970.99/297.16 , a__U53(tt()) -> tt() 970.99/297.16 , a__U61(X1, X2) -> U61(X1, X2) 970.99/297.16 , a__U61(tt(), L) -> s(a__length(mark(L))) 970.99/297.16 , a__length(X) -> length(X) 970.99/297.16 , a__length(cons(N, L)) -> 970.99/297.16 a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), 970.99/297.16 and(isNat(N), isNatKind(N))), 970.99/297.16 L) 970.99/297.16 , a__length(nil()) -> 0() 970.99/297.16 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 970.99/297.16 , mark(0()) -> 0() 970.99/297.16 , mark(zeros()) -> a__zeros() 970.99/297.16 , mark(tt()) -> tt() 970.99/297.16 , mark(s(X)) -> s(mark(X)) 970.99/297.16 , mark(length(X)) -> a__length(mark(X)) 970.99/297.16 , mark(isNatIListKind(X)) -> a__isNatIListKind(X) 970.99/297.16 , mark(nil()) -> nil() 970.99/297.16 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 970.99/297.16 , mark(isNat(X)) -> a__isNat(X) 970.99/297.16 , mark(isNatKind(X)) -> a__isNatKind(X) 970.99/297.16 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 970.99/297.16 , mark(U12(X)) -> a__U12(mark(X)) 970.99/297.16 , mark(isNatList(X)) -> a__isNatList(X) 970.99/297.16 , mark(U21(X1, X2)) -> a__U21(mark(X1), X2) 970.99/297.16 , mark(U22(X)) -> a__U22(mark(X)) 970.99/297.16 , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 970.99/297.16 , mark(U32(X)) -> a__U32(mark(X)) 970.99/297.16 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 970.99/297.16 , mark(U42(X1, X2)) -> a__U42(mark(X1), X2) 970.99/297.16 , mark(U43(X)) -> a__U43(mark(X)) 970.99/297.16 , mark(isNatIList(X)) -> a__isNatIList(X) 970.99/297.16 , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) 970.99/297.16 , mark(U52(X1, X2)) -> a__U52(mark(X1), X2) 970.99/297.16 , mark(U53(X)) -> a__U53(mark(X)) 970.99/297.16 , mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 970.99/297.16 , a__and(X1, X2) -> and(X1, X2) 970.99/297.16 , a__and(tt(), X) -> mark(X) 970.99/297.16 , a__isNatIListKind(X) -> isNatIListKind(X) 970.99/297.16 , a__isNatIListKind(cons(V1, V2)) -> 970.99/297.16 a__and(a__isNatKind(V1), isNatIListKind(V2)) 970.99/297.16 , a__isNatIListKind(zeros()) -> tt() 970.99/297.16 , a__isNatIListKind(nil()) -> tt() 970.99/297.16 , a__isNatKind(X) -> isNatKind(X) 970.99/297.16 , a__isNatKind(0()) -> tt() 970.99/297.16 , a__isNatKind(s(V1)) -> a__isNatKind(V1) 970.99/297.16 , a__isNatKind(length(V1)) -> a__isNatIListKind(V1) } 970.99/297.16 Weak DPs: 970.99/297.16 { a__zeros^#() -> c_1() 970.99/297.16 , a__zeros^#() -> c_2() 970.99/297.16 , a__U12^#(tt()) -> c_6() 970.99/297.16 , a__isNatList^#(nil()) -> c_9() 970.99/297.16 , a__U22^#(tt()) -> c_13() 970.99/297.16 , a__isNat^#(0()) -> c_15() 970.99/297.16 , a__U32^#(tt()) -> c_21() 970.99/297.16 , a__U43^#(tt()) -> c_27() 970.99/297.16 , a__isNatIList^#(zeros()) -> c_31() 970.99/297.16 , a__U53^#(tt()) -> c_37() 970.99/297.16 , a__length^#(nil()) -> c_42() 970.99/297.16 , mark^#(0()) -> c_44() 970.99/297.16 , mark^#(zeros()) -> c_45(a__zeros^#()) 970.99/297.16 , mark^#(tt()) -> c_46() 970.99/297.16 , mark^#(nil()) -> c_50() 970.99/297.16 , a__isNatIListKind^#(zeros()) -> c_73() 970.99/297.16 , a__isNatIListKind^#(nil()) -> c_74() 970.99/297.16 , a__isNatKind^#(0()) -> c_76() } 970.99/297.16 Obligation: 970.99/297.16 runtime complexity 970.99/297.16 Answer: 970.99/297.16 MAYBE 970.99/297.16 970.99/297.16 Empty strict component of the problem is NOT empty. 970.99/297.16 970.99/297.16 970.99/297.16 Arrrr.. 970.99/297.17 EOF