MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { a____(X1, X2) -> __(X1, X2) , a____(X, nil()) -> mark(X) , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) , a____(nil(), X) -> mark(X) , mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) , mark(nil()) -> nil() , mark(tt()) -> tt() , mark(isPalListKind(X)) -> a__isPalListKind(X) , mark(and(X1, X2)) -> a__and(mark(X1), X2) , mark(isPal(X)) -> a__isPal(X) , mark(a()) -> a() , mark(e()) -> e() , mark(i()) -> i() , mark(o()) -> o() , mark(u()) -> u() , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) , mark(U12(X)) -> a__U12(mark(X)) , mark(isNeList(X)) -> a__isNeList(X) , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) , mark(U22(X1, X2)) -> a__U22(mark(X1), X2) , mark(isList(X)) -> a__isList(X) , mark(U23(X)) -> a__U23(mark(X)) , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) , mark(U32(X)) -> a__U32(mark(X)) , mark(isQid(X)) -> a__isQid(X) , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) , mark(U42(X1, X2)) -> a__U42(mark(X1), X2) , mark(U43(X)) -> a__U43(mark(X)) , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) , mark(U52(X1, X2)) -> a__U52(mark(X1), X2) , mark(U53(X)) -> a__U53(mark(X)) , mark(U61(X1, X2)) -> a__U61(mark(X1), X2) , mark(U62(X)) -> a__U62(mark(X)) , mark(U71(X1, X2)) -> a__U71(mark(X1), X2) , mark(U72(X)) -> a__U72(mark(X)) , mark(isNePal(X)) -> a__isNePal(X) , a__U11(X1, X2) -> U11(X1, X2) , a__U11(tt(), V) -> a__U12(a__isNeList(V)) , a__U12(X) -> U12(X) , a__U12(tt()) -> tt() , a__isNeList(V) -> a__U31(a__isPalListKind(V), V) , a__isNeList(X) -> isNeList(X) , a__isNeList(__(V1, V2)) -> a__U41(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2) , a__isNeList(__(V1, V2)) -> a__U51(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2) , a__U21(X1, X2, X3) -> U21(X1, X2, X3) , a__U21(tt(), V1, V2) -> a__U22(a__isList(V1), V2) , a__U22(X1, X2) -> U22(X1, X2) , a__U22(tt(), V2) -> a__U23(a__isList(V2)) , a__isList(V) -> a__U11(a__isPalListKind(V), V) , a__isList(X) -> isList(X) , a__isList(__(V1, V2)) -> a__U21(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2) , a__isList(nil()) -> tt() , a__U23(X) -> U23(X) , a__U23(tt()) -> tt() , a__U31(X1, X2) -> U31(X1, X2) , a__U31(tt(), V) -> a__U32(a__isQid(V)) , a__U32(X) -> U32(X) , a__U32(tt()) -> tt() , a__isQid(X) -> isQid(X) , a__isQid(a()) -> tt() , a__isQid(e()) -> tt() , a__isQid(i()) -> tt() , a__isQid(o()) -> tt() , a__isQid(u()) -> tt() , a__U41(X1, X2, X3) -> U41(X1, X2, X3) , a__U41(tt(), V1, V2) -> a__U42(a__isList(V1), V2) , a__U42(X1, X2) -> U42(X1, X2) , a__U42(tt(), V2) -> a__U43(a__isNeList(V2)) , a__U43(X) -> U43(X) , a__U43(tt()) -> tt() , a__U51(X1, X2, X3) -> U51(X1, X2, X3) , a__U51(tt(), V1, V2) -> a__U52(a__isNeList(V1), V2) , a__U52(X1, X2) -> U52(X1, X2) , a__U52(tt(), V2) -> a__U53(a__isList(V2)) , a__U53(X) -> U53(X) , a__U53(tt()) -> tt() , a__U61(X1, X2) -> U61(X1, X2) , a__U61(tt(), V) -> a__U62(a__isQid(V)) , a__U62(X) -> U62(X) , a__U62(tt()) -> tt() , a__U71(X1, X2) -> U71(X1, X2) , a__U71(tt(), V) -> a__U72(a__isNePal(V)) , a__U72(X) -> U72(X) , a__U72(tt()) -> tt() , a__isNePal(V) -> a__U61(a__isPalListKind(V), V) , a__isNePal(X) -> isNePal(X) , a__isNePal(__(I, __(P, I))) -> a__and(a__and(a__isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P))) , a__and(X1, X2) -> and(X1, X2) , a__and(tt(), X) -> mark(X) , a__isPalListKind(X) -> isPalListKind(X) , a__isPalListKind(__(V1, V2)) -> a__and(a__isPalListKind(V1), isPalListKind(V2)) , a__isPalListKind(nil()) -> tt() , a__isPalListKind(a()) -> tt() , a__isPalListKind(e()) -> tt() , a__isPalListKind(i()) -> tt() , a__isPalListKind(o()) -> tt() , a__isPalListKind(u()) -> tt() , a__isPal(V) -> a__U71(a__isPalListKind(V), V) , a__isPal(X) -> isPal(X) , a__isPal(nil()) -> tt() } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 60.0 seconds. 2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { a____^#(X1, X2) -> c_1(X1, X2) , a____^#(X, nil()) -> c_2(mark^#(X)) , a____^#(__(X, Y), Z) -> c_3(a____^#(mark(X), a____(mark(Y), mark(Z)))) , a____^#(nil(), X) -> c_4(mark^#(X)) , mark^#(__(X1, X2)) -> c_5(a____^#(mark(X1), mark(X2))) , mark^#(nil()) -> c_6() , mark^#(tt()) -> c_7() , mark^#(isPalListKind(X)) -> c_8(a__isPalListKind^#(X)) , mark^#(and(X1, X2)) -> c_9(a__and^#(mark(X1), X2)) , mark^#(isPal(X)) -> c_10(a__isPal^#(X)) , mark^#(a()) -> c_11() , mark^#(e()) -> c_12() , mark^#(i()) -> c_13() , mark^#(o()) -> c_14() , mark^#(u()) -> c_15() , mark^#(U11(X1, X2)) -> c_16(a__U11^#(mark(X1), X2)) , mark^#(U12(X)) -> c_17(a__U12^#(mark(X))) , mark^#(isNeList(X)) -> c_18(a__isNeList^#(X)) , mark^#(U21(X1, X2, X3)) -> c_19(a__U21^#(mark(X1), X2, X3)) , mark^#(U22(X1, X2)) -> c_20(a__U22^#(mark(X1), X2)) , mark^#(isList(X)) -> c_21(a__isList^#(X)) , mark^#(U23(X)) -> c_22(a__U23^#(mark(X))) , mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2)) , mark^#(U32(X)) -> c_24(a__U32^#(mark(X))) , mark^#(isQid(X)) -> c_25(a__isQid^#(X)) , mark^#(U41(X1, X2, X3)) -> c_26(a__U41^#(mark(X1), X2, X3)) , mark^#(U42(X1, X2)) -> c_27(a__U42^#(mark(X1), X2)) , mark^#(U43(X)) -> c_28(a__U43^#(mark(X))) , mark^#(U51(X1, X2, X3)) -> c_29(a__U51^#(mark(X1), X2, X3)) , mark^#(U52(X1, X2)) -> c_30(a__U52^#(mark(X1), X2)) , mark^#(U53(X)) -> c_31(a__U53^#(mark(X))) , mark^#(U61(X1, X2)) -> c_32(a__U61^#(mark(X1), X2)) , mark^#(U62(X)) -> c_33(a__U62^#(mark(X))) , mark^#(U71(X1, X2)) -> c_34(a__U71^#(mark(X1), X2)) , mark^#(U72(X)) -> c_35(a__U72^#(mark(X))) , mark^#(isNePal(X)) -> c_36(a__isNePal^#(X)) , a__isPalListKind^#(X) -> c_90(X) , a__isPalListKind^#(__(V1, V2)) -> c_91(a__and^#(a__isPalListKind(V1), isPalListKind(V2))) , a__isPalListKind^#(nil()) -> c_92() , a__isPalListKind^#(a()) -> c_93() , a__isPalListKind^#(e()) -> c_94() , a__isPalListKind^#(i()) -> c_95() , a__isPalListKind^#(o()) -> c_96() , a__isPalListKind^#(u()) -> c_97() , a__and^#(X1, X2) -> c_88(X1, X2) , a__and^#(tt(), X) -> c_89(mark^#(X)) , a__isPal^#(V) -> c_98(a__U71^#(a__isPalListKind(V), V)) , a__isPal^#(X) -> c_99(X) , a__isPal^#(nil()) -> c_100() , a__U11^#(X1, X2) -> c_37(X1, X2) , a__U11^#(tt(), V) -> c_38(a__U12^#(a__isNeList(V))) , a__U12^#(X) -> c_39(X) , a__U12^#(tt()) -> c_40() , a__isNeList^#(V) -> c_41(a__U31^#(a__isPalListKind(V), V)) , a__isNeList^#(X) -> c_42(X) , a__isNeList^#(__(V1, V2)) -> c_43(a__U41^#(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)) , a__isNeList^#(__(V1, V2)) -> c_44(a__U51^#(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)) , a__U21^#(X1, X2, X3) -> c_45(X1, X2, X3) , a__U21^#(tt(), V1, V2) -> c_46(a__U22^#(a__isList(V1), V2)) , a__U22^#(X1, X2) -> c_47(X1, X2) , a__U22^#(tt(), V2) -> c_48(a__U23^#(a__isList(V2))) , a__isList^#(V) -> c_49(a__U11^#(a__isPalListKind(V), V)) , a__isList^#(X) -> c_50(X) , a__isList^#(__(V1, V2)) -> c_51(a__U21^#(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)) , a__isList^#(nil()) -> c_52() , a__U23^#(X) -> c_53(X) , a__U23^#(tt()) -> c_54() , a__U31^#(X1, X2) -> c_55(X1, X2) , a__U31^#(tt(), V) -> c_56(a__U32^#(a__isQid(V))) , a__U32^#(X) -> c_57(X) , a__U32^#(tt()) -> c_58() , a__isQid^#(X) -> c_59(X) , a__isQid^#(a()) -> c_60() , a__isQid^#(e()) -> c_61() , a__isQid^#(i()) -> c_62() , a__isQid^#(o()) -> c_63() , a__isQid^#(u()) -> c_64() , a__U41^#(X1, X2, X3) -> c_65(X1, X2, X3) , a__U41^#(tt(), V1, V2) -> c_66(a__U42^#(a__isList(V1), V2)) , a__U42^#(X1, X2) -> c_67(X1, X2) , a__U42^#(tt(), V2) -> c_68(a__U43^#(a__isNeList(V2))) , a__U43^#(X) -> c_69(X) , a__U43^#(tt()) -> c_70() , a__U51^#(X1, X2, X3) -> c_71(X1, X2, X3) , a__U51^#(tt(), V1, V2) -> c_72(a__U52^#(a__isNeList(V1), V2)) , a__U52^#(X1, X2) -> c_73(X1, X2) , a__U52^#(tt(), V2) -> c_74(a__U53^#(a__isList(V2))) , a__U53^#(X) -> c_75(X) , a__U53^#(tt()) -> c_76() , a__U61^#(X1, X2) -> c_77(X1, X2) , a__U61^#(tt(), V) -> c_78(a__U62^#(a__isQid(V))) , a__U62^#(X) -> c_79(X) , a__U62^#(tt()) -> c_80() , a__U71^#(X1, X2) -> c_81(X1, X2) , a__U71^#(tt(), V) -> c_82(a__U72^#(a__isNePal(V))) , a__U72^#(X) -> c_83(X) , a__U72^#(tt()) -> c_84() , a__isNePal^#(V) -> c_85(a__U61^#(a__isPalListKind(V), V)) , a__isNePal^#(X) -> c_86(X) , a__isNePal^#(__(I, __(P, I))) -> c_87(a__and^#(a__and(a__isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a____^#(X1, X2) -> c_1(X1, X2) , a____^#(X, nil()) -> c_2(mark^#(X)) , a____^#(__(X, Y), Z) -> c_3(a____^#(mark(X), a____(mark(Y), mark(Z)))) , a____^#(nil(), X) -> c_4(mark^#(X)) , mark^#(__(X1, X2)) -> c_5(a____^#(mark(X1), mark(X2))) , mark^#(nil()) -> c_6() , mark^#(tt()) -> c_7() , mark^#(isPalListKind(X)) -> c_8(a__isPalListKind^#(X)) , mark^#(and(X1, X2)) -> c_9(a__and^#(mark(X1), X2)) , mark^#(isPal(X)) -> c_10(a__isPal^#(X)) , mark^#(a()) -> c_11() , mark^#(e()) -> c_12() , mark^#(i()) -> c_13() , mark^#(o()) -> c_14() , mark^#(u()) -> c_15() , mark^#(U11(X1, X2)) -> c_16(a__U11^#(mark(X1), X2)) , mark^#(U12(X)) -> c_17(a__U12^#(mark(X))) , mark^#(isNeList(X)) -> c_18(a__isNeList^#(X)) , mark^#(U21(X1, X2, X3)) -> c_19(a__U21^#(mark(X1), X2, X3)) , mark^#(U22(X1, X2)) -> c_20(a__U22^#(mark(X1), X2)) , mark^#(isList(X)) -> c_21(a__isList^#(X)) , mark^#(U23(X)) -> c_22(a__U23^#(mark(X))) , mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2)) , mark^#(U32(X)) -> c_24(a__U32^#(mark(X))) , mark^#(isQid(X)) -> c_25(a__isQid^#(X)) , mark^#(U41(X1, X2, X3)) -> c_26(a__U41^#(mark(X1), X2, X3)) , mark^#(U42(X1, X2)) -> c_27(a__U42^#(mark(X1), X2)) , mark^#(U43(X)) -> c_28(a__U43^#(mark(X))) , mark^#(U51(X1, X2, X3)) -> c_29(a__U51^#(mark(X1), X2, X3)) , mark^#(U52(X1, X2)) -> c_30(a__U52^#(mark(X1), X2)) , mark^#(U53(X)) -> c_31(a__U53^#(mark(X))) , mark^#(U61(X1, X2)) -> c_32(a__U61^#(mark(X1), X2)) , mark^#(U62(X)) -> c_33(a__U62^#(mark(X))) , mark^#(U71(X1, X2)) -> c_34(a__U71^#(mark(X1), X2)) , mark^#(U72(X)) -> c_35(a__U72^#(mark(X))) , mark^#(isNePal(X)) -> c_36(a__isNePal^#(X)) , a__isPalListKind^#(X) -> c_90(X) , a__isPalListKind^#(__(V1, V2)) -> c_91(a__and^#(a__isPalListKind(V1), isPalListKind(V2))) , a__isPalListKind^#(nil()) -> c_92() , a__isPalListKind^#(a()) -> c_93() , a__isPalListKind^#(e()) -> c_94() , a__isPalListKind^#(i()) -> c_95() , a__isPalListKind^#(o()) -> c_96() , a__isPalListKind^#(u()) -> c_97() , a__and^#(X1, X2) -> c_88(X1, X2) , a__and^#(tt(), X) -> c_89(mark^#(X)) , a__isPal^#(V) -> c_98(a__U71^#(a__isPalListKind(V), V)) , a__isPal^#(X) -> c_99(X) , a__isPal^#(nil()) -> c_100() , a__U11^#(X1, X2) -> c_37(X1, X2) , a__U11^#(tt(), V) -> c_38(a__U12^#(a__isNeList(V))) , a__U12^#(X) -> c_39(X) , a__U12^#(tt()) -> c_40() , a__isNeList^#(V) -> c_41(a__U31^#(a__isPalListKind(V), V)) , a__isNeList^#(X) -> c_42(X) , a__isNeList^#(__(V1, V2)) -> c_43(a__U41^#(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)) , a__isNeList^#(__(V1, V2)) -> c_44(a__U51^#(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)) , a__U21^#(X1, X2, X3) -> c_45(X1, X2, X3) , a__U21^#(tt(), V1, V2) -> c_46(a__U22^#(a__isList(V1), V2)) , a__U22^#(X1, X2) -> c_47(X1, X2) , a__U22^#(tt(), V2) -> c_48(a__U23^#(a__isList(V2))) , a__isList^#(V) -> c_49(a__U11^#(a__isPalListKind(V), V)) , a__isList^#(X) -> c_50(X) , a__isList^#(__(V1, V2)) -> c_51(a__U21^#(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)) , a__isList^#(nil()) -> c_52() , a__U23^#(X) -> c_53(X) , a__U23^#(tt()) -> c_54() , a__U31^#(X1, X2) -> c_55(X1, X2) , a__U31^#(tt(), V) -> c_56(a__U32^#(a__isQid(V))) , a__U32^#(X) -> c_57(X) , a__U32^#(tt()) -> c_58() , a__isQid^#(X) -> c_59(X) , a__isQid^#(a()) -> c_60() , a__isQid^#(e()) -> c_61() , a__isQid^#(i()) -> c_62() , a__isQid^#(o()) -> c_63() , a__isQid^#(u()) -> c_64() , a__U41^#(X1, X2, X3) -> c_65(X1, X2, X3) , a__U41^#(tt(), V1, V2) -> c_66(a__U42^#(a__isList(V1), V2)) , a__U42^#(X1, X2) -> c_67(X1, X2) , a__U42^#(tt(), V2) -> c_68(a__U43^#(a__isNeList(V2))) , a__U43^#(X) -> c_69(X) , a__U43^#(tt()) -> c_70() , a__U51^#(X1, X2, X3) -> c_71(X1, X2, X3) , a__U51^#(tt(), V1, V2) -> c_72(a__U52^#(a__isNeList(V1), V2)) , a__U52^#(X1, X2) -> c_73(X1, X2) , a__U52^#(tt(), V2) -> c_74(a__U53^#(a__isList(V2))) , a__U53^#(X) -> c_75(X) , a__U53^#(tt()) -> c_76() , a__U61^#(X1, X2) -> c_77(X1, X2) , a__U61^#(tt(), V) -> c_78(a__U62^#(a__isQid(V))) , a__U62^#(X) -> c_79(X) , a__U62^#(tt()) -> c_80() , a__U71^#(X1, X2) -> c_81(X1, X2) , a__U71^#(tt(), V) -> c_82(a__U72^#(a__isNePal(V))) , a__U72^#(X) -> c_83(X) , a__U72^#(tt()) -> c_84() , a__isNePal^#(V) -> c_85(a__U61^#(a__isPalListKind(V), V)) , a__isNePal^#(X) -> c_86(X) , a__isNePal^#(__(I, __(P, I))) -> c_87(a__and^#(a__and(a__isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))) } Strict Trs: { a____(X1, X2) -> __(X1, X2) , a____(X, nil()) -> mark(X) , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) , a____(nil(), X) -> mark(X) , mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) , mark(nil()) -> nil() , mark(tt()) -> tt() , mark(isPalListKind(X)) -> a__isPalListKind(X) , mark(and(X1, X2)) -> a__and(mark(X1), X2) , mark(isPal(X)) -> a__isPal(X) , mark(a()) -> a() , mark(e()) -> e() , mark(i()) -> i() , mark(o()) -> o() , mark(u()) -> u() , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) , mark(U12(X)) -> a__U12(mark(X)) , mark(isNeList(X)) -> a__isNeList(X) , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) , mark(U22(X1, X2)) -> a__U22(mark(X1), X2) , mark(isList(X)) -> a__isList(X) , mark(U23(X)) -> a__U23(mark(X)) , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) , mark(U32(X)) -> a__U32(mark(X)) , mark(isQid(X)) -> a__isQid(X) , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) , mark(U42(X1, X2)) -> a__U42(mark(X1), X2) , mark(U43(X)) -> a__U43(mark(X)) , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) , mark(U52(X1, X2)) -> a__U52(mark(X1), X2) , mark(U53(X)) -> a__U53(mark(X)) , mark(U61(X1, X2)) -> a__U61(mark(X1), X2) , mark(U62(X)) -> a__U62(mark(X)) , mark(U71(X1, X2)) -> a__U71(mark(X1), X2) , mark(U72(X)) -> a__U72(mark(X)) , mark(isNePal(X)) -> a__isNePal(X) , a__U11(X1, X2) -> U11(X1, X2) , a__U11(tt(), V) -> a__U12(a__isNeList(V)) , a__U12(X) -> U12(X) , a__U12(tt()) -> tt() , a__isNeList(V) -> a__U31(a__isPalListKind(V), V) , a__isNeList(X) -> isNeList(X) , a__isNeList(__(V1, V2)) -> a__U41(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2) , a__isNeList(__(V1, V2)) -> a__U51(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2) , a__U21(X1, X2, X3) -> U21(X1, X2, X3) , a__U21(tt(), V1, V2) -> a__U22(a__isList(V1), V2) , a__U22(X1, X2) -> U22(X1, X2) , a__U22(tt(), V2) -> a__U23(a__isList(V2)) , a__isList(V) -> a__U11(a__isPalListKind(V), V) , a__isList(X) -> isList(X) , a__isList(__(V1, V2)) -> a__U21(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2) , a__isList(nil()) -> tt() , a__U23(X) -> U23(X) , a__U23(tt()) -> tt() , a__U31(X1, X2) -> U31(X1, X2) , a__U31(tt(), V) -> a__U32(a__isQid(V)) , a__U32(X) -> U32(X) , a__U32(tt()) -> tt() , a__isQid(X) -> isQid(X) , a__isQid(a()) -> tt() , a__isQid(e()) -> tt() , a__isQid(i()) -> tt() , a__isQid(o()) -> tt() , a__isQid(u()) -> tt() , a__U41(X1, X2, X3) -> U41(X1, X2, X3) , a__U41(tt(), V1, V2) -> a__U42(a__isList(V1), V2) , a__U42(X1, X2) -> U42(X1, X2) , a__U42(tt(), V2) -> a__U43(a__isNeList(V2)) , a__U43(X) -> U43(X) , a__U43(tt()) -> tt() , a__U51(X1, X2, X3) -> U51(X1, X2, X3) , a__U51(tt(), V1, V2) -> a__U52(a__isNeList(V1), V2) , a__U52(X1, X2) -> U52(X1, X2) , a__U52(tt(), V2) -> a__U53(a__isList(V2)) , a__U53(X) -> U53(X) , a__U53(tt()) -> tt() , a__U61(X1, X2) -> U61(X1, X2) , a__U61(tt(), V) -> a__U62(a__isQid(V)) , a__U62(X) -> U62(X) , a__U62(tt()) -> tt() , a__U71(X1, X2) -> U71(X1, X2) , a__U71(tt(), V) -> a__U72(a__isNePal(V)) , a__U72(X) -> U72(X) , a__U72(tt()) -> tt() , a__isNePal(V) -> a__U61(a__isPalListKind(V), V) , a__isNePal(X) -> isNePal(X) , a__isNePal(__(I, __(P, I))) -> a__and(a__and(a__isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P))) , a__and(X1, X2) -> and(X1, X2) , a__and(tt(), X) -> mark(X) , a__isPalListKind(X) -> isPalListKind(X) , a__isPalListKind(__(V1, V2)) -> a__and(a__isPalListKind(V1), isPalListKind(V2)) , a__isPalListKind(nil()) -> tt() , a__isPalListKind(a()) -> tt() , a__isPalListKind(e()) -> tt() , a__isPalListKind(i()) -> tt() , a__isPalListKind(o()) -> tt() , a__isPalListKind(u()) -> tt() , a__isPal(V) -> a__U71(a__isPalListKind(V), V) , a__isPal(X) -> isPal(X) , a__isPal(nil()) -> tt() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {6,7,11,12,13,14,15,39,40,41,42,43,44,49,53,65,67,71,73,74,75,76,77,83,89,93,97} by applications of Pre({6,7,11,12,13,14,15,39,40,41,42,43,44,49,53,65,67,71,73,74,75,76,77,83,89,93,97}) = {1,2,4,8,10,17,21,22,24,25,28,31,33,35,37,45,46,48,50,51,52,55,58,60,61,63,66,68,69,70,72,78,80,81,82,84,86,87,88,90,91,92,94,95,96,99}. Here rules are labeled as follows: DPs: { 1: a____^#(X1, X2) -> c_1(X1, X2) , 2: a____^#(X, nil()) -> c_2(mark^#(X)) , 3: a____^#(__(X, Y), Z) -> c_3(a____^#(mark(X), a____(mark(Y), mark(Z)))) , 4: a____^#(nil(), X) -> c_4(mark^#(X)) , 5: mark^#(__(X1, X2)) -> c_5(a____^#(mark(X1), mark(X2))) , 6: mark^#(nil()) -> c_6() , 7: mark^#(tt()) -> c_7() , 8: mark^#(isPalListKind(X)) -> c_8(a__isPalListKind^#(X)) , 9: mark^#(and(X1, X2)) -> c_9(a__and^#(mark(X1), X2)) , 10: mark^#(isPal(X)) -> c_10(a__isPal^#(X)) , 11: mark^#(a()) -> c_11() , 12: mark^#(e()) -> c_12() , 13: mark^#(i()) -> c_13() , 14: mark^#(o()) -> c_14() , 15: mark^#(u()) -> c_15() , 16: mark^#(U11(X1, X2)) -> c_16(a__U11^#(mark(X1), X2)) , 17: mark^#(U12(X)) -> c_17(a__U12^#(mark(X))) , 18: mark^#(isNeList(X)) -> c_18(a__isNeList^#(X)) , 19: mark^#(U21(X1, X2, X3)) -> c_19(a__U21^#(mark(X1), X2, X3)) , 20: mark^#(U22(X1, X2)) -> c_20(a__U22^#(mark(X1), X2)) , 21: mark^#(isList(X)) -> c_21(a__isList^#(X)) , 22: mark^#(U23(X)) -> c_22(a__U23^#(mark(X))) , 23: mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2)) , 24: mark^#(U32(X)) -> c_24(a__U32^#(mark(X))) , 25: mark^#(isQid(X)) -> c_25(a__isQid^#(X)) , 26: mark^#(U41(X1, X2, X3)) -> c_26(a__U41^#(mark(X1), X2, X3)) , 27: mark^#(U42(X1, X2)) -> c_27(a__U42^#(mark(X1), X2)) , 28: mark^#(U43(X)) -> c_28(a__U43^#(mark(X))) , 29: mark^#(U51(X1, X2, X3)) -> c_29(a__U51^#(mark(X1), X2, X3)) , 30: mark^#(U52(X1, X2)) -> c_30(a__U52^#(mark(X1), X2)) , 31: mark^#(U53(X)) -> c_31(a__U53^#(mark(X))) , 32: mark^#(U61(X1, X2)) -> c_32(a__U61^#(mark(X1), X2)) , 33: mark^#(U62(X)) -> c_33(a__U62^#(mark(X))) , 34: mark^#(U71(X1, X2)) -> c_34(a__U71^#(mark(X1), X2)) , 35: mark^#(U72(X)) -> c_35(a__U72^#(mark(X))) , 36: mark^#(isNePal(X)) -> c_36(a__isNePal^#(X)) , 37: a__isPalListKind^#(X) -> c_90(X) , 38: a__isPalListKind^#(__(V1, V2)) -> c_91(a__and^#(a__isPalListKind(V1), isPalListKind(V2))) , 39: a__isPalListKind^#(nil()) -> c_92() , 40: a__isPalListKind^#(a()) -> c_93() , 41: a__isPalListKind^#(e()) -> c_94() , 42: a__isPalListKind^#(i()) -> c_95() , 43: a__isPalListKind^#(o()) -> c_96() , 44: a__isPalListKind^#(u()) -> c_97() , 45: a__and^#(X1, X2) -> c_88(X1, X2) , 46: a__and^#(tt(), X) -> c_89(mark^#(X)) , 47: a__isPal^#(V) -> c_98(a__U71^#(a__isPalListKind(V), V)) , 48: a__isPal^#(X) -> c_99(X) , 49: a__isPal^#(nil()) -> c_100() , 50: a__U11^#(X1, X2) -> c_37(X1, X2) , 51: a__U11^#(tt(), V) -> c_38(a__U12^#(a__isNeList(V))) , 52: a__U12^#(X) -> c_39(X) , 53: a__U12^#(tt()) -> c_40() , 54: a__isNeList^#(V) -> c_41(a__U31^#(a__isPalListKind(V), V)) , 55: a__isNeList^#(X) -> c_42(X) , 56: a__isNeList^#(__(V1, V2)) -> c_43(a__U41^#(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)) , 57: a__isNeList^#(__(V1, V2)) -> c_44(a__U51^#(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)) , 58: a__U21^#(X1, X2, X3) -> c_45(X1, X2, X3) , 59: a__U21^#(tt(), V1, V2) -> c_46(a__U22^#(a__isList(V1), V2)) , 60: a__U22^#(X1, X2) -> c_47(X1, X2) , 61: a__U22^#(tt(), V2) -> c_48(a__U23^#(a__isList(V2))) , 62: a__isList^#(V) -> c_49(a__U11^#(a__isPalListKind(V), V)) , 63: a__isList^#(X) -> c_50(X) , 64: a__isList^#(__(V1, V2)) -> c_51(a__U21^#(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)) , 65: a__isList^#(nil()) -> c_52() , 66: a__U23^#(X) -> c_53(X) , 67: a__U23^#(tt()) -> c_54() , 68: a__U31^#(X1, X2) -> c_55(X1, X2) , 69: a__U31^#(tt(), V) -> c_56(a__U32^#(a__isQid(V))) , 70: a__U32^#(X) -> c_57(X) , 71: a__U32^#(tt()) -> c_58() , 72: a__isQid^#(X) -> c_59(X) , 73: a__isQid^#(a()) -> c_60() , 74: a__isQid^#(e()) -> c_61() , 75: a__isQid^#(i()) -> c_62() , 76: a__isQid^#(o()) -> c_63() , 77: a__isQid^#(u()) -> c_64() , 78: a__U41^#(X1, X2, X3) -> c_65(X1, X2, X3) , 79: a__U41^#(tt(), V1, V2) -> c_66(a__U42^#(a__isList(V1), V2)) , 80: a__U42^#(X1, X2) -> c_67(X1, X2) , 81: a__U42^#(tt(), V2) -> c_68(a__U43^#(a__isNeList(V2))) , 82: a__U43^#(X) -> c_69(X) , 83: a__U43^#(tt()) -> c_70() , 84: a__U51^#(X1, X2, X3) -> c_71(X1, X2, X3) , 85: a__U51^#(tt(), V1, V2) -> c_72(a__U52^#(a__isNeList(V1), V2)) , 86: a__U52^#(X1, X2) -> c_73(X1, X2) , 87: a__U52^#(tt(), V2) -> c_74(a__U53^#(a__isList(V2))) , 88: a__U53^#(X) -> c_75(X) , 89: a__U53^#(tt()) -> c_76() , 90: a__U61^#(X1, X2) -> c_77(X1, X2) , 91: a__U61^#(tt(), V) -> c_78(a__U62^#(a__isQid(V))) , 92: a__U62^#(X) -> c_79(X) , 93: a__U62^#(tt()) -> c_80() , 94: a__U71^#(X1, X2) -> c_81(X1, X2) , 95: a__U71^#(tt(), V) -> c_82(a__U72^#(a__isNePal(V))) , 96: a__U72^#(X) -> c_83(X) , 97: a__U72^#(tt()) -> c_84() , 98: a__isNePal^#(V) -> c_85(a__U61^#(a__isPalListKind(V), V)) , 99: a__isNePal^#(X) -> c_86(X) , 100: a__isNePal^#(__(I, __(P, I))) -> c_87(a__and^#(a__and(a__isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a____^#(X1, X2) -> c_1(X1, X2) , a____^#(X, nil()) -> c_2(mark^#(X)) , a____^#(__(X, Y), Z) -> c_3(a____^#(mark(X), a____(mark(Y), mark(Z)))) , a____^#(nil(), X) -> c_4(mark^#(X)) , mark^#(__(X1, X2)) -> c_5(a____^#(mark(X1), mark(X2))) , mark^#(isPalListKind(X)) -> c_8(a__isPalListKind^#(X)) , mark^#(and(X1, X2)) -> c_9(a__and^#(mark(X1), X2)) , mark^#(isPal(X)) -> c_10(a__isPal^#(X)) , mark^#(U11(X1, X2)) -> c_16(a__U11^#(mark(X1), X2)) , mark^#(U12(X)) -> c_17(a__U12^#(mark(X))) , mark^#(isNeList(X)) -> c_18(a__isNeList^#(X)) , mark^#(U21(X1, X2, X3)) -> c_19(a__U21^#(mark(X1), X2, X3)) , mark^#(U22(X1, X2)) -> c_20(a__U22^#(mark(X1), X2)) , mark^#(isList(X)) -> c_21(a__isList^#(X)) , mark^#(U23(X)) -> c_22(a__U23^#(mark(X))) , mark^#(U31(X1, X2)) -> c_23(a__U31^#(mark(X1), X2)) , mark^#(U32(X)) -> c_24(a__U32^#(mark(X))) , mark^#(isQid(X)) -> c_25(a__isQid^#(X)) , mark^#(U41(X1, X2, X3)) -> c_26(a__U41^#(mark(X1), X2, X3)) , mark^#(U42(X1, X2)) -> c_27(a__U42^#(mark(X1), X2)) , mark^#(U43(X)) -> c_28(a__U43^#(mark(X))) , mark^#(U51(X1, X2, X3)) -> c_29(a__U51^#(mark(X1), X2, X3)) , mark^#(U52(X1, X2)) -> c_30(a__U52^#(mark(X1), X2)) , mark^#(U53(X)) -> c_31(a__U53^#(mark(X))) , mark^#(U61(X1, X2)) -> c_32(a__U61^#(mark(X1), X2)) , mark^#(U62(X)) -> c_33(a__U62^#(mark(X))) , mark^#(U71(X1, X2)) -> c_34(a__U71^#(mark(X1), X2)) , mark^#(U72(X)) -> c_35(a__U72^#(mark(X))) , mark^#(isNePal(X)) -> c_36(a__isNePal^#(X)) , a__isPalListKind^#(X) -> c_90(X) , a__isPalListKind^#(__(V1, V2)) -> c_91(a__and^#(a__isPalListKind(V1), isPalListKind(V2))) , a__and^#(X1, X2) -> c_88(X1, X2) , a__and^#(tt(), X) -> c_89(mark^#(X)) , a__isPal^#(V) -> c_98(a__U71^#(a__isPalListKind(V), V)) , a__isPal^#(X) -> c_99(X) , a__U11^#(X1, X2) -> c_37(X1, X2) , a__U11^#(tt(), V) -> c_38(a__U12^#(a__isNeList(V))) , a__U12^#(X) -> c_39(X) , a__isNeList^#(V) -> c_41(a__U31^#(a__isPalListKind(V), V)) , a__isNeList^#(X) -> c_42(X) , a__isNeList^#(__(V1, V2)) -> c_43(a__U41^#(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)) , a__isNeList^#(__(V1, V2)) -> c_44(a__U51^#(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)) , a__U21^#(X1, X2, X3) -> c_45(X1, X2, X3) , a__U21^#(tt(), V1, V2) -> c_46(a__U22^#(a__isList(V1), V2)) , a__U22^#(X1, X2) -> c_47(X1, X2) , a__U22^#(tt(), V2) -> c_48(a__U23^#(a__isList(V2))) , a__isList^#(V) -> c_49(a__U11^#(a__isPalListKind(V), V)) , a__isList^#(X) -> c_50(X) , a__isList^#(__(V1, V2)) -> c_51(a__U21^#(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2)) , a__U23^#(X) -> c_53(X) , a__U31^#(X1, X2) -> c_55(X1, X2) , a__U31^#(tt(), V) -> c_56(a__U32^#(a__isQid(V))) , a__U32^#(X) -> c_57(X) , a__isQid^#(X) -> c_59(X) , a__U41^#(X1, X2, X3) -> c_65(X1, X2, X3) , a__U41^#(tt(), V1, V2) -> c_66(a__U42^#(a__isList(V1), V2)) , a__U42^#(X1, X2) -> c_67(X1, X2) , a__U42^#(tt(), V2) -> c_68(a__U43^#(a__isNeList(V2))) , a__U43^#(X) -> c_69(X) , a__U51^#(X1, X2, X3) -> c_71(X1, X2, X3) , a__U51^#(tt(), V1, V2) -> c_72(a__U52^#(a__isNeList(V1), V2)) , a__U52^#(X1, X2) -> c_73(X1, X2) , a__U52^#(tt(), V2) -> c_74(a__U53^#(a__isList(V2))) , a__U53^#(X) -> c_75(X) , a__U61^#(X1, X2) -> c_77(X1, X2) , a__U61^#(tt(), V) -> c_78(a__U62^#(a__isQid(V))) , a__U62^#(X) -> c_79(X) , a__U71^#(X1, X2) -> c_81(X1, X2) , a__U71^#(tt(), V) -> c_82(a__U72^#(a__isNePal(V))) , a__U72^#(X) -> c_83(X) , a__isNePal^#(V) -> c_85(a__U61^#(a__isPalListKind(V), V)) , a__isNePal^#(X) -> c_86(X) , a__isNePal^#(__(I, __(P, I))) -> c_87(a__and^#(a__and(a__isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))) } Strict Trs: { a____(X1, X2) -> __(X1, X2) , a____(X, nil()) -> mark(X) , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) , a____(nil(), X) -> mark(X) , mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) , mark(nil()) -> nil() , mark(tt()) -> tt() , mark(isPalListKind(X)) -> a__isPalListKind(X) , mark(and(X1, X2)) -> a__and(mark(X1), X2) , mark(isPal(X)) -> a__isPal(X) , mark(a()) -> a() , mark(e()) -> e() , mark(i()) -> i() , mark(o()) -> o() , mark(u()) -> u() , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) , mark(U12(X)) -> a__U12(mark(X)) , mark(isNeList(X)) -> a__isNeList(X) , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) , mark(U22(X1, X2)) -> a__U22(mark(X1), X2) , mark(isList(X)) -> a__isList(X) , mark(U23(X)) -> a__U23(mark(X)) , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) , mark(U32(X)) -> a__U32(mark(X)) , mark(isQid(X)) -> a__isQid(X) , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) , mark(U42(X1, X2)) -> a__U42(mark(X1), X2) , mark(U43(X)) -> a__U43(mark(X)) , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) , mark(U52(X1, X2)) -> a__U52(mark(X1), X2) , mark(U53(X)) -> a__U53(mark(X)) , mark(U61(X1, X2)) -> a__U61(mark(X1), X2) , mark(U62(X)) -> a__U62(mark(X)) , mark(U71(X1, X2)) -> a__U71(mark(X1), X2) , mark(U72(X)) -> a__U72(mark(X)) , mark(isNePal(X)) -> a__isNePal(X) , a__U11(X1, X2) -> U11(X1, X2) , a__U11(tt(), V) -> a__U12(a__isNeList(V)) , a__U12(X) -> U12(X) , a__U12(tt()) -> tt() , a__isNeList(V) -> a__U31(a__isPalListKind(V), V) , a__isNeList(X) -> isNeList(X) , a__isNeList(__(V1, V2)) -> a__U41(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2) , a__isNeList(__(V1, V2)) -> a__U51(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2) , a__U21(X1, X2, X3) -> U21(X1, X2, X3) , a__U21(tt(), V1, V2) -> a__U22(a__isList(V1), V2) , a__U22(X1, X2) -> U22(X1, X2) , a__U22(tt(), V2) -> a__U23(a__isList(V2)) , a__isList(V) -> a__U11(a__isPalListKind(V), V) , a__isList(X) -> isList(X) , a__isList(__(V1, V2)) -> a__U21(a__and(a__isPalListKind(V1), isPalListKind(V2)), V1, V2) , a__isList(nil()) -> tt() , a__U23(X) -> U23(X) , a__U23(tt()) -> tt() , a__U31(X1, X2) -> U31(X1, X2) , a__U31(tt(), V) -> a__U32(a__isQid(V)) , a__U32(X) -> U32(X) , a__U32(tt()) -> tt() , a__isQid(X) -> isQid(X) , a__isQid(a()) -> tt() , a__isQid(e()) -> tt() , a__isQid(i()) -> tt() , a__isQid(o()) -> tt() , a__isQid(u()) -> tt() , a__U41(X1, X2, X3) -> U41(X1, X2, X3) , a__U41(tt(), V1, V2) -> a__U42(a__isList(V1), V2) , a__U42(X1, X2) -> U42(X1, X2) , a__U42(tt(), V2) -> a__U43(a__isNeList(V2)) , a__U43(X) -> U43(X) , a__U43(tt()) -> tt() , a__U51(X1, X2, X3) -> U51(X1, X2, X3) , a__U51(tt(), V1, V2) -> a__U52(a__isNeList(V1), V2) , a__U52(X1, X2) -> U52(X1, X2) , a__U52(tt(), V2) -> a__U53(a__isList(V2)) , a__U53(X) -> U53(X) , a__U53(tt()) -> tt() , a__U61(X1, X2) -> U61(X1, X2) , a__U61(tt(), V) -> a__U62(a__isQid(V)) , a__U62(X) -> U62(X) , a__U62(tt()) -> tt() , a__U71(X1, X2) -> U71(X1, X2) , a__U71(tt(), V) -> a__U72(a__isNePal(V)) , a__U72(X) -> U72(X) , a__U72(tt()) -> tt() , a__isNePal(V) -> a__U61(a__isPalListKind(V), V) , a__isNePal(X) -> isNePal(X) , a__isNePal(__(I, __(P, I))) -> a__and(a__and(a__isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P))) , a__and(X1, X2) -> and(X1, X2) , a__and(tt(), X) -> mark(X) , a__isPalListKind(X) -> isPalListKind(X) , a__isPalListKind(__(V1, V2)) -> a__and(a__isPalListKind(V1), isPalListKind(V2)) , a__isPalListKind(nil()) -> tt() , a__isPalListKind(a()) -> tt() , a__isPalListKind(e()) -> tt() , a__isPalListKind(i()) -> tt() , a__isPalListKind(o()) -> tt() , a__isPalListKind(u()) -> tt() , a__isPal(V) -> a__U71(a__isPalListKind(V), V) , a__isPal(X) -> isPal(X) , a__isPal(nil()) -> tt() } Weak DPs: { mark^#(nil()) -> c_6() , mark^#(tt()) -> c_7() , mark^#(a()) -> c_11() , mark^#(e()) -> c_12() , mark^#(i()) -> c_13() , mark^#(o()) -> c_14() , mark^#(u()) -> c_15() , a__isPalListKind^#(nil()) -> c_92() , a__isPalListKind^#(a()) -> c_93() , a__isPalListKind^#(e()) -> c_94() , a__isPalListKind^#(i()) -> c_95() , a__isPalListKind^#(o()) -> c_96() , a__isPalListKind^#(u()) -> c_97() , a__isPal^#(nil()) -> c_100() , a__U12^#(tt()) -> c_40() , a__isList^#(nil()) -> c_52() , a__U23^#(tt()) -> c_54() , a__U32^#(tt()) -> c_58() , a__isQid^#(a()) -> c_60() , a__isQid^#(e()) -> c_61() , a__isQid^#(i()) -> c_62() , a__isQid^#(o()) -> c_63() , a__isQid^#(u()) -> c_64() , a__U43^#(tt()) -> c_70() , a__U53^#(tt()) -> c_76() , a__U62^#(tt()) -> c_80() , a__U72^#(tt()) -> c_84() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. 3) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 30.0 seconds. 2) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 3) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis Arrrr..