MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) , active(U101(tt(), M, N)) -> mark(U102(isNatKind(M), M, N)) , active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) , active(U102(tt(), M, N)) -> mark(U103(isNat(N), M, N)) , active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2)) , active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2)) , active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) , active(isNatKind(0())) -> mark(tt()) , active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) , active(U103(tt(), M, N)) -> mark(U104(isNatKind(N), M, N)) , active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2)) , active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2)) , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) , active(isNat(0())) -> mark(tt()) , active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) , active(U104(tt(), M, N)) -> mark(plus(x(N, M), N)) , active(plus(X1, X2)) -> plus(X1, active(X2)) , active(plus(X1, X2)) -> plus(active(X1), X2) , active(plus(N, s(M))) -> mark(U81(isNat(M), M, N)) , active(plus(N, 0())) -> mark(U71(isNat(N), N)) , active(x(X1, X2)) -> x(X1, active(X2)) , active(x(X1, X2)) -> x(active(X1), X2) , active(x(N, s(M))) -> mark(U101(isNat(M), M, N)) , active(x(N, 0())) -> mark(U91(isNat(N), N)) , active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) , active(U11(tt(), V1, V2)) -> mark(U12(isNatKind(V1), V1, V2)) , active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) , active(U12(tt(), V1, V2)) -> mark(U13(isNatKind(V2), V1, V2)) , active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) , active(U13(tt(), V1, V2)) -> mark(U14(isNatKind(V2), V1, V2)) , active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) , active(U14(tt(), V1, V2)) -> mark(U15(isNat(V1), V2)) , active(U15(X1, X2)) -> U15(active(X1), X2) , active(U15(tt(), V2)) -> mark(U16(isNat(V2))) , active(U16(X)) -> U16(active(X)) , active(U16(tt())) -> mark(tt()) , active(U21(X1, X2)) -> U21(active(X1), X2) , active(U21(tt(), V1)) -> mark(U22(isNatKind(V1), V1)) , active(U22(X1, X2)) -> U22(active(X1), X2) , active(U22(tt(), V1)) -> mark(U23(isNat(V1))) , active(U23(X)) -> U23(active(X)) , active(U23(tt())) -> mark(tt()) , active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) , active(U31(tt(), V1, V2)) -> mark(U32(isNatKind(V1), V1, V2)) , active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) , active(U32(tt(), V1, V2)) -> mark(U33(isNatKind(V2), V1, V2)) , active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) , active(U33(tt(), V1, V2)) -> mark(U34(isNatKind(V2), V1, V2)) , active(U34(X1, X2, X3)) -> U34(active(X1), X2, X3) , active(U34(tt(), V1, V2)) -> mark(U35(isNat(V1), V2)) , active(U35(X1, X2)) -> U35(active(X1), X2) , active(U35(tt(), V2)) -> mark(U36(isNat(V2))) , active(U36(X)) -> U36(active(X)) , active(U36(tt())) -> mark(tt()) , active(U41(X1, X2)) -> U41(active(X1), X2) , active(U41(tt(), V2)) -> mark(U42(isNatKind(V2))) , active(U42(X)) -> U42(active(X)) , active(U42(tt())) -> mark(tt()) , active(U51(X)) -> U51(active(X)) , active(U51(tt())) -> mark(tt()) , active(U61(X1, X2)) -> U61(active(X1), X2) , active(U61(tt(), V2)) -> mark(U62(isNatKind(V2))) , active(U62(X)) -> U62(active(X)) , active(U62(tt())) -> mark(tt()) , active(U71(X1, X2)) -> U71(active(X1), X2) , active(U71(tt(), N)) -> mark(U72(isNatKind(N), N)) , active(U72(X1, X2)) -> U72(active(X1), X2) , active(U72(tt(), N)) -> mark(N) , active(U81(X1, X2, X3)) -> U81(active(X1), X2, X3) , active(U81(tt(), M, N)) -> mark(U82(isNatKind(M), M, N)) , active(U82(X1, X2, X3)) -> U82(active(X1), X2, X3) , active(U82(tt(), M, N)) -> mark(U83(isNat(N), M, N)) , active(U83(X1, X2, X3)) -> U83(active(X1), X2, X3) , active(U83(tt(), M, N)) -> mark(U84(isNatKind(N), M, N)) , active(U84(X1, X2, X3)) -> U84(active(X1), X2, X3) , active(U84(tt(), M, N)) -> mark(s(plus(N, M))) , active(s(X)) -> s(active(X)) , active(U91(X1, X2)) -> U91(active(X1), X2) , active(U91(tt(), N)) -> mark(U92(isNatKind(N))) , active(U92(X)) -> U92(active(X)) , active(U92(tt())) -> mark(0()) , U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) , U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) , U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) , U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) , isNatKind(ok(X)) -> ok(isNatKind(X)) , U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) , U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) , isNat(ok(X)) -> ok(isNat(X)) , U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) , U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) , plus(X1, mark(X2)) -> mark(plus(X1, X2)) , plus(mark(X1), X2) -> mark(plus(X1, X2)) , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) , x(X1, mark(X2)) -> mark(x(X1, X2)) , x(mark(X1), X2) -> mark(x(X1, X2)) , x(ok(X1), ok(X2)) -> ok(x(X1, X2)) , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) , U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) , U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) , U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) , U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) , U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) , U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) , U15(mark(X1), X2) -> mark(U15(X1, X2)) , U15(ok(X1), ok(X2)) -> ok(U15(X1, X2)) , U16(mark(X)) -> mark(U16(X)) , U16(ok(X)) -> ok(U16(X)) , U21(mark(X1), X2) -> mark(U21(X1, X2)) , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)) , U22(mark(X1), X2) -> mark(U22(X1, X2)) , U22(ok(X1), ok(X2)) -> ok(U22(X1, X2)) , U23(mark(X)) -> mark(U23(X)) , U23(ok(X)) -> ok(U23(X)) , U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) , U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) , U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) , U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) , U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) , U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) , U34(mark(X1), X2, X3) -> mark(U34(X1, X2, X3)) , U34(ok(X1), ok(X2), ok(X3)) -> ok(U34(X1, X2, X3)) , U35(mark(X1), X2) -> mark(U35(X1, X2)) , U35(ok(X1), ok(X2)) -> ok(U35(X1, X2)) , U36(mark(X)) -> mark(U36(X)) , U36(ok(X)) -> ok(U36(X)) , U41(mark(X1), X2) -> mark(U41(X1, X2)) , U41(ok(X1), ok(X2)) -> ok(U41(X1, X2)) , U42(mark(X)) -> mark(U42(X)) , U42(ok(X)) -> ok(U42(X)) , U51(mark(X)) -> mark(U51(X)) , U51(ok(X)) -> ok(U51(X)) , U61(mark(X1), X2) -> mark(U61(X1, X2)) , U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) , U62(mark(X)) -> mark(U62(X)) , U62(ok(X)) -> ok(U62(X)) , U71(mark(X1), X2) -> mark(U71(X1, X2)) , U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) , U72(mark(X1), X2) -> mark(U72(X1, X2)) , U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) , U81(mark(X1), X2, X3) -> mark(U81(X1, X2, X3)) , U81(ok(X1), ok(X2), ok(X3)) -> ok(U81(X1, X2, X3)) , U82(mark(X1), X2, X3) -> mark(U82(X1, X2, X3)) , U82(ok(X1), ok(X2), ok(X3)) -> ok(U82(X1, X2, X3)) , U83(mark(X1), X2, X3) -> mark(U83(X1, X2, X3)) , U83(ok(X1), ok(X2), ok(X3)) -> ok(U83(X1, X2, X3)) , U84(mark(X1), X2, X3) -> mark(U84(X1, X2, X3)) , U84(ok(X1), ok(X2), ok(X3)) -> ok(U84(X1, X2, X3)) , s(mark(X)) -> mark(s(X)) , s(ok(X)) -> ok(s(X)) , U91(mark(X1), X2) -> mark(U91(X1, X2)) , U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) , U92(mark(X)) -> mark(U92(X)) , U92(ok(X)) -> ok(U92(X)) , proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) , proper(tt()) -> ok(tt()) , proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) , proper(isNatKind(X)) -> isNatKind(proper(X)) , proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) , proper(isNat(X)) -> isNat(proper(X)) , proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) , proper(x(X1, X2)) -> x(proper(X1), proper(X2)) , proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) , proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) , proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) , proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) , proper(U15(X1, X2)) -> U15(proper(X1), proper(X2)) , proper(U16(X)) -> U16(proper(X)) , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)) , proper(U22(X1, X2)) -> U22(proper(X1), proper(X2)) , proper(U23(X)) -> U23(proper(X)) , proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) , proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) , proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) , proper(U34(X1, X2, X3)) -> U34(proper(X1), proper(X2), proper(X3)) , proper(U35(X1, X2)) -> U35(proper(X1), proper(X2)) , proper(U36(X)) -> U36(proper(X)) , proper(U41(X1, X2)) -> U41(proper(X1), proper(X2)) , proper(U42(X)) -> U42(proper(X)) , proper(U51(X)) -> U51(proper(X)) , proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) , proper(U62(X)) -> U62(proper(X)) , proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) , proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) , proper(U81(X1, X2, X3)) -> U81(proper(X1), proper(X2), proper(X3)) , proper(U82(X1, X2, X3)) -> U82(proper(X1), proper(X2), proper(X3)) , proper(U83(X1, X2, X3)) -> U83(proper(X1), proper(X2), proper(X3)) , proper(U84(X1, X2, X3)) -> U84(proper(X1), proper(X2), proper(X3)) , proper(s(X)) -> s(proper(X)) , proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) , proper(U92(X)) -> U92(proper(X)) , proper(0()) -> ok(0()) , top(mark(X)) -> top(proper(X)) , top(ok(X)) -> top(active(X)) } 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) '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) '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 3) '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 perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { active^#(U101(X1, X2, X3)) -> c_1(U101^#(active(X1), X2, X3)) , active^#(U101(tt(), M, N)) -> c_2(U102^#(isNatKind(M), M, N)) , active^#(U102(X1, X2, X3)) -> c_3(U102^#(active(X1), X2, X3)) , active^#(U102(tt(), M, N)) -> c_4(U103^#(isNat(N), M, N)) , active^#(isNatKind(plus(V1, V2))) -> c_5(U41^#(isNatKind(V1), V2)) , active^#(isNatKind(x(V1, V2))) -> c_6(U61^#(isNatKind(V1), V2)) , active^#(isNatKind(s(V1))) -> c_7(U51^#(isNatKind(V1))) , active^#(isNatKind(0())) -> c_8() , active^#(U103(X1, X2, X3)) -> c_9(U103^#(active(X1), X2, X3)) , active^#(U103(tt(), M, N)) -> c_10(U104^#(isNatKind(N), M, N)) , active^#(isNat(plus(V1, V2))) -> c_11(U11^#(isNatKind(V1), V1, V2)) , active^#(isNat(x(V1, V2))) -> c_12(U31^#(isNatKind(V1), V1, V2)) , active^#(isNat(s(V1))) -> c_13(U21^#(isNatKind(V1), V1)) , active^#(isNat(0())) -> c_14() , active^#(U104(X1, X2, X3)) -> c_15(U104^#(active(X1), X2, X3)) , active^#(U104(tt(), M, N)) -> c_16(plus^#(x(N, M), N)) , active^#(plus(X1, X2)) -> c_17(plus^#(X1, active(X2))) , active^#(plus(X1, X2)) -> c_18(plus^#(active(X1), X2)) , active^#(plus(N, s(M))) -> c_19(U81^#(isNat(M), M, N)) , active^#(plus(N, 0())) -> c_20(U71^#(isNat(N), N)) , active^#(x(X1, X2)) -> c_21(x^#(X1, active(X2))) , active^#(x(X1, X2)) -> c_22(x^#(active(X1), X2)) , active^#(x(N, s(M))) -> c_23(U101^#(isNat(M), M, N)) , active^#(x(N, 0())) -> c_24(U91^#(isNat(N), N)) , active^#(U11(X1, X2, X3)) -> c_25(U11^#(active(X1), X2, X3)) , active^#(U11(tt(), V1, V2)) -> c_26(U12^#(isNatKind(V1), V1, V2)) , active^#(U12(X1, X2, X3)) -> c_27(U12^#(active(X1), X2, X3)) , active^#(U12(tt(), V1, V2)) -> c_28(U13^#(isNatKind(V2), V1, V2)) , active^#(U13(X1, X2, X3)) -> c_29(U13^#(active(X1), X2, X3)) , active^#(U13(tt(), V1, V2)) -> c_30(U14^#(isNatKind(V2), V1, V2)) , active^#(U14(X1, X2, X3)) -> c_31(U14^#(active(X1), X2, X3)) , active^#(U14(tt(), V1, V2)) -> c_32(U15^#(isNat(V1), V2)) , active^#(U15(X1, X2)) -> c_33(U15^#(active(X1), X2)) , active^#(U15(tt(), V2)) -> c_34(U16^#(isNat(V2))) , active^#(U16(X)) -> c_35(U16^#(active(X))) , active^#(U16(tt())) -> c_36() , active^#(U21(X1, X2)) -> c_37(U21^#(active(X1), X2)) , active^#(U21(tt(), V1)) -> c_38(U22^#(isNatKind(V1), V1)) , active^#(U22(X1, X2)) -> c_39(U22^#(active(X1), X2)) , active^#(U22(tt(), V1)) -> c_40(U23^#(isNat(V1))) , active^#(U23(X)) -> c_41(U23^#(active(X))) , active^#(U23(tt())) -> c_42() , active^#(U31(X1, X2, X3)) -> c_43(U31^#(active(X1), X2, X3)) , active^#(U31(tt(), V1, V2)) -> c_44(U32^#(isNatKind(V1), V1, V2)) , active^#(U32(X1, X2, X3)) -> c_45(U32^#(active(X1), X2, X3)) , active^#(U32(tt(), V1, V2)) -> c_46(U33^#(isNatKind(V2), V1, V2)) , active^#(U33(X1, X2, X3)) -> c_47(U33^#(active(X1), X2, X3)) , active^#(U33(tt(), V1, V2)) -> c_48(U34^#(isNatKind(V2), V1, V2)) , active^#(U34(X1, X2, X3)) -> c_49(U34^#(active(X1), X2, X3)) , active^#(U34(tt(), V1, V2)) -> c_50(U35^#(isNat(V1), V2)) , active^#(U35(X1, X2)) -> c_51(U35^#(active(X1), X2)) , active^#(U35(tt(), V2)) -> c_52(U36^#(isNat(V2))) , active^#(U36(X)) -> c_53(U36^#(active(X))) , active^#(U36(tt())) -> c_54() , active^#(U41(X1, X2)) -> c_55(U41^#(active(X1), X2)) , active^#(U41(tt(), V2)) -> c_56(U42^#(isNatKind(V2))) , active^#(U42(X)) -> c_57(U42^#(active(X))) , active^#(U42(tt())) -> c_58() , active^#(U51(X)) -> c_59(U51^#(active(X))) , active^#(U51(tt())) -> c_60() , active^#(U61(X1, X2)) -> c_61(U61^#(active(X1), X2)) , active^#(U61(tt(), V2)) -> c_62(U62^#(isNatKind(V2))) , active^#(U62(X)) -> c_63(U62^#(active(X))) , active^#(U62(tt())) -> c_64() , active^#(U71(X1, X2)) -> c_65(U71^#(active(X1), X2)) , active^#(U71(tt(), N)) -> c_66(U72^#(isNatKind(N), N)) , active^#(U72(X1, X2)) -> c_67(U72^#(active(X1), X2)) , active^#(U72(tt(), N)) -> c_68(N) , active^#(U81(X1, X2, X3)) -> c_69(U81^#(active(X1), X2, X3)) , active^#(U81(tt(), M, N)) -> c_70(U82^#(isNatKind(M), M, N)) , active^#(U82(X1, X2, X3)) -> c_71(U82^#(active(X1), X2, X3)) , active^#(U82(tt(), M, N)) -> c_72(U83^#(isNat(N), M, N)) , active^#(U83(X1, X2, X3)) -> c_73(U83^#(active(X1), X2, X3)) , active^#(U83(tt(), M, N)) -> c_74(U84^#(isNatKind(N), M, N)) , active^#(U84(X1, X2, X3)) -> c_75(U84^#(active(X1), X2, X3)) , active^#(U84(tt(), M, N)) -> c_76(s^#(plus(N, M))) , active^#(s(X)) -> c_77(s^#(active(X))) , active^#(U91(X1, X2)) -> c_78(U91^#(active(X1), X2)) , active^#(U91(tt(), N)) -> c_79(U92^#(isNatKind(N))) , active^#(U92(X)) -> c_80(U92^#(active(X))) , active^#(U92(tt())) -> c_81() , U101^#(mark(X1), X2, X3) -> c_82(U101^#(X1, X2, X3)) , U101^#(ok(X1), ok(X2), ok(X3)) -> c_83(U101^#(X1, X2, X3)) , U102^#(mark(X1), X2, X3) -> c_84(U102^#(X1, X2, X3)) , U102^#(ok(X1), ok(X2), ok(X3)) -> c_85(U102^#(X1, X2, X3)) , U103^#(mark(X1), X2, X3) -> c_87(U103^#(X1, X2, X3)) , U103^#(ok(X1), ok(X2), ok(X3)) -> c_88(U103^#(X1, X2, X3)) , U41^#(mark(X1), X2) -> c_128(U41^#(X1, X2)) , U41^#(ok(X1), ok(X2)) -> c_129(U41^#(X1, X2)) , U61^#(mark(X1), X2) -> c_134(U61^#(X1, X2)) , U61^#(ok(X1), ok(X2)) -> c_135(U61^#(X1, X2)) , U51^#(mark(X)) -> c_132(U51^#(X)) , U51^#(ok(X)) -> c_133(U51^#(X)) , U104^#(mark(X1), X2, X3) -> c_90(U104^#(X1, X2, X3)) , U104^#(ok(X1), ok(X2), ok(X3)) -> c_91(U104^#(X1, X2, X3)) , U11^#(mark(X1), X2, X3) -> c_98(U11^#(X1, X2, X3)) , U11^#(ok(X1), ok(X2), ok(X3)) -> c_99(U11^#(X1, X2, X3)) , U31^#(mark(X1), X2, X3) -> c_116(U31^#(X1, X2, X3)) , U31^#(ok(X1), ok(X2), ok(X3)) -> c_117(U31^#(X1, X2, X3)) , U21^#(mark(X1), X2) -> c_110(U21^#(X1, X2)) , U21^#(ok(X1), ok(X2)) -> c_111(U21^#(X1, X2)) , plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) , plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) , plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) , U81^#(mark(X1), X2, X3) -> c_142(U81^#(X1, X2, X3)) , U81^#(ok(X1), ok(X2), ok(X3)) -> c_143(U81^#(X1, X2, X3)) , U71^#(mark(X1), X2) -> c_138(U71^#(X1, X2)) , U71^#(ok(X1), ok(X2)) -> c_139(U71^#(X1, X2)) , x^#(X1, mark(X2)) -> c_95(x^#(X1, X2)) , x^#(mark(X1), X2) -> c_96(x^#(X1, X2)) , x^#(ok(X1), ok(X2)) -> c_97(x^#(X1, X2)) , U91^#(mark(X1), X2) -> c_152(U91^#(X1, X2)) , U91^#(ok(X1), ok(X2)) -> c_153(U91^#(X1, X2)) , U12^#(mark(X1), X2, X3) -> c_100(U12^#(X1, X2, X3)) , U12^#(ok(X1), ok(X2), ok(X3)) -> c_101(U12^#(X1, X2, X3)) , U13^#(mark(X1), X2, X3) -> c_102(U13^#(X1, X2, X3)) , U13^#(ok(X1), ok(X2), ok(X3)) -> c_103(U13^#(X1, X2, X3)) , U14^#(mark(X1), X2, X3) -> c_104(U14^#(X1, X2, X3)) , U14^#(ok(X1), ok(X2), ok(X3)) -> c_105(U14^#(X1, X2, X3)) , U15^#(mark(X1), X2) -> c_106(U15^#(X1, X2)) , U15^#(ok(X1), ok(X2)) -> c_107(U15^#(X1, X2)) , U16^#(mark(X)) -> c_108(U16^#(X)) , U16^#(ok(X)) -> c_109(U16^#(X)) , U22^#(mark(X1), X2) -> c_112(U22^#(X1, X2)) , U22^#(ok(X1), ok(X2)) -> c_113(U22^#(X1, X2)) , U23^#(mark(X)) -> c_114(U23^#(X)) , U23^#(ok(X)) -> c_115(U23^#(X)) , U32^#(mark(X1), X2, X3) -> c_118(U32^#(X1, X2, X3)) , U32^#(ok(X1), ok(X2), ok(X3)) -> c_119(U32^#(X1, X2, X3)) , U33^#(mark(X1), X2, X3) -> c_120(U33^#(X1, X2, X3)) , U33^#(ok(X1), ok(X2), ok(X3)) -> c_121(U33^#(X1, X2, X3)) , U34^#(mark(X1), X2, X3) -> c_122(U34^#(X1, X2, X3)) , U34^#(ok(X1), ok(X2), ok(X3)) -> c_123(U34^#(X1, X2, X3)) , U35^#(mark(X1), X2) -> c_124(U35^#(X1, X2)) , U35^#(ok(X1), ok(X2)) -> c_125(U35^#(X1, X2)) , U36^#(mark(X)) -> c_126(U36^#(X)) , U36^#(ok(X)) -> c_127(U36^#(X)) , U42^#(mark(X)) -> c_130(U42^#(X)) , U42^#(ok(X)) -> c_131(U42^#(X)) , U62^#(mark(X)) -> c_136(U62^#(X)) , U62^#(ok(X)) -> c_137(U62^#(X)) , U72^#(mark(X1), X2) -> c_140(U72^#(X1, X2)) , U72^#(ok(X1), ok(X2)) -> c_141(U72^#(X1, X2)) , U82^#(mark(X1), X2, X3) -> c_144(U82^#(X1, X2, X3)) , U82^#(ok(X1), ok(X2), ok(X3)) -> c_145(U82^#(X1, X2, X3)) , U83^#(mark(X1), X2, X3) -> c_146(U83^#(X1, X2, X3)) , U83^#(ok(X1), ok(X2), ok(X3)) -> c_147(U83^#(X1, X2, X3)) , U84^#(mark(X1), X2, X3) -> c_148(U84^#(X1, X2, X3)) , U84^#(ok(X1), ok(X2), ok(X3)) -> c_149(U84^#(X1, X2, X3)) , s^#(mark(X)) -> c_150(s^#(X)) , s^#(ok(X)) -> c_151(s^#(X)) , U92^#(mark(X)) -> c_154(U92^#(X)) , U92^#(ok(X)) -> c_155(U92^#(X)) , isNatKind^#(ok(X)) -> c_86(isNatKind^#(X)) , isNat^#(ok(X)) -> c_89(isNat^#(X)) , proper^#(U101(X1, X2, X3)) -> c_156(U101^#(proper(X1), proper(X2), proper(X3))) , proper^#(tt()) -> c_157() , proper^#(U102(X1, X2, X3)) -> c_158(U102^#(proper(X1), proper(X2), proper(X3))) , proper^#(isNatKind(X)) -> c_159(isNatKind^#(proper(X))) , proper^#(U103(X1, X2, X3)) -> c_160(U103^#(proper(X1), proper(X2), proper(X3))) , proper^#(isNat(X)) -> c_161(isNat^#(proper(X))) , proper^#(U104(X1, X2, X3)) -> c_162(U104^#(proper(X1), proper(X2), proper(X3))) , proper^#(plus(X1, X2)) -> c_163(plus^#(proper(X1), proper(X2))) , proper^#(x(X1, X2)) -> c_164(x^#(proper(X1), proper(X2))) , proper^#(U11(X1, X2, X3)) -> c_165(U11^#(proper(X1), proper(X2), proper(X3))) , proper^#(U12(X1, X2, X3)) -> c_166(U12^#(proper(X1), proper(X2), proper(X3))) , proper^#(U13(X1, X2, X3)) -> c_167(U13^#(proper(X1), proper(X2), proper(X3))) , proper^#(U14(X1, X2, X3)) -> c_168(U14^#(proper(X1), proper(X2), proper(X3))) , proper^#(U15(X1, X2)) -> c_169(U15^#(proper(X1), proper(X2))) , proper^#(U16(X)) -> c_170(U16^#(proper(X))) , proper^#(U21(X1, X2)) -> c_171(U21^#(proper(X1), proper(X2))) , proper^#(U22(X1, X2)) -> c_172(U22^#(proper(X1), proper(X2))) , proper^#(U23(X)) -> c_173(U23^#(proper(X))) , proper^#(U31(X1, X2, X3)) -> c_174(U31^#(proper(X1), proper(X2), proper(X3))) , proper^#(U32(X1, X2, X3)) -> c_175(U32^#(proper(X1), proper(X2), proper(X3))) , proper^#(U33(X1, X2, X3)) -> c_176(U33^#(proper(X1), proper(X2), proper(X3))) , proper^#(U34(X1, X2, X3)) -> c_177(U34^#(proper(X1), proper(X2), proper(X3))) , proper^#(U35(X1, X2)) -> c_178(U35^#(proper(X1), proper(X2))) , proper^#(U36(X)) -> c_179(U36^#(proper(X))) , proper^#(U41(X1, X2)) -> c_180(U41^#(proper(X1), proper(X2))) , proper^#(U42(X)) -> c_181(U42^#(proper(X))) , proper^#(U51(X)) -> c_182(U51^#(proper(X))) , proper^#(U61(X1, X2)) -> c_183(U61^#(proper(X1), proper(X2))) , proper^#(U62(X)) -> c_184(U62^#(proper(X))) , proper^#(U71(X1, X2)) -> c_185(U71^#(proper(X1), proper(X2))) , proper^#(U72(X1, X2)) -> c_186(U72^#(proper(X1), proper(X2))) , proper^#(U81(X1, X2, X3)) -> c_187(U81^#(proper(X1), proper(X2), proper(X3))) , proper^#(U82(X1, X2, X3)) -> c_188(U82^#(proper(X1), proper(X2), proper(X3))) , proper^#(U83(X1, X2, X3)) -> c_189(U83^#(proper(X1), proper(X2), proper(X3))) , proper^#(U84(X1, X2, X3)) -> c_190(U84^#(proper(X1), proper(X2), proper(X3))) , proper^#(s(X)) -> c_191(s^#(proper(X))) , proper^#(U91(X1, X2)) -> c_192(U91^#(proper(X1), proper(X2))) , proper^#(U92(X)) -> c_193(U92^#(proper(X))) , proper^#(0()) -> c_194() , top^#(mark(X)) -> c_195(top^#(proper(X))) , top^#(ok(X)) -> c_196(top^#(active(X))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { active^#(U101(X1, X2, X3)) -> c_1(U101^#(active(X1), X2, X3)) , active^#(U101(tt(), M, N)) -> c_2(U102^#(isNatKind(M), M, N)) , active^#(U102(X1, X2, X3)) -> c_3(U102^#(active(X1), X2, X3)) , active^#(U102(tt(), M, N)) -> c_4(U103^#(isNat(N), M, N)) , active^#(isNatKind(plus(V1, V2))) -> c_5(U41^#(isNatKind(V1), V2)) , active^#(isNatKind(x(V1, V2))) -> c_6(U61^#(isNatKind(V1), V2)) , active^#(isNatKind(s(V1))) -> c_7(U51^#(isNatKind(V1))) , active^#(isNatKind(0())) -> c_8() , active^#(U103(X1, X2, X3)) -> c_9(U103^#(active(X1), X2, X3)) , active^#(U103(tt(), M, N)) -> c_10(U104^#(isNatKind(N), M, N)) , active^#(isNat(plus(V1, V2))) -> c_11(U11^#(isNatKind(V1), V1, V2)) , active^#(isNat(x(V1, V2))) -> c_12(U31^#(isNatKind(V1), V1, V2)) , active^#(isNat(s(V1))) -> c_13(U21^#(isNatKind(V1), V1)) , active^#(isNat(0())) -> c_14() , active^#(U104(X1, X2, X3)) -> c_15(U104^#(active(X1), X2, X3)) , active^#(U104(tt(), M, N)) -> c_16(plus^#(x(N, M), N)) , active^#(plus(X1, X2)) -> c_17(plus^#(X1, active(X2))) , active^#(plus(X1, X2)) -> c_18(plus^#(active(X1), X2)) , active^#(plus(N, s(M))) -> c_19(U81^#(isNat(M), M, N)) , active^#(plus(N, 0())) -> c_20(U71^#(isNat(N), N)) , active^#(x(X1, X2)) -> c_21(x^#(X1, active(X2))) , active^#(x(X1, X2)) -> c_22(x^#(active(X1), X2)) , active^#(x(N, s(M))) -> c_23(U101^#(isNat(M), M, N)) , active^#(x(N, 0())) -> c_24(U91^#(isNat(N), N)) , active^#(U11(X1, X2, X3)) -> c_25(U11^#(active(X1), X2, X3)) , active^#(U11(tt(), V1, V2)) -> c_26(U12^#(isNatKind(V1), V1, V2)) , active^#(U12(X1, X2, X3)) -> c_27(U12^#(active(X1), X2, X3)) , active^#(U12(tt(), V1, V2)) -> c_28(U13^#(isNatKind(V2), V1, V2)) , active^#(U13(X1, X2, X3)) -> c_29(U13^#(active(X1), X2, X3)) , active^#(U13(tt(), V1, V2)) -> c_30(U14^#(isNatKind(V2), V1, V2)) , active^#(U14(X1, X2, X3)) -> c_31(U14^#(active(X1), X2, X3)) , active^#(U14(tt(), V1, V2)) -> c_32(U15^#(isNat(V1), V2)) , active^#(U15(X1, X2)) -> c_33(U15^#(active(X1), X2)) , active^#(U15(tt(), V2)) -> c_34(U16^#(isNat(V2))) , active^#(U16(X)) -> c_35(U16^#(active(X))) , active^#(U16(tt())) -> c_36() , active^#(U21(X1, X2)) -> c_37(U21^#(active(X1), X2)) , active^#(U21(tt(), V1)) -> c_38(U22^#(isNatKind(V1), V1)) , active^#(U22(X1, X2)) -> c_39(U22^#(active(X1), X2)) , active^#(U22(tt(), V1)) -> c_40(U23^#(isNat(V1))) , active^#(U23(X)) -> c_41(U23^#(active(X))) , active^#(U23(tt())) -> c_42() , active^#(U31(X1, X2, X3)) -> c_43(U31^#(active(X1), X2, X3)) , active^#(U31(tt(), V1, V2)) -> c_44(U32^#(isNatKind(V1), V1, V2)) , active^#(U32(X1, X2, X3)) -> c_45(U32^#(active(X1), X2, X3)) , active^#(U32(tt(), V1, V2)) -> c_46(U33^#(isNatKind(V2), V1, V2)) , active^#(U33(X1, X2, X3)) -> c_47(U33^#(active(X1), X2, X3)) , active^#(U33(tt(), V1, V2)) -> c_48(U34^#(isNatKind(V2), V1, V2)) , active^#(U34(X1, X2, X3)) -> c_49(U34^#(active(X1), X2, X3)) , active^#(U34(tt(), V1, V2)) -> c_50(U35^#(isNat(V1), V2)) , active^#(U35(X1, X2)) -> c_51(U35^#(active(X1), X2)) , active^#(U35(tt(), V2)) -> c_52(U36^#(isNat(V2))) , active^#(U36(X)) -> c_53(U36^#(active(X))) , active^#(U36(tt())) -> c_54() , active^#(U41(X1, X2)) -> c_55(U41^#(active(X1), X2)) , active^#(U41(tt(), V2)) -> c_56(U42^#(isNatKind(V2))) , active^#(U42(X)) -> c_57(U42^#(active(X))) , active^#(U42(tt())) -> c_58() , active^#(U51(X)) -> c_59(U51^#(active(X))) , active^#(U51(tt())) -> c_60() , active^#(U61(X1, X2)) -> c_61(U61^#(active(X1), X2)) , active^#(U61(tt(), V2)) -> c_62(U62^#(isNatKind(V2))) , active^#(U62(X)) -> c_63(U62^#(active(X))) , active^#(U62(tt())) -> c_64() , active^#(U71(X1, X2)) -> c_65(U71^#(active(X1), X2)) , active^#(U71(tt(), N)) -> c_66(U72^#(isNatKind(N), N)) , active^#(U72(X1, X2)) -> c_67(U72^#(active(X1), X2)) , active^#(U72(tt(), N)) -> c_68(N) , active^#(U81(X1, X2, X3)) -> c_69(U81^#(active(X1), X2, X3)) , active^#(U81(tt(), M, N)) -> c_70(U82^#(isNatKind(M), M, N)) , active^#(U82(X1, X2, X3)) -> c_71(U82^#(active(X1), X2, X3)) , active^#(U82(tt(), M, N)) -> c_72(U83^#(isNat(N), M, N)) , active^#(U83(X1, X2, X3)) -> c_73(U83^#(active(X1), X2, X3)) , active^#(U83(tt(), M, N)) -> c_74(U84^#(isNatKind(N), M, N)) , active^#(U84(X1, X2, X3)) -> c_75(U84^#(active(X1), X2, X3)) , active^#(U84(tt(), M, N)) -> c_76(s^#(plus(N, M))) , active^#(s(X)) -> c_77(s^#(active(X))) , active^#(U91(X1, X2)) -> c_78(U91^#(active(X1), X2)) , active^#(U91(tt(), N)) -> c_79(U92^#(isNatKind(N))) , active^#(U92(X)) -> c_80(U92^#(active(X))) , active^#(U92(tt())) -> c_81() , U101^#(mark(X1), X2, X3) -> c_82(U101^#(X1, X2, X3)) , U101^#(ok(X1), ok(X2), ok(X3)) -> c_83(U101^#(X1, X2, X3)) , U102^#(mark(X1), X2, X3) -> c_84(U102^#(X1, X2, X3)) , U102^#(ok(X1), ok(X2), ok(X3)) -> c_85(U102^#(X1, X2, X3)) , U103^#(mark(X1), X2, X3) -> c_87(U103^#(X1, X2, X3)) , U103^#(ok(X1), ok(X2), ok(X3)) -> c_88(U103^#(X1, X2, X3)) , U41^#(mark(X1), X2) -> c_128(U41^#(X1, X2)) , U41^#(ok(X1), ok(X2)) -> c_129(U41^#(X1, X2)) , U61^#(mark(X1), X2) -> c_134(U61^#(X1, X2)) , U61^#(ok(X1), ok(X2)) -> c_135(U61^#(X1, X2)) , U51^#(mark(X)) -> c_132(U51^#(X)) , U51^#(ok(X)) -> c_133(U51^#(X)) , U104^#(mark(X1), X2, X3) -> c_90(U104^#(X1, X2, X3)) , U104^#(ok(X1), ok(X2), ok(X3)) -> c_91(U104^#(X1, X2, X3)) , U11^#(mark(X1), X2, X3) -> c_98(U11^#(X1, X2, X3)) , U11^#(ok(X1), ok(X2), ok(X3)) -> c_99(U11^#(X1, X2, X3)) , U31^#(mark(X1), X2, X3) -> c_116(U31^#(X1, X2, X3)) , U31^#(ok(X1), ok(X2), ok(X3)) -> c_117(U31^#(X1, X2, X3)) , U21^#(mark(X1), X2) -> c_110(U21^#(X1, X2)) , U21^#(ok(X1), ok(X2)) -> c_111(U21^#(X1, X2)) , plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) , plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) , plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) , U81^#(mark(X1), X2, X3) -> c_142(U81^#(X1, X2, X3)) , U81^#(ok(X1), ok(X2), ok(X3)) -> c_143(U81^#(X1, X2, X3)) , U71^#(mark(X1), X2) -> c_138(U71^#(X1, X2)) , U71^#(ok(X1), ok(X2)) -> c_139(U71^#(X1, X2)) , x^#(X1, mark(X2)) -> c_95(x^#(X1, X2)) , x^#(mark(X1), X2) -> c_96(x^#(X1, X2)) , x^#(ok(X1), ok(X2)) -> c_97(x^#(X1, X2)) , U91^#(mark(X1), X2) -> c_152(U91^#(X1, X2)) , U91^#(ok(X1), ok(X2)) -> c_153(U91^#(X1, X2)) , U12^#(mark(X1), X2, X3) -> c_100(U12^#(X1, X2, X3)) , U12^#(ok(X1), ok(X2), ok(X3)) -> c_101(U12^#(X1, X2, X3)) , U13^#(mark(X1), X2, X3) -> c_102(U13^#(X1, X2, X3)) , U13^#(ok(X1), ok(X2), ok(X3)) -> c_103(U13^#(X1, X2, X3)) , U14^#(mark(X1), X2, X3) -> c_104(U14^#(X1, X2, X3)) , U14^#(ok(X1), ok(X2), ok(X3)) -> c_105(U14^#(X1, X2, X3)) , U15^#(mark(X1), X2) -> c_106(U15^#(X1, X2)) , U15^#(ok(X1), ok(X2)) -> c_107(U15^#(X1, X2)) , U16^#(mark(X)) -> c_108(U16^#(X)) , U16^#(ok(X)) -> c_109(U16^#(X)) , U22^#(mark(X1), X2) -> c_112(U22^#(X1, X2)) , U22^#(ok(X1), ok(X2)) -> c_113(U22^#(X1, X2)) , U23^#(mark(X)) -> c_114(U23^#(X)) , U23^#(ok(X)) -> c_115(U23^#(X)) , U32^#(mark(X1), X2, X3) -> c_118(U32^#(X1, X2, X3)) , U32^#(ok(X1), ok(X2), ok(X3)) -> c_119(U32^#(X1, X2, X3)) , U33^#(mark(X1), X2, X3) -> c_120(U33^#(X1, X2, X3)) , U33^#(ok(X1), ok(X2), ok(X3)) -> c_121(U33^#(X1, X2, X3)) , U34^#(mark(X1), X2, X3) -> c_122(U34^#(X1, X2, X3)) , U34^#(ok(X1), ok(X2), ok(X3)) -> c_123(U34^#(X1, X2, X3)) , U35^#(mark(X1), X2) -> c_124(U35^#(X1, X2)) , U35^#(ok(X1), ok(X2)) -> c_125(U35^#(X1, X2)) , U36^#(mark(X)) -> c_126(U36^#(X)) , U36^#(ok(X)) -> c_127(U36^#(X)) , U42^#(mark(X)) -> c_130(U42^#(X)) , U42^#(ok(X)) -> c_131(U42^#(X)) , U62^#(mark(X)) -> c_136(U62^#(X)) , U62^#(ok(X)) -> c_137(U62^#(X)) , U72^#(mark(X1), X2) -> c_140(U72^#(X1, X2)) , U72^#(ok(X1), ok(X2)) -> c_141(U72^#(X1, X2)) , U82^#(mark(X1), X2, X3) -> c_144(U82^#(X1, X2, X3)) , U82^#(ok(X1), ok(X2), ok(X3)) -> c_145(U82^#(X1, X2, X3)) , U83^#(mark(X1), X2, X3) -> c_146(U83^#(X1, X2, X3)) , U83^#(ok(X1), ok(X2), ok(X3)) -> c_147(U83^#(X1, X2, X3)) , U84^#(mark(X1), X2, X3) -> c_148(U84^#(X1, X2, X3)) , U84^#(ok(X1), ok(X2), ok(X3)) -> c_149(U84^#(X1, X2, X3)) , s^#(mark(X)) -> c_150(s^#(X)) , s^#(ok(X)) -> c_151(s^#(X)) , U92^#(mark(X)) -> c_154(U92^#(X)) , U92^#(ok(X)) -> c_155(U92^#(X)) , isNatKind^#(ok(X)) -> c_86(isNatKind^#(X)) , isNat^#(ok(X)) -> c_89(isNat^#(X)) , proper^#(U101(X1, X2, X3)) -> c_156(U101^#(proper(X1), proper(X2), proper(X3))) , proper^#(tt()) -> c_157() , proper^#(U102(X1, X2, X3)) -> c_158(U102^#(proper(X1), proper(X2), proper(X3))) , proper^#(isNatKind(X)) -> c_159(isNatKind^#(proper(X))) , proper^#(U103(X1, X2, X3)) -> c_160(U103^#(proper(X1), proper(X2), proper(X3))) , proper^#(isNat(X)) -> c_161(isNat^#(proper(X))) , proper^#(U104(X1, X2, X3)) -> c_162(U104^#(proper(X1), proper(X2), proper(X3))) , proper^#(plus(X1, X2)) -> c_163(plus^#(proper(X1), proper(X2))) , proper^#(x(X1, X2)) -> c_164(x^#(proper(X1), proper(X2))) , proper^#(U11(X1, X2, X3)) -> c_165(U11^#(proper(X1), proper(X2), proper(X3))) , proper^#(U12(X1, X2, X3)) -> c_166(U12^#(proper(X1), proper(X2), proper(X3))) , proper^#(U13(X1, X2, X3)) -> c_167(U13^#(proper(X1), proper(X2), proper(X3))) , proper^#(U14(X1, X2, X3)) -> c_168(U14^#(proper(X1), proper(X2), proper(X3))) , proper^#(U15(X1, X2)) -> c_169(U15^#(proper(X1), proper(X2))) , proper^#(U16(X)) -> c_170(U16^#(proper(X))) , proper^#(U21(X1, X2)) -> c_171(U21^#(proper(X1), proper(X2))) , proper^#(U22(X1, X2)) -> c_172(U22^#(proper(X1), proper(X2))) , proper^#(U23(X)) -> c_173(U23^#(proper(X))) , proper^#(U31(X1, X2, X3)) -> c_174(U31^#(proper(X1), proper(X2), proper(X3))) , proper^#(U32(X1, X2, X3)) -> c_175(U32^#(proper(X1), proper(X2), proper(X3))) , proper^#(U33(X1, X2, X3)) -> c_176(U33^#(proper(X1), proper(X2), proper(X3))) , proper^#(U34(X1, X2, X3)) -> c_177(U34^#(proper(X1), proper(X2), proper(X3))) , proper^#(U35(X1, X2)) -> c_178(U35^#(proper(X1), proper(X2))) , proper^#(U36(X)) -> c_179(U36^#(proper(X))) , proper^#(U41(X1, X2)) -> c_180(U41^#(proper(X1), proper(X2))) , proper^#(U42(X)) -> c_181(U42^#(proper(X))) , proper^#(U51(X)) -> c_182(U51^#(proper(X))) , proper^#(U61(X1, X2)) -> c_183(U61^#(proper(X1), proper(X2))) , proper^#(U62(X)) -> c_184(U62^#(proper(X))) , proper^#(U71(X1, X2)) -> c_185(U71^#(proper(X1), proper(X2))) , proper^#(U72(X1, X2)) -> c_186(U72^#(proper(X1), proper(X2))) , proper^#(U81(X1, X2, X3)) -> c_187(U81^#(proper(X1), proper(X2), proper(X3))) , proper^#(U82(X1, X2, X3)) -> c_188(U82^#(proper(X1), proper(X2), proper(X3))) , proper^#(U83(X1, X2, X3)) -> c_189(U83^#(proper(X1), proper(X2), proper(X3))) , proper^#(U84(X1, X2, X3)) -> c_190(U84^#(proper(X1), proper(X2), proper(X3))) , proper^#(s(X)) -> c_191(s^#(proper(X))) , proper^#(U91(X1, X2)) -> c_192(U91^#(proper(X1), proper(X2))) , proper^#(U92(X)) -> c_193(U92^#(proper(X))) , proper^#(0()) -> c_194() , top^#(mark(X)) -> c_195(top^#(proper(X))) , top^#(ok(X)) -> c_196(top^#(active(X))) } Strict Trs: { active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) , active(U101(tt(), M, N)) -> mark(U102(isNatKind(M), M, N)) , active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) , active(U102(tt(), M, N)) -> mark(U103(isNat(N), M, N)) , active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2)) , active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2)) , active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) , active(isNatKind(0())) -> mark(tt()) , active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) , active(U103(tt(), M, N)) -> mark(U104(isNatKind(N), M, N)) , active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2)) , active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2)) , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) , active(isNat(0())) -> mark(tt()) , active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) , active(U104(tt(), M, N)) -> mark(plus(x(N, M), N)) , active(plus(X1, X2)) -> plus(X1, active(X2)) , active(plus(X1, X2)) -> plus(active(X1), X2) , active(plus(N, s(M))) -> mark(U81(isNat(M), M, N)) , active(plus(N, 0())) -> mark(U71(isNat(N), N)) , active(x(X1, X2)) -> x(X1, active(X2)) , active(x(X1, X2)) -> x(active(X1), X2) , active(x(N, s(M))) -> mark(U101(isNat(M), M, N)) , active(x(N, 0())) -> mark(U91(isNat(N), N)) , active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) , active(U11(tt(), V1, V2)) -> mark(U12(isNatKind(V1), V1, V2)) , active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) , active(U12(tt(), V1, V2)) -> mark(U13(isNatKind(V2), V1, V2)) , active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) , active(U13(tt(), V1, V2)) -> mark(U14(isNatKind(V2), V1, V2)) , active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) , active(U14(tt(), V1, V2)) -> mark(U15(isNat(V1), V2)) , active(U15(X1, X2)) -> U15(active(X1), X2) , active(U15(tt(), V2)) -> mark(U16(isNat(V2))) , active(U16(X)) -> U16(active(X)) , active(U16(tt())) -> mark(tt()) , active(U21(X1, X2)) -> U21(active(X1), X2) , active(U21(tt(), V1)) -> mark(U22(isNatKind(V1), V1)) , active(U22(X1, X2)) -> U22(active(X1), X2) , active(U22(tt(), V1)) -> mark(U23(isNat(V1))) , active(U23(X)) -> U23(active(X)) , active(U23(tt())) -> mark(tt()) , active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) , active(U31(tt(), V1, V2)) -> mark(U32(isNatKind(V1), V1, V2)) , active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) , active(U32(tt(), V1, V2)) -> mark(U33(isNatKind(V2), V1, V2)) , active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) , active(U33(tt(), V1, V2)) -> mark(U34(isNatKind(V2), V1, V2)) , active(U34(X1, X2, X3)) -> U34(active(X1), X2, X3) , active(U34(tt(), V1, V2)) -> mark(U35(isNat(V1), V2)) , active(U35(X1, X2)) -> U35(active(X1), X2) , active(U35(tt(), V2)) -> mark(U36(isNat(V2))) , active(U36(X)) -> U36(active(X)) , active(U36(tt())) -> mark(tt()) , active(U41(X1, X2)) -> U41(active(X1), X2) , active(U41(tt(), V2)) -> mark(U42(isNatKind(V2))) , active(U42(X)) -> U42(active(X)) , active(U42(tt())) -> mark(tt()) , active(U51(X)) -> U51(active(X)) , active(U51(tt())) -> mark(tt()) , active(U61(X1, X2)) -> U61(active(X1), X2) , active(U61(tt(), V2)) -> mark(U62(isNatKind(V2))) , active(U62(X)) -> U62(active(X)) , active(U62(tt())) -> mark(tt()) , active(U71(X1, X2)) -> U71(active(X1), X2) , active(U71(tt(), N)) -> mark(U72(isNatKind(N), N)) , active(U72(X1, X2)) -> U72(active(X1), X2) , active(U72(tt(), N)) -> mark(N) , active(U81(X1, X2, X3)) -> U81(active(X1), X2, X3) , active(U81(tt(), M, N)) -> mark(U82(isNatKind(M), M, N)) , active(U82(X1, X2, X3)) -> U82(active(X1), X2, X3) , active(U82(tt(), M, N)) -> mark(U83(isNat(N), M, N)) , active(U83(X1, X2, X3)) -> U83(active(X1), X2, X3) , active(U83(tt(), M, N)) -> mark(U84(isNatKind(N), M, N)) , active(U84(X1, X2, X3)) -> U84(active(X1), X2, X3) , active(U84(tt(), M, N)) -> mark(s(plus(N, M))) , active(s(X)) -> s(active(X)) , active(U91(X1, X2)) -> U91(active(X1), X2) , active(U91(tt(), N)) -> mark(U92(isNatKind(N))) , active(U92(X)) -> U92(active(X)) , active(U92(tt())) -> mark(0()) , U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) , U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) , U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) , U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) , isNatKind(ok(X)) -> ok(isNatKind(X)) , U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) , U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) , isNat(ok(X)) -> ok(isNat(X)) , U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) , U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) , plus(X1, mark(X2)) -> mark(plus(X1, X2)) , plus(mark(X1), X2) -> mark(plus(X1, X2)) , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) , x(X1, mark(X2)) -> mark(x(X1, X2)) , x(mark(X1), X2) -> mark(x(X1, X2)) , x(ok(X1), ok(X2)) -> ok(x(X1, X2)) , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) , U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) , U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) , U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) , U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) , U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) , U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) , U15(mark(X1), X2) -> mark(U15(X1, X2)) , U15(ok(X1), ok(X2)) -> ok(U15(X1, X2)) , U16(mark(X)) -> mark(U16(X)) , U16(ok(X)) -> ok(U16(X)) , U21(mark(X1), X2) -> mark(U21(X1, X2)) , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)) , U22(mark(X1), X2) -> mark(U22(X1, X2)) , U22(ok(X1), ok(X2)) -> ok(U22(X1, X2)) , U23(mark(X)) -> mark(U23(X)) , U23(ok(X)) -> ok(U23(X)) , U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) , U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) , U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) , U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) , U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) , U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) , U34(mark(X1), X2, X3) -> mark(U34(X1, X2, X3)) , U34(ok(X1), ok(X2), ok(X3)) -> ok(U34(X1, X2, X3)) , U35(mark(X1), X2) -> mark(U35(X1, X2)) , U35(ok(X1), ok(X2)) -> ok(U35(X1, X2)) , U36(mark(X)) -> mark(U36(X)) , U36(ok(X)) -> ok(U36(X)) , U41(mark(X1), X2) -> mark(U41(X1, X2)) , U41(ok(X1), ok(X2)) -> ok(U41(X1, X2)) , U42(mark(X)) -> mark(U42(X)) , U42(ok(X)) -> ok(U42(X)) , U51(mark(X)) -> mark(U51(X)) , U51(ok(X)) -> ok(U51(X)) , U61(mark(X1), X2) -> mark(U61(X1, X2)) , U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) , U62(mark(X)) -> mark(U62(X)) , U62(ok(X)) -> ok(U62(X)) , U71(mark(X1), X2) -> mark(U71(X1, X2)) , U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) , U72(mark(X1), X2) -> mark(U72(X1, X2)) , U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) , U81(mark(X1), X2, X3) -> mark(U81(X1, X2, X3)) , U81(ok(X1), ok(X2), ok(X3)) -> ok(U81(X1, X2, X3)) , U82(mark(X1), X2, X3) -> mark(U82(X1, X2, X3)) , U82(ok(X1), ok(X2), ok(X3)) -> ok(U82(X1, X2, X3)) , U83(mark(X1), X2, X3) -> mark(U83(X1, X2, X3)) , U83(ok(X1), ok(X2), ok(X3)) -> ok(U83(X1, X2, X3)) , U84(mark(X1), X2, X3) -> mark(U84(X1, X2, X3)) , U84(ok(X1), ok(X2), ok(X3)) -> ok(U84(X1, X2, X3)) , s(mark(X)) -> mark(s(X)) , s(ok(X)) -> ok(s(X)) , U91(mark(X1), X2) -> mark(U91(X1, X2)) , U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) , U92(mark(X)) -> mark(U92(X)) , U92(ok(X)) -> ok(U92(X)) , proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) , proper(tt()) -> ok(tt()) , proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) , proper(isNatKind(X)) -> isNatKind(proper(X)) , proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) , proper(isNat(X)) -> isNat(proper(X)) , proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) , proper(x(X1, X2)) -> x(proper(X1), proper(X2)) , proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) , proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) , proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) , proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) , proper(U15(X1, X2)) -> U15(proper(X1), proper(X2)) , proper(U16(X)) -> U16(proper(X)) , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)) , proper(U22(X1, X2)) -> U22(proper(X1), proper(X2)) , proper(U23(X)) -> U23(proper(X)) , proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) , proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) , proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) , proper(U34(X1, X2, X3)) -> U34(proper(X1), proper(X2), proper(X3)) , proper(U35(X1, X2)) -> U35(proper(X1), proper(X2)) , proper(U36(X)) -> U36(proper(X)) , proper(U41(X1, X2)) -> U41(proper(X1), proper(X2)) , proper(U42(X)) -> U42(proper(X)) , proper(U51(X)) -> U51(proper(X)) , proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) , proper(U62(X)) -> U62(proper(X)) , proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) , proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) , proper(U81(X1, X2, X3)) -> U81(proper(X1), proper(X2), proper(X3)) , proper(U82(X1, X2, X3)) -> U82(proper(X1), proper(X2), proper(X3)) , proper(U83(X1, X2, X3)) -> U83(proper(X1), proper(X2), proper(X3)) , proper(U84(X1, X2, X3)) -> U84(proper(X1), proper(X2), proper(X3)) , proper(s(X)) -> s(proper(X)) , proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) , proper(U92(X)) -> U92(proper(X)) , proper(0()) -> ok(0()) , top(mark(X)) -> top(proper(X)) , top(ok(X)) -> top(active(X)) } Obligation: runtime complexity Answer: MAYBE Consider the dependency graph: 1: active^#(U101(X1, X2, X3)) -> c_1(U101^#(active(X1), X2, X3)) -->_1 U101^#(ok(X1), ok(X2), ok(X3)) -> c_83(U101^#(X1, X2, X3)) :83 -->_1 U101^#(mark(X1), X2, X3) -> c_82(U101^#(X1, X2, X3)) :82 2: active^#(U101(tt(), M, N)) -> c_2(U102^#(isNatKind(M), M, N)) -->_1 U102^#(ok(X1), ok(X2), ok(X3)) -> c_85(U102^#(X1, X2, X3)) :85 -->_1 U102^#(mark(X1), X2, X3) -> c_84(U102^#(X1, X2, X3)) :84 3: active^#(U102(X1, X2, X3)) -> c_3(U102^#(active(X1), X2, X3)) -->_1 U102^#(ok(X1), ok(X2), ok(X3)) -> c_85(U102^#(X1, X2, X3)) :85 -->_1 U102^#(mark(X1), X2, X3) -> c_84(U102^#(X1, X2, X3)) :84 4: active^#(U102(tt(), M, N)) -> c_4(U103^#(isNat(N), M, N)) -->_1 U103^#(ok(X1), ok(X2), ok(X3)) -> c_88(U103^#(X1, X2, X3)) :87 -->_1 U103^#(mark(X1), X2, X3) -> c_87(U103^#(X1, X2, X3)) :86 5: active^#(isNatKind(plus(V1, V2))) -> c_5(U41^#(isNatKind(V1), V2)) -->_1 U41^#(ok(X1), ok(X2)) -> c_129(U41^#(X1, X2)) :89 -->_1 U41^#(mark(X1), X2) -> c_128(U41^#(X1, X2)) :88 6: active^#(isNatKind(x(V1, V2))) -> c_6(U61^#(isNatKind(V1), V2)) -->_1 U61^#(ok(X1), ok(X2)) -> c_135(U61^#(X1, X2)) :91 -->_1 U61^#(mark(X1), X2) -> c_134(U61^#(X1, X2)) :90 7: active^#(isNatKind(s(V1))) -> c_7(U51^#(isNatKind(V1))) -->_1 U51^#(ok(X)) -> c_133(U51^#(X)) :93 -->_1 U51^#(mark(X)) -> c_132(U51^#(X)) :92 8: active^#(isNatKind(0())) -> c_8() 9: active^#(U103(X1, X2, X3)) -> c_9(U103^#(active(X1), X2, X3)) -->_1 U103^#(ok(X1), ok(X2), ok(X3)) -> c_88(U103^#(X1, X2, X3)) :87 -->_1 U103^#(mark(X1), X2, X3) -> c_87(U103^#(X1, X2, X3)) :86 10: active^#(U103(tt(), M, N)) -> c_10(U104^#(isNatKind(N), M, N)) -->_1 U104^#(ok(X1), ok(X2), ok(X3)) -> c_91(U104^#(X1, X2, X3)) :95 -->_1 U104^#(mark(X1), X2, X3) -> c_90(U104^#(X1, X2, X3)) :94 11: active^#(isNat(plus(V1, V2))) -> c_11(U11^#(isNatKind(V1), V1, V2)) -->_1 U11^#(ok(X1), ok(X2), ok(X3)) -> c_99(U11^#(X1, X2, X3)) :97 -->_1 U11^#(mark(X1), X2, X3) -> c_98(U11^#(X1, X2, X3)) :96 12: active^#(isNat(x(V1, V2))) -> c_12(U31^#(isNatKind(V1), V1, V2)) -->_1 U31^#(ok(X1), ok(X2), ok(X3)) -> c_117(U31^#(X1, X2, X3)) :99 -->_1 U31^#(mark(X1), X2, X3) -> c_116(U31^#(X1, X2, X3)) :98 13: active^#(isNat(s(V1))) -> c_13(U21^#(isNatKind(V1), V1)) -->_1 U21^#(ok(X1), ok(X2)) -> c_111(U21^#(X1, X2)) :101 -->_1 U21^#(mark(X1), X2) -> c_110(U21^#(X1, X2)) :100 14: active^#(isNat(0())) -> c_14() 15: active^#(U104(X1, X2, X3)) -> c_15(U104^#(active(X1), X2, X3)) -->_1 U104^#(ok(X1), ok(X2), ok(X3)) -> c_91(U104^#(X1, X2, X3)) :95 -->_1 U104^#(mark(X1), X2, X3) -> c_90(U104^#(X1, X2, X3)) :94 16: active^#(U104(tt(), M, N)) -> c_16(plus^#(x(N, M), N)) -->_1 plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) :104 -->_1 plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) :103 -->_1 plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) :102 17: active^#(plus(X1, X2)) -> c_17(plus^#(X1, active(X2))) -->_1 plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) :104 -->_1 plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) :103 -->_1 plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) :102 18: active^#(plus(X1, X2)) -> c_18(plus^#(active(X1), X2)) -->_1 plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) :104 -->_1 plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) :103 -->_1 plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) :102 19: active^#(plus(N, s(M))) -> c_19(U81^#(isNat(M), M, N)) -->_1 U81^#(ok(X1), ok(X2), ok(X3)) -> c_143(U81^#(X1, X2, X3)) :106 -->_1 U81^#(mark(X1), X2, X3) -> c_142(U81^#(X1, X2, X3)) :105 20: active^#(plus(N, 0())) -> c_20(U71^#(isNat(N), N)) -->_1 U71^#(ok(X1), ok(X2)) -> c_139(U71^#(X1, X2)) :108 -->_1 U71^#(mark(X1), X2) -> c_138(U71^#(X1, X2)) :107 21: active^#(x(X1, X2)) -> c_21(x^#(X1, active(X2))) -->_1 x^#(ok(X1), ok(X2)) -> c_97(x^#(X1, X2)) :111 -->_1 x^#(mark(X1), X2) -> c_96(x^#(X1, X2)) :110 -->_1 x^#(X1, mark(X2)) -> c_95(x^#(X1, X2)) :109 22: active^#(x(X1, X2)) -> c_22(x^#(active(X1), X2)) -->_1 x^#(ok(X1), ok(X2)) -> c_97(x^#(X1, X2)) :111 -->_1 x^#(mark(X1), X2) -> c_96(x^#(X1, X2)) :110 -->_1 x^#(X1, mark(X2)) -> c_95(x^#(X1, X2)) :109 23: active^#(x(N, s(M))) -> c_23(U101^#(isNat(M), M, N)) -->_1 U101^#(ok(X1), ok(X2), ok(X3)) -> c_83(U101^#(X1, X2, X3)) :83 -->_1 U101^#(mark(X1), X2, X3) -> c_82(U101^#(X1, X2, X3)) :82 24: active^#(x(N, 0())) -> c_24(U91^#(isNat(N), N)) -->_1 U91^#(ok(X1), ok(X2)) -> c_153(U91^#(X1, X2)) :113 -->_1 U91^#(mark(X1), X2) -> c_152(U91^#(X1, X2)) :112 25: active^#(U11(X1, X2, X3)) -> c_25(U11^#(active(X1), X2, X3)) -->_1 U11^#(ok(X1), ok(X2), ok(X3)) -> c_99(U11^#(X1, X2, X3)) :97 -->_1 U11^#(mark(X1), X2, X3) -> c_98(U11^#(X1, X2, X3)) :96 26: active^#(U11(tt(), V1, V2)) -> c_26(U12^#(isNatKind(V1), V1, V2)) -->_1 U12^#(ok(X1), ok(X2), ok(X3)) -> c_101(U12^#(X1, X2, X3)) :115 -->_1 U12^#(mark(X1), X2, X3) -> c_100(U12^#(X1, X2, X3)) :114 27: active^#(U12(X1, X2, X3)) -> c_27(U12^#(active(X1), X2, X3)) -->_1 U12^#(ok(X1), ok(X2), ok(X3)) -> c_101(U12^#(X1, X2, X3)) :115 -->_1 U12^#(mark(X1), X2, X3) -> c_100(U12^#(X1, X2, X3)) :114 28: active^#(U12(tt(), V1, V2)) -> c_28(U13^#(isNatKind(V2), V1, V2)) -->_1 U13^#(ok(X1), ok(X2), ok(X3)) -> c_103(U13^#(X1, X2, X3)) :117 -->_1 U13^#(mark(X1), X2, X3) -> c_102(U13^#(X1, X2, X3)) :116 29: active^#(U13(X1, X2, X3)) -> c_29(U13^#(active(X1), X2, X3)) -->_1 U13^#(ok(X1), ok(X2), ok(X3)) -> c_103(U13^#(X1, X2, X3)) :117 -->_1 U13^#(mark(X1), X2, X3) -> c_102(U13^#(X1, X2, X3)) :116 30: active^#(U13(tt(), V1, V2)) -> c_30(U14^#(isNatKind(V2), V1, V2)) -->_1 U14^#(ok(X1), ok(X2), ok(X3)) -> c_105(U14^#(X1, X2, X3)) :119 -->_1 U14^#(mark(X1), X2, X3) -> c_104(U14^#(X1, X2, X3)) :118 31: active^#(U14(X1, X2, X3)) -> c_31(U14^#(active(X1), X2, X3)) -->_1 U14^#(ok(X1), ok(X2), ok(X3)) -> c_105(U14^#(X1, X2, X3)) :119 -->_1 U14^#(mark(X1), X2, X3) -> c_104(U14^#(X1, X2, X3)) :118 32: active^#(U14(tt(), V1, V2)) -> c_32(U15^#(isNat(V1), V2)) -->_1 U15^#(ok(X1), ok(X2)) -> c_107(U15^#(X1, X2)) :121 -->_1 U15^#(mark(X1), X2) -> c_106(U15^#(X1, X2)) :120 33: active^#(U15(X1, X2)) -> c_33(U15^#(active(X1), X2)) -->_1 U15^#(ok(X1), ok(X2)) -> c_107(U15^#(X1, X2)) :121 -->_1 U15^#(mark(X1), X2) -> c_106(U15^#(X1, X2)) :120 34: active^#(U15(tt(), V2)) -> c_34(U16^#(isNat(V2))) -->_1 U16^#(ok(X)) -> c_109(U16^#(X)) :123 -->_1 U16^#(mark(X)) -> c_108(U16^#(X)) :122 35: active^#(U16(X)) -> c_35(U16^#(active(X))) -->_1 U16^#(ok(X)) -> c_109(U16^#(X)) :123 -->_1 U16^#(mark(X)) -> c_108(U16^#(X)) :122 36: active^#(U16(tt())) -> c_36() 37: active^#(U21(X1, X2)) -> c_37(U21^#(active(X1), X2)) -->_1 U21^#(ok(X1), ok(X2)) -> c_111(U21^#(X1, X2)) :101 -->_1 U21^#(mark(X1), X2) -> c_110(U21^#(X1, X2)) :100 38: active^#(U21(tt(), V1)) -> c_38(U22^#(isNatKind(V1), V1)) -->_1 U22^#(ok(X1), ok(X2)) -> c_113(U22^#(X1, X2)) :125 -->_1 U22^#(mark(X1), X2) -> c_112(U22^#(X1, X2)) :124 39: active^#(U22(X1, X2)) -> c_39(U22^#(active(X1), X2)) -->_1 U22^#(ok(X1), ok(X2)) -> c_113(U22^#(X1, X2)) :125 -->_1 U22^#(mark(X1), X2) -> c_112(U22^#(X1, X2)) :124 40: active^#(U22(tt(), V1)) -> c_40(U23^#(isNat(V1))) -->_1 U23^#(ok(X)) -> c_115(U23^#(X)) :127 -->_1 U23^#(mark(X)) -> c_114(U23^#(X)) :126 41: active^#(U23(X)) -> c_41(U23^#(active(X))) -->_1 U23^#(ok(X)) -> c_115(U23^#(X)) :127 -->_1 U23^#(mark(X)) -> c_114(U23^#(X)) :126 42: active^#(U23(tt())) -> c_42() 43: active^#(U31(X1, X2, X3)) -> c_43(U31^#(active(X1), X2, X3)) -->_1 U31^#(ok(X1), ok(X2), ok(X3)) -> c_117(U31^#(X1, X2, X3)) :99 -->_1 U31^#(mark(X1), X2, X3) -> c_116(U31^#(X1, X2, X3)) :98 44: active^#(U31(tt(), V1, V2)) -> c_44(U32^#(isNatKind(V1), V1, V2)) -->_1 U32^#(ok(X1), ok(X2), ok(X3)) -> c_119(U32^#(X1, X2, X3)) :129 -->_1 U32^#(mark(X1), X2, X3) -> c_118(U32^#(X1, X2, X3)) :128 45: active^#(U32(X1, X2, X3)) -> c_45(U32^#(active(X1), X2, X3)) -->_1 U32^#(ok(X1), ok(X2), ok(X3)) -> c_119(U32^#(X1, X2, X3)) :129 -->_1 U32^#(mark(X1), X2, X3) -> c_118(U32^#(X1, X2, X3)) :128 46: active^#(U32(tt(), V1, V2)) -> c_46(U33^#(isNatKind(V2), V1, V2)) -->_1 U33^#(ok(X1), ok(X2), ok(X3)) -> c_121(U33^#(X1, X2, X3)) :131 -->_1 U33^#(mark(X1), X2, X3) -> c_120(U33^#(X1, X2, X3)) :130 47: active^#(U33(X1, X2, X3)) -> c_47(U33^#(active(X1), X2, X3)) -->_1 U33^#(ok(X1), ok(X2), ok(X3)) -> c_121(U33^#(X1, X2, X3)) :131 -->_1 U33^#(mark(X1), X2, X3) -> c_120(U33^#(X1, X2, X3)) :130 48: active^#(U33(tt(), V1, V2)) -> c_48(U34^#(isNatKind(V2), V1, V2)) -->_1 U34^#(ok(X1), ok(X2), ok(X3)) -> c_123(U34^#(X1, X2, X3)) :133 -->_1 U34^#(mark(X1), X2, X3) -> c_122(U34^#(X1, X2, X3)) :132 49: active^#(U34(X1, X2, X3)) -> c_49(U34^#(active(X1), X2, X3)) -->_1 U34^#(ok(X1), ok(X2), ok(X3)) -> c_123(U34^#(X1, X2, X3)) :133 -->_1 U34^#(mark(X1), X2, X3) -> c_122(U34^#(X1, X2, X3)) :132 50: active^#(U34(tt(), V1, V2)) -> c_50(U35^#(isNat(V1), V2)) -->_1 U35^#(ok(X1), ok(X2)) -> c_125(U35^#(X1, X2)) :135 -->_1 U35^#(mark(X1), X2) -> c_124(U35^#(X1, X2)) :134 51: active^#(U35(X1, X2)) -> c_51(U35^#(active(X1), X2)) -->_1 U35^#(ok(X1), ok(X2)) -> c_125(U35^#(X1, X2)) :135 -->_1 U35^#(mark(X1), X2) -> c_124(U35^#(X1, X2)) :134 52: active^#(U35(tt(), V2)) -> c_52(U36^#(isNat(V2))) -->_1 U36^#(ok(X)) -> c_127(U36^#(X)) :137 -->_1 U36^#(mark(X)) -> c_126(U36^#(X)) :136 53: active^#(U36(X)) -> c_53(U36^#(active(X))) -->_1 U36^#(ok(X)) -> c_127(U36^#(X)) :137 -->_1 U36^#(mark(X)) -> c_126(U36^#(X)) :136 54: active^#(U36(tt())) -> c_54() 55: active^#(U41(X1, X2)) -> c_55(U41^#(active(X1), X2)) -->_1 U41^#(ok(X1), ok(X2)) -> c_129(U41^#(X1, X2)) :89 -->_1 U41^#(mark(X1), X2) -> c_128(U41^#(X1, X2)) :88 56: active^#(U41(tt(), V2)) -> c_56(U42^#(isNatKind(V2))) -->_1 U42^#(ok(X)) -> c_131(U42^#(X)) :139 -->_1 U42^#(mark(X)) -> c_130(U42^#(X)) :138 57: active^#(U42(X)) -> c_57(U42^#(active(X))) -->_1 U42^#(ok(X)) -> c_131(U42^#(X)) :139 -->_1 U42^#(mark(X)) -> c_130(U42^#(X)) :138 58: active^#(U42(tt())) -> c_58() 59: active^#(U51(X)) -> c_59(U51^#(active(X))) -->_1 U51^#(ok(X)) -> c_133(U51^#(X)) :93 -->_1 U51^#(mark(X)) -> c_132(U51^#(X)) :92 60: active^#(U51(tt())) -> c_60() 61: active^#(U61(X1, X2)) -> c_61(U61^#(active(X1), X2)) -->_1 U61^#(ok(X1), ok(X2)) -> c_135(U61^#(X1, X2)) :91 -->_1 U61^#(mark(X1), X2) -> c_134(U61^#(X1, X2)) :90 62: active^#(U61(tt(), V2)) -> c_62(U62^#(isNatKind(V2))) -->_1 U62^#(ok(X)) -> c_137(U62^#(X)) :141 -->_1 U62^#(mark(X)) -> c_136(U62^#(X)) :140 63: active^#(U62(X)) -> c_63(U62^#(active(X))) -->_1 U62^#(ok(X)) -> c_137(U62^#(X)) :141 -->_1 U62^#(mark(X)) -> c_136(U62^#(X)) :140 64: active^#(U62(tt())) -> c_64() 65: active^#(U71(X1, X2)) -> c_65(U71^#(active(X1), X2)) -->_1 U71^#(ok(X1), ok(X2)) -> c_139(U71^#(X1, X2)) :108 -->_1 U71^#(mark(X1), X2) -> c_138(U71^#(X1, X2)) :107 66: active^#(U71(tt(), N)) -> c_66(U72^#(isNatKind(N), N)) -->_1 U72^#(ok(X1), ok(X2)) -> c_141(U72^#(X1, X2)) :143 -->_1 U72^#(mark(X1), X2) -> c_140(U72^#(X1, X2)) :142 67: active^#(U72(X1, X2)) -> c_67(U72^#(active(X1), X2)) -->_1 U72^#(ok(X1), ok(X2)) -> c_141(U72^#(X1, X2)) :143 -->_1 U72^#(mark(X1), X2) -> c_140(U72^#(X1, X2)) :142 68: active^#(U72(tt(), N)) -> c_68(N) -->_1 top^#(ok(X)) -> c_196(top^#(active(X))) :196 -->_1 top^#(mark(X)) -> c_195(top^#(proper(X))) :195 -->_1 proper^#(U92(X)) -> c_193(U92^#(proper(X))) :193 -->_1 proper^#(U91(X1, X2)) -> c_192(U91^#(proper(X1), proper(X2))) :192 -->_1 proper^#(s(X)) -> c_191(s^#(proper(X))) :191 -->_1 proper^#(U84(X1, X2, X3)) -> c_190(U84^#(proper(X1), proper(X2), proper(X3))) :190 -->_1 proper^#(U83(X1, X2, X3)) -> c_189(U83^#(proper(X1), proper(X2), proper(X3))) :189 -->_1 proper^#(U82(X1, X2, X3)) -> c_188(U82^#(proper(X1), proper(X2), proper(X3))) :188 -->_1 proper^#(U81(X1, X2, X3)) -> c_187(U81^#(proper(X1), proper(X2), proper(X3))) :187 -->_1 proper^#(U72(X1, X2)) -> c_186(U72^#(proper(X1), proper(X2))) :186 -->_1 proper^#(U71(X1, X2)) -> c_185(U71^#(proper(X1), proper(X2))) :185 -->_1 proper^#(U62(X)) -> c_184(U62^#(proper(X))) :184 -->_1 proper^#(U61(X1, X2)) -> c_183(U61^#(proper(X1), proper(X2))) :183 -->_1 proper^#(U51(X)) -> c_182(U51^#(proper(X))) :182 -->_1 proper^#(U42(X)) -> c_181(U42^#(proper(X))) :181 -->_1 proper^#(U41(X1, X2)) -> c_180(U41^#(proper(X1), proper(X2))) :180 -->_1 proper^#(U36(X)) -> c_179(U36^#(proper(X))) :179 -->_1 proper^#(U35(X1, X2)) -> c_178(U35^#(proper(X1), proper(X2))) :178 -->_1 proper^#(U34(X1, X2, X3)) -> c_177(U34^#(proper(X1), proper(X2), proper(X3))) :177 -->_1 proper^#(U33(X1, X2, X3)) -> c_176(U33^#(proper(X1), proper(X2), proper(X3))) :176 -->_1 proper^#(U32(X1, X2, X3)) -> c_175(U32^#(proper(X1), proper(X2), proper(X3))) :175 -->_1 proper^#(U31(X1, X2, X3)) -> c_174(U31^#(proper(X1), proper(X2), proper(X3))) :174 -->_1 proper^#(U23(X)) -> c_173(U23^#(proper(X))) :173 -->_1 proper^#(U22(X1, X2)) -> c_172(U22^#(proper(X1), proper(X2))) :172 -->_1 proper^#(U21(X1, X2)) -> c_171(U21^#(proper(X1), proper(X2))) :171 -->_1 proper^#(U16(X)) -> c_170(U16^#(proper(X))) :170 -->_1 proper^#(U15(X1, X2)) -> c_169(U15^#(proper(X1), proper(X2))) :169 -->_1 proper^#(U14(X1, X2, X3)) -> c_168(U14^#(proper(X1), proper(X2), proper(X3))) :168 -->_1 proper^#(U13(X1, X2, X3)) -> c_167(U13^#(proper(X1), proper(X2), proper(X3))) :167 -->_1 proper^#(U12(X1, X2, X3)) -> c_166(U12^#(proper(X1), proper(X2), proper(X3))) :166 -->_1 proper^#(U11(X1, X2, X3)) -> c_165(U11^#(proper(X1), proper(X2), proper(X3))) :165 -->_1 proper^#(x(X1, X2)) -> c_164(x^#(proper(X1), proper(X2))) :164 -->_1 proper^#(plus(X1, X2)) -> c_163(plus^#(proper(X1), proper(X2))) :163 -->_1 proper^#(U104(X1, X2, X3)) -> c_162(U104^#(proper(X1), proper(X2), proper(X3))) :162 -->_1 proper^#(isNat(X)) -> c_161(isNat^#(proper(X))) :161 -->_1 proper^#(U103(X1, X2, X3)) -> c_160(U103^#(proper(X1), proper(X2), proper(X3))) :160 -->_1 proper^#(isNatKind(X)) -> c_159(isNatKind^#(proper(X))) :159 -->_1 proper^#(U102(X1, X2, X3)) -> c_158(U102^#(proper(X1), proper(X2), proper(X3))) :158 -->_1 proper^#(U101(X1, X2, X3)) -> c_156(U101^#(proper(X1), proper(X2), proper(X3))) :156 -->_1 isNat^#(ok(X)) -> c_89(isNat^#(X)) :155 -->_1 isNatKind^#(ok(X)) -> c_86(isNatKind^#(X)) :154 -->_1 U92^#(ok(X)) -> c_155(U92^#(X)) :153 -->_1 U92^#(mark(X)) -> c_154(U92^#(X)) :152 -->_1 s^#(ok(X)) -> c_151(s^#(X)) :151 -->_1 s^#(mark(X)) -> c_150(s^#(X)) :150 -->_1 U84^#(ok(X1), ok(X2), ok(X3)) -> c_149(U84^#(X1, X2, X3)) :149 -->_1 U84^#(mark(X1), X2, X3) -> c_148(U84^#(X1, X2, X3)) :148 -->_1 U83^#(ok(X1), ok(X2), ok(X3)) -> c_147(U83^#(X1, X2, X3)) :147 -->_1 U83^#(mark(X1), X2, X3) -> c_146(U83^#(X1, X2, X3)) :146 -->_1 U82^#(ok(X1), ok(X2), ok(X3)) -> c_145(U82^#(X1, X2, X3)) :145 -->_1 U82^#(mark(X1), X2, X3) -> c_144(U82^#(X1, X2, X3)) :144 -->_1 U72^#(ok(X1), ok(X2)) -> c_141(U72^#(X1, X2)) :143 -->_1 U72^#(mark(X1), X2) -> c_140(U72^#(X1, X2)) :142 -->_1 U62^#(ok(X)) -> c_137(U62^#(X)) :141 -->_1 U62^#(mark(X)) -> c_136(U62^#(X)) :140 -->_1 U42^#(ok(X)) -> c_131(U42^#(X)) :139 -->_1 U42^#(mark(X)) -> c_130(U42^#(X)) :138 -->_1 U36^#(ok(X)) -> c_127(U36^#(X)) :137 -->_1 U36^#(mark(X)) -> c_126(U36^#(X)) :136 -->_1 U35^#(ok(X1), ok(X2)) -> c_125(U35^#(X1, X2)) :135 -->_1 U35^#(mark(X1), X2) -> c_124(U35^#(X1, X2)) :134 -->_1 U34^#(ok(X1), ok(X2), ok(X3)) -> c_123(U34^#(X1, X2, X3)) :133 -->_1 U34^#(mark(X1), X2, X3) -> c_122(U34^#(X1, X2, X3)) :132 -->_1 U33^#(ok(X1), ok(X2), ok(X3)) -> c_121(U33^#(X1, X2, X3)) :131 -->_1 U33^#(mark(X1), X2, X3) -> c_120(U33^#(X1, X2, X3)) :130 -->_1 U32^#(ok(X1), ok(X2), ok(X3)) -> c_119(U32^#(X1, X2, X3)) :129 -->_1 U32^#(mark(X1), X2, X3) -> c_118(U32^#(X1, X2, X3)) :128 -->_1 U23^#(ok(X)) -> c_115(U23^#(X)) :127 -->_1 U23^#(mark(X)) -> c_114(U23^#(X)) :126 -->_1 U22^#(ok(X1), ok(X2)) -> c_113(U22^#(X1, X2)) :125 -->_1 U22^#(mark(X1), X2) -> c_112(U22^#(X1, X2)) :124 -->_1 U16^#(ok(X)) -> c_109(U16^#(X)) :123 -->_1 U16^#(mark(X)) -> c_108(U16^#(X)) :122 -->_1 U15^#(ok(X1), ok(X2)) -> c_107(U15^#(X1, X2)) :121 -->_1 U15^#(mark(X1), X2) -> c_106(U15^#(X1, X2)) :120 -->_1 U14^#(ok(X1), ok(X2), ok(X3)) -> c_105(U14^#(X1, X2, X3)) :119 -->_1 U14^#(mark(X1), X2, X3) -> c_104(U14^#(X1, X2, X3)) :118 -->_1 U13^#(ok(X1), ok(X2), ok(X3)) -> c_103(U13^#(X1, X2, X3)) :117 -->_1 U13^#(mark(X1), X2, X3) -> c_102(U13^#(X1, X2, X3)) :116 -->_1 U12^#(ok(X1), ok(X2), ok(X3)) -> c_101(U12^#(X1, X2, X3)) :115 -->_1 U12^#(mark(X1), X2, X3) -> c_100(U12^#(X1, X2, X3)) :114 -->_1 U91^#(ok(X1), ok(X2)) -> c_153(U91^#(X1, X2)) :113 -->_1 U91^#(mark(X1), X2) -> c_152(U91^#(X1, X2)) :112 -->_1 x^#(ok(X1), ok(X2)) -> c_97(x^#(X1, X2)) :111 -->_1 x^#(mark(X1), X2) -> c_96(x^#(X1, X2)) :110 -->_1 x^#(X1, mark(X2)) -> c_95(x^#(X1, X2)) :109 -->_1 U71^#(ok(X1), ok(X2)) -> c_139(U71^#(X1, X2)) :108 -->_1 U71^#(mark(X1), X2) -> c_138(U71^#(X1, X2)) :107 -->_1 U81^#(ok(X1), ok(X2), ok(X3)) -> c_143(U81^#(X1, X2, X3)) :106 -->_1 U81^#(mark(X1), X2, X3) -> c_142(U81^#(X1, X2, X3)) :105 -->_1 plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) :104 -->_1 plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) :103 -->_1 plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) :102 -->_1 U21^#(ok(X1), ok(X2)) -> c_111(U21^#(X1, X2)) :101 -->_1 U21^#(mark(X1), X2) -> c_110(U21^#(X1, X2)) :100 -->_1 U31^#(ok(X1), ok(X2), ok(X3)) -> c_117(U31^#(X1, X2, X3)) :99 -->_1 U31^#(mark(X1), X2, X3) -> c_116(U31^#(X1, X2, X3)) :98 -->_1 U11^#(ok(X1), ok(X2), ok(X3)) -> c_99(U11^#(X1, X2, X3)) :97 -->_1 U11^#(mark(X1), X2, X3) -> c_98(U11^#(X1, X2, X3)) :96 -->_1 U104^#(ok(X1), ok(X2), ok(X3)) -> c_91(U104^#(X1, X2, X3)) :95 -->_1 U104^#(mark(X1), X2, X3) -> c_90(U104^#(X1, X2, X3)) :94 -->_1 U51^#(ok(X)) -> c_133(U51^#(X)) :93 -->_1 U51^#(mark(X)) -> c_132(U51^#(X)) :92 -->_1 U61^#(ok(X1), ok(X2)) -> c_135(U61^#(X1, X2)) :91 -->_1 U61^#(mark(X1), X2) -> c_134(U61^#(X1, X2)) :90 -->_1 U41^#(ok(X1), ok(X2)) -> c_129(U41^#(X1, X2)) :89 -->_1 U41^#(mark(X1), X2) -> c_128(U41^#(X1, X2)) :88 -->_1 U103^#(ok(X1), ok(X2), ok(X3)) -> c_88(U103^#(X1, X2, X3)) :87 -->_1 U103^#(mark(X1), X2, X3) -> c_87(U103^#(X1, X2, X3)) :86 -->_1 U102^#(ok(X1), ok(X2), ok(X3)) -> c_85(U102^#(X1, X2, X3)) :85 -->_1 U102^#(mark(X1), X2, X3) -> c_84(U102^#(X1, X2, X3)) :84 -->_1 U101^#(ok(X1), ok(X2), ok(X3)) -> c_83(U101^#(X1, X2, X3)) :83 -->_1 U101^#(mark(X1), X2, X3) -> c_82(U101^#(X1, X2, X3)) :82 -->_1 active^#(U92(X)) -> c_80(U92^#(active(X))) :80 -->_1 active^#(U91(tt(), N)) -> c_79(U92^#(isNatKind(N))) :79 -->_1 active^#(U91(X1, X2)) -> c_78(U91^#(active(X1), X2)) :78 -->_1 active^#(s(X)) -> c_77(s^#(active(X))) :77 -->_1 active^#(U84(tt(), M, N)) -> c_76(s^#(plus(N, M))) :76 -->_1 active^#(U84(X1, X2, X3)) -> c_75(U84^#(active(X1), X2, X3)) :75 -->_1 active^#(U83(tt(), M, N)) -> c_74(U84^#(isNatKind(N), M, N)) :74 -->_1 active^#(U83(X1, X2, X3)) -> c_73(U83^#(active(X1), X2, X3)) :73 -->_1 active^#(U82(tt(), M, N)) -> c_72(U83^#(isNat(N), M, N)) :72 -->_1 active^#(U82(X1, X2, X3)) -> c_71(U82^#(active(X1), X2, X3)) :71 -->_1 active^#(U81(tt(), M, N)) -> c_70(U82^#(isNatKind(M), M, N)) :70 -->_1 active^#(U81(X1, X2, X3)) -> c_69(U81^#(active(X1), X2, X3)) :69 -->_1 proper^#(0()) -> c_194() :194 -->_1 proper^#(tt()) -> c_157() :157 -->_1 active^#(U92(tt())) -> c_81() :81 -->_1 active^#(U72(tt(), N)) -> c_68(N) :68 -->_1 active^#(U72(X1, X2)) -> c_67(U72^#(active(X1), X2)) :67 -->_1 active^#(U71(tt(), N)) -> c_66(U72^#(isNatKind(N), N)) :66 -->_1 active^#(U71(X1, X2)) -> c_65(U71^#(active(X1), X2)) :65 -->_1 active^#(U62(tt())) -> c_64() :64 -->_1 active^#(U62(X)) -> c_63(U62^#(active(X))) :63 -->_1 active^#(U61(tt(), V2)) -> c_62(U62^#(isNatKind(V2))) :62 -->_1 active^#(U61(X1, X2)) -> c_61(U61^#(active(X1), X2)) :61 -->_1 active^#(U51(tt())) -> c_60() :60 -->_1 active^#(U51(X)) -> c_59(U51^#(active(X))) :59 -->_1 active^#(U42(tt())) -> c_58() :58 -->_1 active^#(U42(X)) -> c_57(U42^#(active(X))) :57 -->_1 active^#(U41(tt(), V2)) -> c_56(U42^#(isNatKind(V2))) :56 -->_1 active^#(U41(X1, X2)) -> c_55(U41^#(active(X1), X2)) :55 -->_1 active^#(U36(tt())) -> c_54() :54 -->_1 active^#(U36(X)) -> c_53(U36^#(active(X))) :53 -->_1 active^#(U35(tt(), V2)) -> c_52(U36^#(isNat(V2))) :52 -->_1 active^#(U35(X1, X2)) -> c_51(U35^#(active(X1), X2)) :51 -->_1 active^#(U34(tt(), V1, V2)) -> c_50(U35^#(isNat(V1), V2)) :50 -->_1 active^#(U34(X1, X2, X3)) -> c_49(U34^#(active(X1), X2, X3)) :49 -->_1 active^#(U33(tt(), V1, V2)) -> c_48(U34^#(isNatKind(V2), V1, V2)) :48 -->_1 active^#(U33(X1, X2, X3)) -> c_47(U33^#(active(X1), X2, X3)) :47 -->_1 active^#(U32(tt(), V1, V2)) -> c_46(U33^#(isNatKind(V2), V1, V2)) :46 -->_1 active^#(U32(X1, X2, X3)) -> c_45(U32^#(active(X1), X2, X3)) :45 -->_1 active^#(U31(tt(), V1, V2)) -> c_44(U32^#(isNatKind(V1), V1, V2)) :44 -->_1 active^#(U31(X1, X2, X3)) -> c_43(U31^#(active(X1), X2, X3)) :43 -->_1 active^#(U23(tt())) -> c_42() :42 -->_1 active^#(U23(X)) -> c_41(U23^#(active(X))) :41 -->_1 active^#(U22(tt(), V1)) -> c_40(U23^#(isNat(V1))) :40 -->_1 active^#(U22(X1, X2)) -> c_39(U22^#(active(X1), X2)) :39 -->_1 active^#(U21(tt(), V1)) -> c_38(U22^#(isNatKind(V1), V1)) :38 -->_1 active^#(U21(X1, X2)) -> c_37(U21^#(active(X1), X2)) :37 -->_1 active^#(U16(tt())) -> c_36() :36 -->_1 active^#(U16(X)) -> c_35(U16^#(active(X))) :35 -->_1 active^#(U15(tt(), V2)) -> c_34(U16^#(isNat(V2))) :34 -->_1 active^#(U15(X1, X2)) -> c_33(U15^#(active(X1), X2)) :33 -->_1 active^#(U14(tt(), V1, V2)) -> c_32(U15^#(isNat(V1), V2)) :32 -->_1 active^#(U14(X1, X2, X3)) -> c_31(U14^#(active(X1), X2, X3)) :31 -->_1 active^#(U13(tt(), V1, V2)) -> c_30(U14^#(isNatKind(V2), V1, V2)) :30 -->_1 active^#(U13(X1, X2, X3)) -> c_29(U13^#(active(X1), X2, X3)) :29 -->_1 active^#(U12(tt(), V1, V2)) -> c_28(U13^#(isNatKind(V2), V1, V2)) :28 -->_1 active^#(U12(X1, X2, X3)) -> c_27(U12^#(active(X1), X2, X3)) :27 -->_1 active^#(U11(tt(), V1, V2)) -> c_26(U12^#(isNatKind(V1), V1, V2)) :26 -->_1 active^#(U11(X1, X2, X3)) -> c_25(U11^#(active(X1), X2, X3)) :25 -->_1 active^#(x(N, 0())) -> c_24(U91^#(isNat(N), N)) :24 -->_1 active^#(x(N, s(M))) -> c_23(U101^#(isNat(M), M, N)) :23 -->_1 active^#(x(X1, X2)) -> c_22(x^#(active(X1), X2)) :22 -->_1 active^#(x(X1, X2)) -> c_21(x^#(X1, active(X2))) :21 -->_1 active^#(plus(N, 0())) -> c_20(U71^#(isNat(N), N)) :20 -->_1 active^#(plus(N, s(M))) -> c_19(U81^#(isNat(M), M, N)) :19 -->_1 active^#(plus(X1, X2)) -> c_18(plus^#(active(X1), X2)) :18 -->_1 active^#(plus(X1, X2)) -> c_17(plus^#(X1, active(X2))) :17 -->_1 active^#(U104(tt(), M, N)) -> c_16(plus^#(x(N, M), N)) :16 -->_1 active^#(U104(X1, X2, X3)) -> c_15(U104^#(active(X1), X2, X3)) :15 -->_1 active^#(isNat(0())) -> c_14() :14 -->_1 active^#(isNat(s(V1))) -> c_13(U21^#(isNatKind(V1), V1)) :13 -->_1 active^#(isNat(x(V1, V2))) -> c_12(U31^#(isNatKind(V1), V1, V2)) :12 -->_1 active^#(isNat(plus(V1, V2))) -> c_11(U11^#(isNatKind(V1), V1, V2)) :11 -->_1 active^#(U103(tt(), M, N)) -> c_10(U104^#(isNatKind(N), M, N)) :10 -->_1 active^#(U103(X1, X2, X3)) -> c_9(U103^#(active(X1), X2, X3)) :9 -->_1 active^#(isNatKind(0())) -> c_8() :8 -->_1 active^#(isNatKind(s(V1))) -> c_7(U51^#(isNatKind(V1))) :7 -->_1 active^#(isNatKind(x(V1, V2))) -> c_6(U61^#(isNatKind(V1), V2)) :6 -->_1 active^#(isNatKind(plus(V1, V2))) -> c_5(U41^#(isNatKind(V1), V2)) :5 -->_1 active^#(U102(tt(), M, N)) -> c_4(U103^#(isNat(N), M, N)) :4 -->_1 active^#(U102(X1, X2, X3)) -> c_3(U102^#(active(X1), X2, X3)) :3 -->_1 active^#(U101(tt(), M, N)) -> c_2(U102^#(isNatKind(M), M, N)) :2 -->_1 active^#(U101(X1, X2, X3)) -> c_1(U101^#(active(X1), X2, X3)) :1 69: active^#(U81(X1, X2, X3)) -> c_69(U81^#(active(X1), X2, X3)) -->_1 U81^#(ok(X1), ok(X2), ok(X3)) -> c_143(U81^#(X1, X2, X3)) :106 -->_1 U81^#(mark(X1), X2, X3) -> c_142(U81^#(X1, X2, X3)) :105 70: active^#(U81(tt(), M, N)) -> c_70(U82^#(isNatKind(M), M, N)) -->_1 U82^#(ok(X1), ok(X2), ok(X3)) -> c_145(U82^#(X1, X2, X3)) :145 -->_1 U82^#(mark(X1), X2, X3) -> c_144(U82^#(X1, X2, X3)) :144 71: active^#(U82(X1, X2, X3)) -> c_71(U82^#(active(X1), X2, X3)) -->_1 U82^#(ok(X1), ok(X2), ok(X3)) -> c_145(U82^#(X1, X2, X3)) :145 -->_1 U82^#(mark(X1), X2, X3) -> c_144(U82^#(X1, X2, X3)) :144 72: active^#(U82(tt(), M, N)) -> c_72(U83^#(isNat(N), M, N)) -->_1 U83^#(ok(X1), ok(X2), ok(X3)) -> c_147(U83^#(X1, X2, X3)) :147 -->_1 U83^#(mark(X1), X2, X3) -> c_146(U83^#(X1, X2, X3)) :146 73: active^#(U83(X1, X2, X3)) -> c_73(U83^#(active(X1), X2, X3)) -->_1 U83^#(ok(X1), ok(X2), ok(X3)) -> c_147(U83^#(X1, X2, X3)) :147 -->_1 U83^#(mark(X1), X2, X3) -> c_146(U83^#(X1, X2, X3)) :146 74: active^#(U83(tt(), M, N)) -> c_74(U84^#(isNatKind(N), M, N)) -->_1 U84^#(ok(X1), ok(X2), ok(X3)) -> c_149(U84^#(X1, X2, X3)) :149 -->_1 U84^#(mark(X1), X2, X3) -> c_148(U84^#(X1, X2, X3)) :148 75: active^#(U84(X1, X2, X3)) -> c_75(U84^#(active(X1), X2, X3)) -->_1 U84^#(ok(X1), ok(X2), ok(X3)) -> c_149(U84^#(X1, X2, X3)) :149 -->_1 U84^#(mark(X1), X2, X3) -> c_148(U84^#(X1, X2, X3)) :148 76: active^#(U84(tt(), M, N)) -> c_76(s^#(plus(N, M))) -->_1 s^#(ok(X)) -> c_151(s^#(X)) :151 -->_1 s^#(mark(X)) -> c_150(s^#(X)) :150 77: active^#(s(X)) -> c_77(s^#(active(X))) -->_1 s^#(ok(X)) -> c_151(s^#(X)) :151 -->_1 s^#(mark(X)) -> c_150(s^#(X)) :150 78: active^#(U91(X1, X2)) -> c_78(U91^#(active(X1), X2)) -->_1 U91^#(ok(X1), ok(X2)) -> c_153(U91^#(X1, X2)) :113 -->_1 U91^#(mark(X1), X2) -> c_152(U91^#(X1, X2)) :112 79: active^#(U91(tt(), N)) -> c_79(U92^#(isNatKind(N))) -->_1 U92^#(ok(X)) -> c_155(U92^#(X)) :153 -->_1 U92^#(mark(X)) -> c_154(U92^#(X)) :152 80: active^#(U92(X)) -> c_80(U92^#(active(X))) -->_1 U92^#(ok(X)) -> c_155(U92^#(X)) :153 -->_1 U92^#(mark(X)) -> c_154(U92^#(X)) :152 81: active^#(U92(tt())) -> c_81() 82: U101^#(mark(X1), X2, X3) -> c_82(U101^#(X1, X2, X3)) -->_1 U101^#(ok(X1), ok(X2), ok(X3)) -> c_83(U101^#(X1, X2, X3)) :83 -->_1 U101^#(mark(X1), X2, X3) -> c_82(U101^#(X1, X2, X3)) :82 83: U101^#(ok(X1), ok(X2), ok(X3)) -> c_83(U101^#(X1, X2, X3)) -->_1 U101^#(ok(X1), ok(X2), ok(X3)) -> c_83(U101^#(X1, X2, X3)) :83 -->_1 U101^#(mark(X1), X2, X3) -> c_82(U101^#(X1, X2, X3)) :82 84: U102^#(mark(X1), X2, X3) -> c_84(U102^#(X1, X2, X3)) -->_1 U102^#(ok(X1), ok(X2), ok(X3)) -> c_85(U102^#(X1, X2, X3)) :85 -->_1 U102^#(mark(X1), X2, X3) -> c_84(U102^#(X1, X2, X3)) :84 85: U102^#(ok(X1), ok(X2), ok(X3)) -> c_85(U102^#(X1, X2, X3)) -->_1 U102^#(ok(X1), ok(X2), ok(X3)) -> c_85(U102^#(X1, X2, X3)) :85 -->_1 U102^#(mark(X1), X2, X3) -> c_84(U102^#(X1, X2, X3)) :84 86: U103^#(mark(X1), X2, X3) -> c_87(U103^#(X1, X2, X3)) -->_1 U103^#(ok(X1), ok(X2), ok(X3)) -> c_88(U103^#(X1, X2, X3)) :87 -->_1 U103^#(mark(X1), X2, X3) -> c_87(U103^#(X1, X2, X3)) :86 87: U103^#(ok(X1), ok(X2), ok(X3)) -> c_88(U103^#(X1, X2, X3)) -->_1 U103^#(ok(X1), ok(X2), ok(X3)) -> c_88(U103^#(X1, X2, X3)) :87 -->_1 U103^#(mark(X1), X2, X3) -> c_87(U103^#(X1, X2, X3)) :86 88: U41^#(mark(X1), X2) -> c_128(U41^#(X1, X2)) -->_1 U41^#(ok(X1), ok(X2)) -> c_129(U41^#(X1, X2)) :89 -->_1 U41^#(mark(X1), X2) -> c_128(U41^#(X1, X2)) :88 89: U41^#(ok(X1), ok(X2)) -> c_129(U41^#(X1, X2)) -->_1 U41^#(ok(X1), ok(X2)) -> c_129(U41^#(X1, X2)) :89 -->_1 U41^#(mark(X1), X2) -> c_128(U41^#(X1, X2)) :88 90: U61^#(mark(X1), X2) -> c_134(U61^#(X1, X2)) -->_1 U61^#(ok(X1), ok(X2)) -> c_135(U61^#(X1, X2)) :91 -->_1 U61^#(mark(X1), X2) -> c_134(U61^#(X1, X2)) :90 91: U61^#(ok(X1), ok(X2)) -> c_135(U61^#(X1, X2)) -->_1 U61^#(ok(X1), ok(X2)) -> c_135(U61^#(X1, X2)) :91 -->_1 U61^#(mark(X1), X2) -> c_134(U61^#(X1, X2)) :90 92: U51^#(mark(X)) -> c_132(U51^#(X)) -->_1 U51^#(ok(X)) -> c_133(U51^#(X)) :93 -->_1 U51^#(mark(X)) -> c_132(U51^#(X)) :92 93: U51^#(ok(X)) -> c_133(U51^#(X)) -->_1 U51^#(ok(X)) -> c_133(U51^#(X)) :93 -->_1 U51^#(mark(X)) -> c_132(U51^#(X)) :92 94: U104^#(mark(X1), X2, X3) -> c_90(U104^#(X1, X2, X3)) -->_1 U104^#(ok(X1), ok(X2), ok(X3)) -> c_91(U104^#(X1, X2, X3)) :95 -->_1 U104^#(mark(X1), X2, X3) -> c_90(U104^#(X1, X2, X3)) :94 95: U104^#(ok(X1), ok(X2), ok(X3)) -> c_91(U104^#(X1, X2, X3)) -->_1 U104^#(ok(X1), ok(X2), ok(X3)) -> c_91(U104^#(X1, X2, X3)) :95 -->_1 U104^#(mark(X1), X2, X3) -> c_90(U104^#(X1, X2, X3)) :94 96: U11^#(mark(X1), X2, X3) -> c_98(U11^#(X1, X2, X3)) -->_1 U11^#(ok(X1), ok(X2), ok(X3)) -> c_99(U11^#(X1, X2, X3)) :97 -->_1 U11^#(mark(X1), X2, X3) -> c_98(U11^#(X1, X2, X3)) :96 97: U11^#(ok(X1), ok(X2), ok(X3)) -> c_99(U11^#(X1, X2, X3)) -->_1 U11^#(ok(X1), ok(X2), ok(X3)) -> c_99(U11^#(X1, X2, X3)) :97 -->_1 U11^#(mark(X1), X2, X3) -> c_98(U11^#(X1, X2, X3)) :96 98: U31^#(mark(X1), X2, X3) -> c_116(U31^#(X1, X2, X3)) -->_1 U31^#(ok(X1), ok(X2), ok(X3)) -> c_117(U31^#(X1, X2, X3)) :99 -->_1 U31^#(mark(X1), X2, X3) -> c_116(U31^#(X1, X2, X3)) :98 99: U31^#(ok(X1), ok(X2), ok(X3)) -> c_117(U31^#(X1, X2, X3)) -->_1 U31^#(ok(X1), ok(X2), ok(X3)) -> c_117(U31^#(X1, X2, X3)) :99 -->_1 U31^#(mark(X1), X2, X3) -> c_116(U31^#(X1, X2, X3)) :98 100: U21^#(mark(X1), X2) -> c_110(U21^#(X1, X2)) -->_1 U21^#(ok(X1), ok(X2)) -> c_111(U21^#(X1, X2)) :101 -->_1 U21^#(mark(X1), X2) -> c_110(U21^#(X1, X2)) :100 101: U21^#(ok(X1), ok(X2)) -> c_111(U21^#(X1, X2)) -->_1 U21^#(ok(X1), ok(X2)) -> c_111(U21^#(X1, X2)) :101 -->_1 U21^#(mark(X1), X2) -> c_110(U21^#(X1, X2)) :100 102: plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) -->_1 plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) :104 -->_1 plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) :103 -->_1 plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) :102 103: plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) -->_1 plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) :104 -->_1 plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) :103 -->_1 plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) :102 104: plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) -->_1 plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) :104 -->_1 plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) :103 -->_1 plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) :102 105: U81^#(mark(X1), X2, X3) -> c_142(U81^#(X1, X2, X3)) -->_1 U81^#(ok(X1), ok(X2), ok(X3)) -> c_143(U81^#(X1, X2, X3)) :106 -->_1 U81^#(mark(X1), X2, X3) -> c_142(U81^#(X1, X2, X3)) :105 106: U81^#(ok(X1), ok(X2), ok(X3)) -> c_143(U81^#(X1, X2, X3)) -->_1 U81^#(ok(X1), ok(X2), ok(X3)) -> c_143(U81^#(X1, X2, X3)) :106 -->_1 U81^#(mark(X1), X2, X3) -> c_142(U81^#(X1, X2, X3)) :105 107: U71^#(mark(X1), X2) -> c_138(U71^#(X1, X2)) -->_1 U71^#(ok(X1), ok(X2)) -> c_139(U71^#(X1, X2)) :108 -->_1 U71^#(mark(X1), X2) -> c_138(U71^#(X1, X2)) :107 108: U71^#(ok(X1), ok(X2)) -> c_139(U71^#(X1, X2)) -->_1 U71^#(ok(X1), ok(X2)) -> c_139(U71^#(X1, X2)) :108 -->_1 U71^#(mark(X1), X2) -> c_138(U71^#(X1, X2)) :107 109: x^#(X1, mark(X2)) -> c_95(x^#(X1, X2)) -->_1 x^#(ok(X1), ok(X2)) -> c_97(x^#(X1, X2)) :111 -->_1 x^#(mark(X1), X2) -> c_96(x^#(X1, X2)) :110 -->_1 x^#(X1, mark(X2)) -> c_95(x^#(X1, X2)) :109 110: x^#(mark(X1), X2) -> c_96(x^#(X1, X2)) -->_1 x^#(ok(X1), ok(X2)) -> c_97(x^#(X1, X2)) :111 -->_1 x^#(mark(X1), X2) -> c_96(x^#(X1, X2)) :110 -->_1 x^#(X1, mark(X2)) -> c_95(x^#(X1, X2)) :109 111: x^#(ok(X1), ok(X2)) -> c_97(x^#(X1, X2)) -->_1 x^#(ok(X1), ok(X2)) -> c_97(x^#(X1, X2)) :111 -->_1 x^#(mark(X1), X2) -> c_96(x^#(X1, X2)) :110 -->_1 x^#(X1, mark(X2)) -> c_95(x^#(X1, X2)) :109 112: U91^#(mark(X1), X2) -> c_152(U91^#(X1, X2)) -->_1 U91^#(ok(X1), ok(X2)) -> c_153(U91^#(X1, X2)) :113 -->_1 U91^#(mark(X1), X2) -> c_152(U91^#(X1, X2)) :112 113: U91^#(ok(X1), ok(X2)) -> c_153(U91^#(X1, X2)) -->_1 U91^#(ok(X1), ok(X2)) -> c_153(U91^#(X1, X2)) :113 -->_1 U91^#(mark(X1), X2) -> c_152(U91^#(X1, X2)) :112 114: U12^#(mark(X1), X2, X3) -> c_100(U12^#(X1, X2, X3)) -->_1 U12^#(ok(X1), ok(X2), ok(X3)) -> c_101(U12^#(X1, X2, X3)) :115 -->_1 U12^#(mark(X1), X2, X3) -> c_100(U12^#(X1, X2, X3)) :114 115: U12^#(ok(X1), ok(X2), ok(X3)) -> c_101(U12^#(X1, X2, X3)) -->_1 U12^#(ok(X1), ok(X2), ok(X3)) -> c_101(U12^#(X1, X2, X3)) :115 -->_1 U12^#(mark(X1), X2, X3) -> c_100(U12^#(X1, X2, X3)) :114 116: U13^#(mark(X1), X2, X3) -> c_102(U13^#(X1, X2, X3)) -->_1 U13^#(ok(X1), ok(X2), ok(X3)) -> c_103(U13^#(X1, X2, X3)) :117 -->_1 U13^#(mark(X1), X2, X3) -> c_102(U13^#(X1, X2, X3)) :116 117: U13^#(ok(X1), ok(X2), ok(X3)) -> c_103(U13^#(X1, X2, X3)) -->_1 U13^#(ok(X1), ok(X2), ok(X3)) -> c_103(U13^#(X1, X2, X3)) :117 -->_1 U13^#(mark(X1), X2, X3) -> c_102(U13^#(X1, X2, X3)) :116 118: U14^#(mark(X1), X2, X3) -> c_104(U14^#(X1, X2, X3)) -->_1 U14^#(ok(X1), ok(X2), ok(X3)) -> c_105(U14^#(X1, X2, X3)) :119 -->_1 U14^#(mark(X1), X2, X3) -> c_104(U14^#(X1, X2, X3)) :118 119: U14^#(ok(X1), ok(X2), ok(X3)) -> c_105(U14^#(X1, X2, X3)) -->_1 U14^#(ok(X1), ok(X2), ok(X3)) -> c_105(U14^#(X1, X2, X3)) :119 -->_1 U14^#(mark(X1), X2, X3) -> c_104(U14^#(X1, X2, X3)) :118 120: U15^#(mark(X1), X2) -> c_106(U15^#(X1, X2)) -->_1 U15^#(ok(X1), ok(X2)) -> c_107(U15^#(X1, X2)) :121 -->_1 U15^#(mark(X1), X2) -> c_106(U15^#(X1, X2)) :120 121: U15^#(ok(X1), ok(X2)) -> c_107(U15^#(X1, X2)) -->_1 U15^#(ok(X1), ok(X2)) -> c_107(U15^#(X1, X2)) :121 -->_1 U15^#(mark(X1), X2) -> c_106(U15^#(X1, X2)) :120 122: U16^#(mark(X)) -> c_108(U16^#(X)) -->_1 U16^#(ok(X)) -> c_109(U16^#(X)) :123 -->_1 U16^#(mark(X)) -> c_108(U16^#(X)) :122 123: U16^#(ok(X)) -> c_109(U16^#(X)) -->_1 U16^#(ok(X)) -> c_109(U16^#(X)) :123 -->_1 U16^#(mark(X)) -> c_108(U16^#(X)) :122 124: U22^#(mark(X1), X2) -> c_112(U22^#(X1, X2)) -->_1 U22^#(ok(X1), ok(X2)) -> c_113(U22^#(X1, X2)) :125 -->_1 U22^#(mark(X1), X2) -> c_112(U22^#(X1, X2)) :124 125: U22^#(ok(X1), ok(X2)) -> c_113(U22^#(X1, X2)) -->_1 U22^#(ok(X1), ok(X2)) -> c_113(U22^#(X1, X2)) :125 -->_1 U22^#(mark(X1), X2) -> c_112(U22^#(X1, X2)) :124 126: U23^#(mark(X)) -> c_114(U23^#(X)) -->_1 U23^#(ok(X)) -> c_115(U23^#(X)) :127 -->_1 U23^#(mark(X)) -> c_114(U23^#(X)) :126 127: U23^#(ok(X)) -> c_115(U23^#(X)) -->_1 U23^#(ok(X)) -> c_115(U23^#(X)) :127 -->_1 U23^#(mark(X)) -> c_114(U23^#(X)) :126 128: U32^#(mark(X1), X2, X3) -> c_118(U32^#(X1, X2, X3)) -->_1 U32^#(ok(X1), ok(X2), ok(X3)) -> c_119(U32^#(X1, X2, X3)) :129 -->_1 U32^#(mark(X1), X2, X3) -> c_118(U32^#(X1, X2, X3)) :128 129: U32^#(ok(X1), ok(X2), ok(X3)) -> c_119(U32^#(X1, X2, X3)) -->_1 U32^#(ok(X1), ok(X2), ok(X3)) -> c_119(U32^#(X1, X2, X3)) :129 -->_1 U32^#(mark(X1), X2, X3) -> c_118(U32^#(X1, X2, X3)) :128 130: U33^#(mark(X1), X2, X3) -> c_120(U33^#(X1, X2, X3)) -->_1 U33^#(ok(X1), ok(X2), ok(X3)) -> c_121(U33^#(X1, X2, X3)) :131 -->_1 U33^#(mark(X1), X2, X3) -> c_120(U33^#(X1, X2, X3)) :130 131: U33^#(ok(X1), ok(X2), ok(X3)) -> c_121(U33^#(X1, X2, X3)) -->_1 U33^#(ok(X1), ok(X2), ok(X3)) -> c_121(U33^#(X1, X2, X3)) :131 -->_1 U33^#(mark(X1), X2, X3) -> c_120(U33^#(X1, X2, X3)) :130 132: U34^#(mark(X1), X2, X3) -> c_122(U34^#(X1, X2, X3)) -->_1 U34^#(ok(X1), ok(X2), ok(X3)) -> c_123(U34^#(X1, X2, X3)) :133 -->_1 U34^#(mark(X1), X2, X3) -> c_122(U34^#(X1, X2, X3)) :132 133: U34^#(ok(X1), ok(X2), ok(X3)) -> c_123(U34^#(X1, X2, X3)) -->_1 U34^#(ok(X1), ok(X2), ok(X3)) -> c_123(U34^#(X1, X2, X3)) :133 -->_1 U34^#(mark(X1), X2, X3) -> c_122(U34^#(X1, X2, X3)) :132 134: U35^#(mark(X1), X2) -> c_124(U35^#(X1, X2)) -->_1 U35^#(ok(X1), ok(X2)) -> c_125(U35^#(X1, X2)) :135 -->_1 U35^#(mark(X1), X2) -> c_124(U35^#(X1, X2)) :134 135: U35^#(ok(X1), ok(X2)) -> c_125(U35^#(X1, X2)) -->_1 U35^#(ok(X1), ok(X2)) -> c_125(U35^#(X1, X2)) :135 -->_1 U35^#(mark(X1), X2) -> c_124(U35^#(X1, X2)) :134 136: U36^#(mark(X)) -> c_126(U36^#(X)) -->_1 U36^#(ok(X)) -> c_127(U36^#(X)) :137 -->_1 U36^#(mark(X)) -> c_126(U36^#(X)) :136 137: U36^#(ok(X)) -> c_127(U36^#(X)) -->_1 U36^#(ok(X)) -> c_127(U36^#(X)) :137 -->_1 U36^#(mark(X)) -> c_126(U36^#(X)) :136 138: U42^#(mark(X)) -> c_130(U42^#(X)) -->_1 U42^#(ok(X)) -> c_131(U42^#(X)) :139 -->_1 U42^#(mark(X)) -> c_130(U42^#(X)) :138 139: U42^#(ok(X)) -> c_131(U42^#(X)) -->_1 U42^#(ok(X)) -> c_131(U42^#(X)) :139 -->_1 U42^#(mark(X)) -> c_130(U42^#(X)) :138 140: U62^#(mark(X)) -> c_136(U62^#(X)) -->_1 U62^#(ok(X)) -> c_137(U62^#(X)) :141 -->_1 U62^#(mark(X)) -> c_136(U62^#(X)) :140 141: U62^#(ok(X)) -> c_137(U62^#(X)) -->_1 U62^#(ok(X)) -> c_137(U62^#(X)) :141 -->_1 U62^#(mark(X)) -> c_136(U62^#(X)) :140 142: U72^#(mark(X1), X2) -> c_140(U72^#(X1, X2)) -->_1 U72^#(ok(X1), ok(X2)) -> c_141(U72^#(X1, X2)) :143 -->_1 U72^#(mark(X1), X2) -> c_140(U72^#(X1, X2)) :142 143: U72^#(ok(X1), ok(X2)) -> c_141(U72^#(X1, X2)) -->_1 U72^#(ok(X1), ok(X2)) -> c_141(U72^#(X1, X2)) :143 -->_1 U72^#(mark(X1), X2) -> c_140(U72^#(X1, X2)) :142 144: U82^#(mark(X1), X2, X3) -> c_144(U82^#(X1, X2, X3)) -->_1 U82^#(ok(X1), ok(X2), ok(X3)) -> c_145(U82^#(X1, X2, X3)) :145 -->_1 U82^#(mark(X1), X2, X3) -> c_144(U82^#(X1, X2, X3)) :144 145: U82^#(ok(X1), ok(X2), ok(X3)) -> c_145(U82^#(X1, X2, X3)) -->_1 U82^#(ok(X1), ok(X2), ok(X3)) -> c_145(U82^#(X1, X2, X3)) :145 -->_1 U82^#(mark(X1), X2, X3) -> c_144(U82^#(X1, X2, X3)) :144 146: U83^#(mark(X1), X2, X3) -> c_146(U83^#(X1, X2, X3)) -->_1 U83^#(ok(X1), ok(X2), ok(X3)) -> c_147(U83^#(X1, X2, X3)) :147 -->_1 U83^#(mark(X1), X2, X3) -> c_146(U83^#(X1, X2, X3)) :146 147: U83^#(ok(X1), ok(X2), ok(X3)) -> c_147(U83^#(X1, X2, X3)) -->_1 U83^#(ok(X1), ok(X2), ok(X3)) -> c_147(U83^#(X1, X2, X3)) :147 -->_1 U83^#(mark(X1), X2, X3) -> c_146(U83^#(X1, X2, X3)) :146 148: U84^#(mark(X1), X2, X3) -> c_148(U84^#(X1, X2, X3)) -->_1 U84^#(ok(X1), ok(X2), ok(X3)) -> c_149(U84^#(X1, X2, X3)) :149 -->_1 U84^#(mark(X1), X2, X3) -> c_148(U84^#(X1, X2, X3)) :148 149: U84^#(ok(X1), ok(X2), ok(X3)) -> c_149(U84^#(X1, X2, X3)) -->_1 U84^#(ok(X1), ok(X2), ok(X3)) -> c_149(U84^#(X1, X2, X3)) :149 -->_1 U84^#(mark(X1), X2, X3) -> c_148(U84^#(X1, X2, X3)) :148 150: s^#(mark(X)) -> c_150(s^#(X)) -->_1 s^#(ok(X)) -> c_151(s^#(X)) :151 -->_1 s^#(mark(X)) -> c_150(s^#(X)) :150 151: s^#(ok(X)) -> c_151(s^#(X)) -->_1 s^#(ok(X)) -> c_151(s^#(X)) :151 -->_1 s^#(mark(X)) -> c_150(s^#(X)) :150 152: U92^#(mark(X)) -> c_154(U92^#(X)) -->_1 U92^#(ok(X)) -> c_155(U92^#(X)) :153 -->_1 U92^#(mark(X)) -> c_154(U92^#(X)) :152 153: U92^#(ok(X)) -> c_155(U92^#(X)) -->_1 U92^#(ok(X)) -> c_155(U92^#(X)) :153 -->_1 U92^#(mark(X)) -> c_154(U92^#(X)) :152 154: isNatKind^#(ok(X)) -> c_86(isNatKind^#(X)) -->_1 isNatKind^#(ok(X)) -> c_86(isNatKind^#(X)) :154 155: isNat^#(ok(X)) -> c_89(isNat^#(X)) -->_1 isNat^#(ok(X)) -> c_89(isNat^#(X)) :155 156: proper^#(U101(X1, X2, X3)) -> c_156(U101^#(proper(X1), proper(X2), proper(X3))) -->_1 U101^#(ok(X1), ok(X2), ok(X3)) -> c_83(U101^#(X1, X2, X3)) :83 -->_1 U101^#(mark(X1), X2, X3) -> c_82(U101^#(X1, X2, X3)) :82 157: proper^#(tt()) -> c_157() 158: proper^#(U102(X1, X2, X3)) -> c_158(U102^#(proper(X1), proper(X2), proper(X3))) -->_1 U102^#(ok(X1), ok(X2), ok(X3)) -> c_85(U102^#(X1, X2, X3)) :85 -->_1 U102^#(mark(X1), X2, X3) -> c_84(U102^#(X1, X2, X3)) :84 159: proper^#(isNatKind(X)) -> c_159(isNatKind^#(proper(X))) -->_1 isNatKind^#(ok(X)) -> c_86(isNatKind^#(X)) :154 160: proper^#(U103(X1, X2, X3)) -> c_160(U103^#(proper(X1), proper(X2), proper(X3))) -->_1 U103^#(ok(X1), ok(X2), ok(X3)) -> c_88(U103^#(X1, X2, X3)) :87 -->_1 U103^#(mark(X1), X2, X3) -> c_87(U103^#(X1, X2, X3)) :86 161: proper^#(isNat(X)) -> c_161(isNat^#(proper(X))) -->_1 isNat^#(ok(X)) -> c_89(isNat^#(X)) :155 162: proper^#(U104(X1, X2, X3)) -> c_162(U104^#(proper(X1), proper(X2), proper(X3))) -->_1 U104^#(ok(X1), ok(X2), ok(X3)) -> c_91(U104^#(X1, X2, X3)) :95 -->_1 U104^#(mark(X1), X2, X3) -> c_90(U104^#(X1, X2, X3)) :94 163: proper^#(plus(X1, X2)) -> c_163(plus^#(proper(X1), proper(X2))) -->_1 plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) :104 -->_1 plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) :103 -->_1 plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) :102 164: proper^#(x(X1, X2)) -> c_164(x^#(proper(X1), proper(X2))) -->_1 x^#(ok(X1), ok(X2)) -> c_97(x^#(X1, X2)) :111 -->_1 x^#(mark(X1), X2) -> c_96(x^#(X1, X2)) :110 -->_1 x^#(X1, mark(X2)) -> c_95(x^#(X1, X2)) :109 165: proper^#(U11(X1, X2, X3)) -> c_165(U11^#(proper(X1), proper(X2), proper(X3))) -->_1 U11^#(ok(X1), ok(X2), ok(X3)) -> c_99(U11^#(X1, X2, X3)) :97 -->_1 U11^#(mark(X1), X2, X3) -> c_98(U11^#(X1, X2, X3)) :96 166: proper^#(U12(X1, X2, X3)) -> c_166(U12^#(proper(X1), proper(X2), proper(X3))) -->_1 U12^#(ok(X1), ok(X2), ok(X3)) -> c_101(U12^#(X1, X2, X3)) :115 -->_1 U12^#(mark(X1), X2, X3) -> c_100(U12^#(X1, X2, X3)) :114 167: proper^#(U13(X1, X2, X3)) -> c_167(U13^#(proper(X1), proper(X2), proper(X3))) -->_1 U13^#(ok(X1), ok(X2), ok(X3)) -> c_103(U13^#(X1, X2, X3)) :117 -->_1 U13^#(mark(X1), X2, X3) -> c_102(U13^#(X1, X2, X3)) :116 168: proper^#(U14(X1, X2, X3)) -> c_168(U14^#(proper(X1), proper(X2), proper(X3))) -->_1 U14^#(ok(X1), ok(X2), ok(X3)) -> c_105(U14^#(X1, X2, X3)) :119 -->_1 U14^#(mark(X1), X2, X3) -> c_104(U14^#(X1, X2, X3)) :118 169: proper^#(U15(X1, X2)) -> c_169(U15^#(proper(X1), proper(X2))) -->_1 U15^#(ok(X1), ok(X2)) -> c_107(U15^#(X1, X2)) :121 -->_1 U15^#(mark(X1), X2) -> c_106(U15^#(X1, X2)) :120 170: proper^#(U16(X)) -> c_170(U16^#(proper(X))) -->_1 U16^#(ok(X)) -> c_109(U16^#(X)) :123 -->_1 U16^#(mark(X)) -> c_108(U16^#(X)) :122 171: proper^#(U21(X1, X2)) -> c_171(U21^#(proper(X1), proper(X2))) -->_1 U21^#(ok(X1), ok(X2)) -> c_111(U21^#(X1, X2)) :101 -->_1 U21^#(mark(X1), X2) -> c_110(U21^#(X1, X2)) :100 172: proper^#(U22(X1, X2)) -> c_172(U22^#(proper(X1), proper(X2))) -->_1 U22^#(ok(X1), ok(X2)) -> c_113(U22^#(X1, X2)) :125 -->_1 U22^#(mark(X1), X2) -> c_112(U22^#(X1, X2)) :124 173: proper^#(U23(X)) -> c_173(U23^#(proper(X))) -->_1 U23^#(ok(X)) -> c_115(U23^#(X)) :127 -->_1 U23^#(mark(X)) -> c_114(U23^#(X)) :126 174: proper^#(U31(X1, X2, X3)) -> c_174(U31^#(proper(X1), proper(X2), proper(X3))) -->_1 U31^#(ok(X1), ok(X2), ok(X3)) -> c_117(U31^#(X1, X2, X3)) :99 -->_1 U31^#(mark(X1), X2, X3) -> c_116(U31^#(X1, X2, X3)) :98 175: proper^#(U32(X1, X2, X3)) -> c_175(U32^#(proper(X1), proper(X2), proper(X3))) -->_1 U32^#(ok(X1), ok(X2), ok(X3)) -> c_119(U32^#(X1, X2, X3)) :129 -->_1 U32^#(mark(X1), X2, X3) -> c_118(U32^#(X1, X2, X3)) :128 176: proper^#(U33(X1, X2, X3)) -> c_176(U33^#(proper(X1), proper(X2), proper(X3))) -->_1 U33^#(ok(X1), ok(X2), ok(X3)) -> c_121(U33^#(X1, X2, X3)) :131 -->_1 U33^#(mark(X1), X2, X3) -> c_120(U33^#(X1, X2, X3)) :130 177: proper^#(U34(X1, X2, X3)) -> c_177(U34^#(proper(X1), proper(X2), proper(X3))) -->_1 U34^#(ok(X1), ok(X2), ok(X3)) -> c_123(U34^#(X1, X2, X3)) :133 -->_1 U34^#(mark(X1), X2, X3) -> c_122(U34^#(X1, X2, X3)) :132 178: proper^#(U35(X1, X2)) -> c_178(U35^#(proper(X1), proper(X2))) -->_1 U35^#(ok(X1), ok(X2)) -> c_125(U35^#(X1, X2)) :135 -->_1 U35^#(mark(X1), X2) -> c_124(U35^#(X1, X2)) :134 179: proper^#(U36(X)) -> c_179(U36^#(proper(X))) -->_1 U36^#(ok(X)) -> c_127(U36^#(X)) :137 -->_1 U36^#(mark(X)) -> c_126(U36^#(X)) :136 180: proper^#(U41(X1, X2)) -> c_180(U41^#(proper(X1), proper(X2))) -->_1 U41^#(ok(X1), ok(X2)) -> c_129(U41^#(X1, X2)) :89 -->_1 U41^#(mark(X1), X2) -> c_128(U41^#(X1, X2)) :88 181: proper^#(U42(X)) -> c_181(U42^#(proper(X))) -->_1 U42^#(ok(X)) -> c_131(U42^#(X)) :139 -->_1 U42^#(mark(X)) -> c_130(U42^#(X)) :138 182: proper^#(U51(X)) -> c_182(U51^#(proper(X))) -->_1 U51^#(ok(X)) -> c_133(U51^#(X)) :93 -->_1 U51^#(mark(X)) -> c_132(U51^#(X)) :92 183: proper^#(U61(X1, X2)) -> c_183(U61^#(proper(X1), proper(X2))) -->_1 U61^#(ok(X1), ok(X2)) -> c_135(U61^#(X1, X2)) :91 -->_1 U61^#(mark(X1), X2) -> c_134(U61^#(X1, X2)) :90 184: proper^#(U62(X)) -> c_184(U62^#(proper(X))) -->_1 U62^#(ok(X)) -> c_137(U62^#(X)) :141 -->_1 U62^#(mark(X)) -> c_136(U62^#(X)) :140 185: proper^#(U71(X1, X2)) -> c_185(U71^#(proper(X1), proper(X2))) -->_1 U71^#(ok(X1), ok(X2)) -> c_139(U71^#(X1, X2)) :108 -->_1 U71^#(mark(X1), X2) -> c_138(U71^#(X1, X2)) :107 186: proper^#(U72(X1, X2)) -> c_186(U72^#(proper(X1), proper(X2))) -->_1 U72^#(ok(X1), ok(X2)) -> c_141(U72^#(X1, X2)) :143 -->_1 U72^#(mark(X1), X2) -> c_140(U72^#(X1, X2)) :142 187: proper^#(U81(X1, X2, X3)) -> c_187(U81^#(proper(X1), proper(X2), proper(X3))) -->_1 U81^#(ok(X1), ok(X2), ok(X3)) -> c_143(U81^#(X1, X2, X3)) :106 -->_1 U81^#(mark(X1), X2, X3) -> c_142(U81^#(X1, X2, X3)) :105 188: proper^#(U82(X1, X2, X3)) -> c_188(U82^#(proper(X1), proper(X2), proper(X3))) -->_1 U82^#(ok(X1), ok(X2), ok(X3)) -> c_145(U82^#(X1, X2, X3)) :145 -->_1 U82^#(mark(X1), X2, X3) -> c_144(U82^#(X1, X2, X3)) :144 189: proper^#(U83(X1, X2, X3)) -> c_189(U83^#(proper(X1), proper(X2), proper(X3))) -->_1 U83^#(ok(X1), ok(X2), ok(X3)) -> c_147(U83^#(X1, X2, X3)) :147 -->_1 U83^#(mark(X1), X2, X3) -> c_146(U83^#(X1, X2, X3)) :146 190: proper^#(U84(X1, X2, X3)) -> c_190(U84^#(proper(X1), proper(X2), proper(X3))) -->_1 U84^#(ok(X1), ok(X2), ok(X3)) -> c_149(U84^#(X1, X2, X3)) :149 -->_1 U84^#(mark(X1), X2, X3) -> c_148(U84^#(X1, X2, X3)) :148 191: proper^#(s(X)) -> c_191(s^#(proper(X))) -->_1 s^#(ok(X)) -> c_151(s^#(X)) :151 -->_1 s^#(mark(X)) -> c_150(s^#(X)) :150 192: proper^#(U91(X1, X2)) -> c_192(U91^#(proper(X1), proper(X2))) -->_1 U91^#(ok(X1), ok(X2)) -> c_153(U91^#(X1, X2)) :113 -->_1 U91^#(mark(X1), X2) -> c_152(U91^#(X1, X2)) :112 193: proper^#(U92(X)) -> c_193(U92^#(proper(X))) -->_1 U92^#(ok(X)) -> c_155(U92^#(X)) :153 -->_1 U92^#(mark(X)) -> c_154(U92^#(X)) :152 194: proper^#(0()) -> c_194() 195: top^#(mark(X)) -> c_195(top^#(proper(X))) -->_1 top^#(ok(X)) -> c_196(top^#(active(X))) :196 -->_1 top^#(mark(X)) -> c_195(top^#(proper(X))) :195 196: top^#(ok(X)) -> c_196(top^#(active(X))) -->_1 top^#(ok(X)) -> c_196(top^#(active(X))) :196 -->_1 top^#(mark(X)) -> c_195(top^#(proper(X))) :195 Only the nodes {82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,104,103,105,106,107,108,109,111,110,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,157,194,195,196} are reachable from nodes {82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,157,194,195,196} that start derivation from marked basic terms. The nodes not reachable are removed from the problem. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { U101^#(mark(X1), X2, X3) -> c_82(U101^#(X1, X2, X3)) , U101^#(ok(X1), ok(X2), ok(X3)) -> c_83(U101^#(X1, X2, X3)) , U102^#(mark(X1), X2, X3) -> c_84(U102^#(X1, X2, X3)) , U102^#(ok(X1), ok(X2), ok(X3)) -> c_85(U102^#(X1, X2, X3)) , U103^#(mark(X1), X2, X3) -> c_87(U103^#(X1, X2, X3)) , U103^#(ok(X1), ok(X2), ok(X3)) -> c_88(U103^#(X1, X2, X3)) , U41^#(mark(X1), X2) -> c_128(U41^#(X1, X2)) , U41^#(ok(X1), ok(X2)) -> c_129(U41^#(X1, X2)) , U61^#(mark(X1), X2) -> c_134(U61^#(X1, X2)) , U61^#(ok(X1), ok(X2)) -> c_135(U61^#(X1, X2)) , U51^#(mark(X)) -> c_132(U51^#(X)) , U51^#(ok(X)) -> c_133(U51^#(X)) , U104^#(mark(X1), X2, X3) -> c_90(U104^#(X1, X2, X3)) , U104^#(ok(X1), ok(X2), ok(X3)) -> c_91(U104^#(X1, X2, X3)) , U11^#(mark(X1), X2, X3) -> c_98(U11^#(X1, X2, X3)) , U11^#(ok(X1), ok(X2), ok(X3)) -> c_99(U11^#(X1, X2, X3)) , U31^#(mark(X1), X2, X3) -> c_116(U31^#(X1, X2, X3)) , U31^#(ok(X1), ok(X2), ok(X3)) -> c_117(U31^#(X1, X2, X3)) , U21^#(mark(X1), X2) -> c_110(U21^#(X1, X2)) , U21^#(ok(X1), ok(X2)) -> c_111(U21^#(X1, X2)) , plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) , plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) , plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) , U81^#(mark(X1), X2, X3) -> c_142(U81^#(X1, X2, X3)) , U81^#(ok(X1), ok(X2), ok(X3)) -> c_143(U81^#(X1, X2, X3)) , U71^#(mark(X1), X2) -> c_138(U71^#(X1, X2)) , U71^#(ok(X1), ok(X2)) -> c_139(U71^#(X1, X2)) , x^#(X1, mark(X2)) -> c_95(x^#(X1, X2)) , x^#(mark(X1), X2) -> c_96(x^#(X1, X2)) , x^#(ok(X1), ok(X2)) -> c_97(x^#(X1, X2)) , U91^#(mark(X1), X2) -> c_152(U91^#(X1, X2)) , U91^#(ok(X1), ok(X2)) -> c_153(U91^#(X1, X2)) , U12^#(mark(X1), X2, X3) -> c_100(U12^#(X1, X2, X3)) , U12^#(ok(X1), ok(X2), ok(X3)) -> c_101(U12^#(X1, X2, X3)) , U13^#(mark(X1), X2, X3) -> c_102(U13^#(X1, X2, X3)) , U13^#(ok(X1), ok(X2), ok(X3)) -> c_103(U13^#(X1, X2, X3)) , U14^#(mark(X1), X2, X3) -> c_104(U14^#(X1, X2, X3)) , U14^#(ok(X1), ok(X2), ok(X3)) -> c_105(U14^#(X1, X2, X3)) , U15^#(mark(X1), X2) -> c_106(U15^#(X1, X2)) , U15^#(ok(X1), ok(X2)) -> c_107(U15^#(X1, X2)) , U16^#(mark(X)) -> c_108(U16^#(X)) , U16^#(ok(X)) -> c_109(U16^#(X)) , U22^#(mark(X1), X2) -> c_112(U22^#(X1, X2)) , U22^#(ok(X1), ok(X2)) -> c_113(U22^#(X1, X2)) , U23^#(mark(X)) -> c_114(U23^#(X)) , U23^#(ok(X)) -> c_115(U23^#(X)) , U32^#(mark(X1), X2, X3) -> c_118(U32^#(X1, X2, X3)) , U32^#(ok(X1), ok(X2), ok(X3)) -> c_119(U32^#(X1, X2, X3)) , U33^#(mark(X1), X2, X3) -> c_120(U33^#(X1, X2, X3)) , U33^#(ok(X1), ok(X2), ok(X3)) -> c_121(U33^#(X1, X2, X3)) , U34^#(mark(X1), X2, X3) -> c_122(U34^#(X1, X2, X3)) , U34^#(ok(X1), ok(X2), ok(X3)) -> c_123(U34^#(X1, X2, X3)) , U35^#(mark(X1), X2) -> c_124(U35^#(X1, X2)) , U35^#(ok(X1), ok(X2)) -> c_125(U35^#(X1, X2)) , U36^#(mark(X)) -> c_126(U36^#(X)) , U36^#(ok(X)) -> c_127(U36^#(X)) , U42^#(mark(X)) -> c_130(U42^#(X)) , U42^#(ok(X)) -> c_131(U42^#(X)) , U62^#(mark(X)) -> c_136(U62^#(X)) , U62^#(ok(X)) -> c_137(U62^#(X)) , U72^#(mark(X1), X2) -> c_140(U72^#(X1, X2)) , U72^#(ok(X1), ok(X2)) -> c_141(U72^#(X1, X2)) , U82^#(mark(X1), X2, X3) -> c_144(U82^#(X1, X2, X3)) , U82^#(ok(X1), ok(X2), ok(X3)) -> c_145(U82^#(X1, X2, X3)) , U83^#(mark(X1), X2, X3) -> c_146(U83^#(X1, X2, X3)) , U83^#(ok(X1), ok(X2), ok(X3)) -> c_147(U83^#(X1, X2, X3)) , U84^#(mark(X1), X2, X3) -> c_148(U84^#(X1, X2, X3)) , U84^#(ok(X1), ok(X2), ok(X3)) -> c_149(U84^#(X1, X2, X3)) , s^#(mark(X)) -> c_150(s^#(X)) , s^#(ok(X)) -> c_151(s^#(X)) , U92^#(mark(X)) -> c_154(U92^#(X)) , U92^#(ok(X)) -> c_155(U92^#(X)) , isNatKind^#(ok(X)) -> c_86(isNatKind^#(X)) , isNat^#(ok(X)) -> c_89(isNat^#(X)) , proper^#(tt()) -> c_157() , proper^#(0()) -> c_194() , top^#(mark(X)) -> c_195(top^#(proper(X))) , top^#(ok(X)) -> c_196(top^#(active(X))) } Strict Trs: { active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) , active(U101(tt(), M, N)) -> mark(U102(isNatKind(M), M, N)) , active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) , active(U102(tt(), M, N)) -> mark(U103(isNat(N), M, N)) , active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2)) , active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2)) , active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) , active(isNatKind(0())) -> mark(tt()) , active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) , active(U103(tt(), M, N)) -> mark(U104(isNatKind(N), M, N)) , active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2)) , active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2)) , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) , active(isNat(0())) -> mark(tt()) , active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) , active(U104(tt(), M, N)) -> mark(plus(x(N, M), N)) , active(plus(X1, X2)) -> plus(X1, active(X2)) , active(plus(X1, X2)) -> plus(active(X1), X2) , active(plus(N, s(M))) -> mark(U81(isNat(M), M, N)) , active(plus(N, 0())) -> mark(U71(isNat(N), N)) , active(x(X1, X2)) -> x(X1, active(X2)) , active(x(X1, X2)) -> x(active(X1), X2) , active(x(N, s(M))) -> mark(U101(isNat(M), M, N)) , active(x(N, 0())) -> mark(U91(isNat(N), N)) , active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) , active(U11(tt(), V1, V2)) -> mark(U12(isNatKind(V1), V1, V2)) , active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) , active(U12(tt(), V1, V2)) -> mark(U13(isNatKind(V2), V1, V2)) , active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) , active(U13(tt(), V1, V2)) -> mark(U14(isNatKind(V2), V1, V2)) , active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) , active(U14(tt(), V1, V2)) -> mark(U15(isNat(V1), V2)) , active(U15(X1, X2)) -> U15(active(X1), X2) , active(U15(tt(), V2)) -> mark(U16(isNat(V2))) , active(U16(X)) -> U16(active(X)) , active(U16(tt())) -> mark(tt()) , active(U21(X1, X2)) -> U21(active(X1), X2) , active(U21(tt(), V1)) -> mark(U22(isNatKind(V1), V1)) , active(U22(X1, X2)) -> U22(active(X1), X2) , active(U22(tt(), V1)) -> mark(U23(isNat(V1))) , active(U23(X)) -> U23(active(X)) , active(U23(tt())) -> mark(tt()) , active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) , active(U31(tt(), V1, V2)) -> mark(U32(isNatKind(V1), V1, V2)) , active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) , active(U32(tt(), V1, V2)) -> mark(U33(isNatKind(V2), V1, V2)) , active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) , active(U33(tt(), V1, V2)) -> mark(U34(isNatKind(V2), V1, V2)) , active(U34(X1, X2, X3)) -> U34(active(X1), X2, X3) , active(U34(tt(), V1, V2)) -> mark(U35(isNat(V1), V2)) , active(U35(X1, X2)) -> U35(active(X1), X2) , active(U35(tt(), V2)) -> mark(U36(isNat(V2))) , active(U36(X)) -> U36(active(X)) , active(U36(tt())) -> mark(tt()) , active(U41(X1, X2)) -> U41(active(X1), X2) , active(U41(tt(), V2)) -> mark(U42(isNatKind(V2))) , active(U42(X)) -> U42(active(X)) , active(U42(tt())) -> mark(tt()) , active(U51(X)) -> U51(active(X)) , active(U51(tt())) -> mark(tt()) , active(U61(X1, X2)) -> U61(active(X1), X2) , active(U61(tt(), V2)) -> mark(U62(isNatKind(V2))) , active(U62(X)) -> U62(active(X)) , active(U62(tt())) -> mark(tt()) , active(U71(X1, X2)) -> U71(active(X1), X2) , active(U71(tt(), N)) -> mark(U72(isNatKind(N), N)) , active(U72(X1, X2)) -> U72(active(X1), X2) , active(U72(tt(), N)) -> mark(N) , active(U81(X1, X2, X3)) -> U81(active(X1), X2, X3) , active(U81(tt(), M, N)) -> mark(U82(isNatKind(M), M, N)) , active(U82(X1, X2, X3)) -> U82(active(X1), X2, X3) , active(U82(tt(), M, N)) -> mark(U83(isNat(N), M, N)) , active(U83(X1, X2, X3)) -> U83(active(X1), X2, X3) , active(U83(tt(), M, N)) -> mark(U84(isNatKind(N), M, N)) , active(U84(X1, X2, X3)) -> U84(active(X1), X2, X3) , active(U84(tt(), M, N)) -> mark(s(plus(N, M))) , active(s(X)) -> s(active(X)) , active(U91(X1, X2)) -> U91(active(X1), X2) , active(U91(tt(), N)) -> mark(U92(isNatKind(N))) , active(U92(X)) -> U92(active(X)) , active(U92(tt())) -> mark(0()) , U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) , U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) , U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) , U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) , isNatKind(ok(X)) -> ok(isNatKind(X)) , U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) , U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) , isNat(ok(X)) -> ok(isNat(X)) , U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) , U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) , plus(X1, mark(X2)) -> mark(plus(X1, X2)) , plus(mark(X1), X2) -> mark(plus(X1, X2)) , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) , x(X1, mark(X2)) -> mark(x(X1, X2)) , x(mark(X1), X2) -> mark(x(X1, X2)) , x(ok(X1), ok(X2)) -> ok(x(X1, X2)) , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) , U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) , U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) , U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) , U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) , U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) , U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) , U15(mark(X1), X2) -> mark(U15(X1, X2)) , U15(ok(X1), ok(X2)) -> ok(U15(X1, X2)) , U16(mark(X)) -> mark(U16(X)) , U16(ok(X)) -> ok(U16(X)) , U21(mark(X1), X2) -> mark(U21(X1, X2)) , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)) , U22(mark(X1), X2) -> mark(U22(X1, X2)) , U22(ok(X1), ok(X2)) -> ok(U22(X1, X2)) , U23(mark(X)) -> mark(U23(X)) , U23(ok(X)) -> ok(U23(X)) , U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) , U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) , U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) , U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) , U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) , U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) , U34(mark(X1), X2, X3) -> mark(U34(X1, X2, X3)) , U34(ok(X1), ok(X2), ok(X3)) -> ok(U34(X1, X2, X3)) , U35(mark(X1), X2) -> mark(U35(X1, X2)) , U35(ok(X1), ok(X2)) -> ok(U35(X1, X2)) , U36(mark(X)) -> mark(U36(X)) , U36(ok(X)) -> ok(U36(X)) , U41(mark(X1), X2) -> mark(U41(X1, X2)) , U41(ok(X1), ok(X2)) -> ok(U41(X1, X2)) , U42(mark(X)) -> mark(U42(X)) , U42(ok(X)) -> ok(U42(X)) , U51(mark(X)) -> mark(U51(X)) , U51(ok(X)) -> ok(U51(X)) , U61(mark(X1), X2) -> mark(U61(X1, X2)) , U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) , U62(mark(X)) -> mark(U62(X)) , U62(ok(X)) -> ok(U62(X)) , U71(mark(X1), X2) -> mark(U71(X1, X2)) , U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) , U72(mark(X1), X2) -> mark(U72(X1, X2)) , U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) , U81(mark(X1), X2, X3) -> mark(U81(X1, X2, X3)) , U81(ok(X1), ok(X2), ok(X3)) -> ok(U81(X1, X2, X3)) , U82(mark(X1), X2, X3) -> mark(U82(X1, X2, X3)) , U82(ok(X1), ok(X2), ok(X3)) -> ok(U82(X1, X2, X3)) , U83(mark(X1), X2, X3) -> mark(U83(X1, X2, X3)) , U83(ok(X1), ok(X2), ok(X3)) -> ok(U83(X1, X2, X3)) , U84(mark(X1), X2, X3) -> mark(U84(X1, X2, X3)) , U84(ok(X1), ok(X2), ok(X3)) -> ok(U84(X1, X2, X3)) , s(mark(X)) -> mark(s(X)) , s(ok(X)) -> ok(s(X)) , U91(mark(X1), X2) -> mark(U91(X1, X2)) , U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) , U92(mark(X)) -> mark(U92(X)) , U92(ok(X)) -> ok(U92(X)) , proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) , proper(tt()) -> ok(tt()) , proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) , proper(isNatKind(X)) -> isNatKind(proper(X)) , proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) , proper(isNat(X)) -> isNat(proper(X)) , proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) , proper(x(X1, X2)) -> x(proper(X1), proper(X2)) , proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) , proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) , proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) , proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) , proper(U15(X1, X2)) -> U15(proper(X1), proper(X2)) , proper(U16(X)) -> U16(proper(X)) , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)) , proper(U22(X1, X2)) -> U22(proper(X1), proper(X2)) , proper(U23(X)) -> U23(proper(X)) , proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) , proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) , proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) , proper(U34(X1, X2, X3)) -> U34(proper(X1), proper(X2), proper(X3)) , proper(U35(X1, X2)) -> U35(proper(X1), proper(X2)) , proper(U36(X)) -> U36(proper(X)) , proper(U41(X1, X2)) -> U41(proper(X1), proper(X2)) , proper(U42(X)) -> U42(proper(X)) , proper(U51(X)) -> U51(proper(X)) , proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) , proper(U62(X)) -> U62(proper(X)) , proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) , proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) , proper(U81(X1, X2, X3)) -> U81(proper(X1), proper(X2), proper(X3)) , proper(U82(X1, X2, X3)) -> U82(proper(X1), proper(X2), proper(X3)) , proper(U83(X1, X2, X3)) -> U83(proper(X1), proper(X2), proper(X3)) , proper(U84(X1, X2, X3)) -> U84(proper(X1), proper(X2), proper(X3)) , proper(s(X)) -> s(proper(X)) , proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) , proper(U92(X)) -> U92(proper(X)) , proper(0()) -> ok(0()) , top(mark(X)) -> top(proper(X)) , top(ok(X)) -> top(active(X)) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {75,76} by applications of Pre({75,76}) = {}. Here rules are labeled as follows: DPs: { 1: U101^#(mark(X1), X2, X3) -> c_82(U101^#(X1, X2, X3)) , 2: U101^#(ok(X1), ok(X2), ok(X3)) -> c_83(U101^#(X1, X2, X3)) , 3: U102^#(mark(X1), X2, X3) -> c_84(U102^#(X1, X2, X3)) , 4: U102^#(ok(X1), ok(X2), ok(X3)) -> c_85(U102^#(X1, X2, X3)) , 5: U103^#(mark(X1), X2, X3) -> c_87(U103^#(X1, X2, X3)) , 6: U103^#(ok(X1), ok(X2), ok(X3)) -> c_88(U103^#(X1, X2, X3)) , 7: U41^#(mark(X1), X2) -> c_128(U41^#(X1, X2)) , 8: U41^#(ok(X1), ok(X2)) -> c_129(U41^#(X1, X2)) , 9: U61^#(mark(X1), X2) -> c_134(U61^#(X1, X2)) , 10: U61^#(ok(X1), ok(X2)) -> c_135(U61^#(X1, X2)) , 11: U51^#(mark(X)) -> c_132(U51^#(X)) , 12: U51^#(ok(X)) -> c_133(U51^#(X)) , 13: U104^#(mark(X1), X2, X3) -> c_90(U104^#(X1, X2, X3)) , 14: U104^#(ok(X1), ok(X2), ok(X3)) -> c_91(U104^#(X1, X2, X3)) , 15: U11^#(mark(X1), X2, X3) -> c_98(U11^#(X1, X2, X3)) , 16: U11^#(ok(X1), ok(X2), ok(X3)) -> c_99(U11^#(X1, X2, X3)) , 17: U31^#(mark(X1), X2, X3) -> c_116(U31^#(X1, X2, X3)) , 18: U31^#(ok(X1), ok(X2), ok(X3)) -> c_117(U31^#(X1, X2, X3)) , 19: U21^#(mark(X1), X2) -> c_110(U21^#(X1, X2)) , 20: U21^#(ok(X1), ok(X2)) -> c_111(U21^#(X1, X2)) , 21: plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) , 22: plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) , 23: plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) , 24: U81^#(mark(X1), X2, X3) -> c_142(U81^#(X1, X2, X3)) , 25: U81^#(ok(X1), ok(X2), ok(X3)) -> c_143(U81^#(X1, X2, X3)) , 26: U71^#(mark(X1), X2) -> c_138(U71^#(X1, X2)) , 27: U71^#(ok(X1), ok(X2)) -> c_139(U71^#(X1, X2)) , 28: x^#(X1, mark(X2)) -> c_95(x^#(X1, X2)) , 29: x^#(mark(X1), X2) -> c_96(x^#(X1, X2)) , 30: x^#(ok(X1), ok(X2)) -> c_97(x^#(X1, X2)) , 31: U91^#(mark(X1), X2) -> c_152(U91^#(X1, X2)) , 32: U91^#(ok(X1), ok(X2)) -> c_153(U91^#(X1, X2)) , 33: U12^#(mark(X1), X2, X3) -> c_100(U12^#(X1, X2, X3)) , 34: U12^#(ok(X1), ok(X2), ok(X3)) -> c_101(U12^#(X1, X2, X3)) , 35: U13^#(mark(X1), X2, X3) -> c_102(U13^#(X1, X2, X3)) , 36: U13^#(ok(X1), ok(X2), ok(X3)) -> c_103(U13^#(X1, X2, X3)) , 37: U14^#(mark(X1), X2, X3) -> c_104(U14^#(X1, X2, X3)) , 38: U14^#(ok(X1), ok(X2), ok(X3)) -> c_105(U14^#(X1, X2, X3)) , 39: U15^#(mark(X1), X2) -> c_106(U15^#(X1, X2)) , 40: U15^#(ok(X1), ok(X2)) -> c_107(U15^#(X1, X2)) , 41: U16^#(mark(X)) -> c_108(U16^#(X)) , 42: U16^#(ok(X)) -> c_109(U16^#(X)) , 43: U22^#(mark(X1), X2) -> c_112(U22^#(X1, X2)) , 44: U22^#(ok(X1), ok(X2)) -> c_113(U22^#(X1, X2)) , 45: U23^#(mark(X)) -> c_114(U23^#(X)) , 46: U23^#(ok(X)) -> c_115(U23^#(X)) , 47: U32^#(mark(X1), X2, X3) -> c_118(U32^#(X1, X2, X3)) , 48: U32^#(ok(X1), ok(X2), ok(X3)) -> c_119(U32^#(X1, X2, X3)) , 49: U33^#(mark(X1), X2, X3) -> c_120(U33^#(X1, X2, X3)) , 50: U33^#(ok(X1), ok(X2), ok(X3)) -> c_121(U33^#(X1, X2, X3)) , 51: U34^#(mark(X1), X2, X3) -> c_122(U34^#(X1, X2, X3)) , 52: U34^#(ok(X1), ok(X2), ok(X3)) -> c_123(U34^#(X1, X2, X3)) , 53: U35^#(mark(X1), X2) -> c_124(U35^#(X1, X2)) , 54: U35^#(ok(X1), ok(X2)) -> c_125(U35^#(X1, X2)) , 55: U36^#(mark(X)) -> c_126(U36^#(X)) , 56: U36^#(ok(X)) -> c_127(U36^#(X)) , 57: U42^#(mark(X)) -> c_130(U42^#(X)) , 58: U42^#(ok(X)) -> c_131(U42^#(X)) , 59: U62^#(mark(X)) -> c_136(U62^#(X)) , 60: U62^#(ok(X)) -> c_137(U62^#(X)) , 61: U72^#(mark(X1), X2) -> c_140(U72^#(X1, X2)) , 62: U72^#(ok(X1), ok(X2)) -> c_141(U72^#(X1, X2)) , 63: U82^#(mark(X1), X2, X3) -> c_144(U82^#(X1, X2, X3)) , 64: U82^#(ok(X1), ok(X2), ok(X3)) -> c_145(U82^#(X1, X2, X3)) , 65: U83^#(mark(X1), X2, X3) -> c_146(U83^#(X1, X2, X3)) , 66: U83^#(ok(X1), ok(X2), ok(X3)) -> c_147(U83^#(X1, X2, X3)) , 67: U84^#(mark(X1), X2, X3) -> c_148(U84^#(X1, X2, X3)) , 68: U84^#(ok(X1), ok(X2), ok(X3)) -> c_149(U84^#(X1, X2, X3)) , 69: s^#(mark(X)) -> c_150(s^#(X)) , 70: s^#(ok(X)) -> c_151(s^#(X)) , 71: U92^#(mark(X)) -> c_154(U92^#(X)) , 72: U92^#(ok(X)) -> c_155(U92^#(X)) , 73: isNatKind^#(ok(X)) -> c_86(isNatKind^#(X)) , 74: isNat^#(ok(X)) -> c_89(isNat^#(X)) , 75: proper^#(tt()) -> c_157() , 76: proper^#(0()) -> c_194() , 77: top^#(mark(X)) -> c_195(top^#(proper(X))) , 78: top^#(ok(X)) -> c_196(top^#(active(X))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { U101^#(mark(X1), X2, X3) -> c_82(U101^#(X1, X2, X3)) , U101^#(ok(X1), ok(X2), ok(X3)) -> c_83(U101^#(X1, X2, X3)) , U102^#(mark(X1), X2, X3) -> c_84(U102^#(X1, X2, X3)) , U102^#(ok(X1), ok(X2), ok(X3)) -> c_85(U102^#(X1, X2, X3)) , U103^#(mark(X1), X2, X3) -> c_87(U103^#(X1, X2, X3)) , U103^#(ok(X1), ok(X2), ok(X3)) -> c_88(U103^#(X1, X2, X3)) , U41^#(mark(X1), X2) -> c_128(U41^#(X1, X2)) , U41^#(ok(X1), ok(X2)) -> c_129(U41^#(X1, X2)) , U61^#(mark(X1), X2) -> c_134(U61^#(X1, X2)) , U61^#(ok(X1), ok(X2)) -> c_135(U61^#(X1, X2)) , U51^#(mark(X)) -> c_132(U51^#(X)) , U51^#(ok(X)) -> c_133(U51^#(X)) , U104^#(mark(X1), X2, X3) -> c_90(U104^#(X1, X2, X3)) , U104^#(ok(X1), ok(X2), ok(X3)) -> c_91(U104^#(X1, X2, X3)) , U11^#(mark(X1), X2, X3) -> c_98(U11^#(X1, X2, X3)) , U11^#(ok(X1), ok(X2), ok(X3)) -> c_99(U11^#(X1, X2, X3)) , U31^#(mark(X1), X2, X3) -> c_116(U31^#(X1, X2, X3)) , U31^#(ok(X1), ok(X2), ok(X3)) -> c_117(U31^#(X1, X2, X3)) , U21^#(mark(X1), X2) -> c_110(U21^#(X1, X2)) , U21^#(ok(X1), ok(X2)) -> c_111(U21^#(X1, X2)) , plus^#(X1, mark(X2)) -> c_92(plus^#(X1, X2)) , plus^#(mark(X1), X2) -> c_93(plus^#(X1, X2)) , plus^#(ok(X1), ok(X2)) -> c_94(plus^#(X1, X2)) , U81^#(mark(X1), X2, X3) -> c_142(U81^#(X1, X2, X3)) , U81^#(ok(X1), ok(X2), ok(X3)) -> c_143(U81^#(X1, X2, X3)) , U71^#(mark(X1), X2) -> c_138(U71^#(X1, X2)) , U71^#(ok(X1), ok(X2)) -> c_139(U71^#(X1, X2)) , x^#(X1, mark(X2)) -> c_95(x^#(X1, X2)) , x^#(mark(X1), X2) -> c_96(x^#(X1, X2)) , x^#(ok(X1), ok(X2)) -> c_97(x^#(X1, X2)) , U91^#(mark(X1), X2) -> c_152(U91^#(X1, X2)) , U91^#(ok(X1), ok(X2)) -> c_153(U91^#(X1, X2)) , U12^#(mark(X1), X2, X3) -> c_100(U12^#(X1, X2, X3)) , U12^#(ok(X1), ok(X2), ok(X3)) -> c_101(U12^#(X1, X2, X3)) , U13^#(mark(X1), X2, X3) -> c_102(U13^#(X1, X2, X3)) , U13^#(ok(X1), ok(X2), ok(X3)) -> c_103(U13^#(X1, X2, X3)) , U14^#(mark(X1), X2, X3) -> c_104(U14^#(X1, X2, X3)) , U14^#(ok(X1), ok(X2), ok(X3)) -> c_105(U14^#(X1, X2, X3)) , U15^#(mark(X1), X2) -> c_106(U15^#(X1, X2)) , U15^#(ok(X1), ok(X2)) -> c_107(U15^#(X1, X2)) , U16^#(mark(X)) -> c_108(U16^#(X)) , U16^#(ok(X)) -> c_109(U16^#(X)) , U22^#(mark(X1), X2) -> c_112(U22^#(X1, X2)) , U22^#(ok(X1), ok(X2)) -> c_113(U22^#(X1, X2)) , U23^#(mark(X)) -> c_114(U23^#(X)) , U23^#(ok(X)) -> c_115(U23^#(X)) , U32^#(mark(X1), X2, X3) -> c_118(U32^#(X1, X2, X3)) , U32^#(ok(X1), ok(X2), ok(X3)) -> c_119(U32^#(X1, X2, X3)) , U33^#(mark(X1), X2, X3) -> c_120(U33^#(X1, X2, X3)) , U33^#(ok(X1), ok(X2), ok(X3)) -> c_121(U33^#(X1, X2, X3)) , U34^#(mark(X1), X2, X3) -> c_122(U34^#(X1, X2, X3)) , U34^#(ok(X1), ok(X2), ok(X3)) -> c_123(U34^#(X1, X2, X3)) , U35^#(mark(X1), X2) -> c_124(U35^#(X1, X2)) , U35^#(ok(X1), ok(X2)) -> c_125(U35^#(X1, X2)) , U36^#(mark(X)) -> c_126(U36^#(X)) , U36^#(ok(X)) -> c_127(U36^#(X)) , U42^#(mark(X)) -> c_130(U42^#(X)) , U42^#(ok(X)) -> c_131(U42^#(X)) , U62^#(mark(X)) -> c_136(U62^#(X)) , U62^#(ok(X)) -> c_137(U62^#(X)) , U72^#(mark(X1), X2) -> c_140(U72^#(X1, X2)) , U72^#(ok(X1), ok(X2)) -> c_141(U72^#(X1, X2)) , U82^#(mark(X1), X2, X3) -> c_144(U82^#(X1, X2, X3)) , U82^#(ok(X1), ok(X2), ok(X3)) -> c_145(U82^#(X1, X2, X3)) , U83^#(mark(X1), X2, X3) -> c_146(U83^#(X1, X2, X3)) , U83^#(ok(X1), ok(X2), ok(X3)) -> c_147(U83^#(X1, X2, X3)) , U84^#(mark(X1), X2, X3) -> c_148(U84^#(X1, X2, X3)) , U84^#(ok(X1), ok(X2), ok(X3)) -> c_149(U84^#(X1, X2, X3)) , s^#(mark(X)) -> c_150(s^#(X)) , s^#(ok(X)) -> c_151(s^#(X)) , U92^#(mark(X)) -> c_154(U92^#(X)) , U92^#(ok(X)) -> c_155(U92^#(X)) , isNatKind^#(ok(X)) -> c_86(isNatKind^#(X)) , isNat^#(ok(X)) -> c_89(isNat^#(X)) , top^#(mark(X)) -> c_195(top^#(proper(X))) , top^#(ok(X)) -> c_196(top^#(active(X))) } Strict Trs: { active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) , active(U101(tt(), M, N)) -> mark(U102(isNatKind(M), M, N)) , active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) , active(U102(tt(), M, N)) -> mark(U103(isNat(N), M, N)) , active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2)) , active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2)) , active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) , active(isNatKind(0())) -> mark(tt()) , active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) , active(U103(tt(), M, N)) -> mark(U104(isNatKind(N), M, N)) , active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2)) , active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2)) , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) , active(isNat(0())) -> mark(tt()) , active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) , active(U104(tt(), M, N)) -> mark(plus(x(N, M), N)) , active(plus(X1, X2)) -> plus(X1, active(X2)) , active(plus(X1, X2)) -> plus(active(X1), X2) , active(plus(N, s(M))) -> mark(U81(isNat(M), M, N)) , active(plus(N, 0())) -> mark(U71(isNat(N), N)) , active(x(X1, X2)) -> x(X1, active(X2)) , active(x(X1, X2)) -> x(active(X1), X2) , active(x(N, s(M))) -> mark(U101(isNat(M), M, N)) , active(x(N, 0())) -> mark(U91(isNat(N), N)) , active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) , active(U11(tt(), V1, V2)) -> mark(U12(isNatKind(V1), V1, V2)) , active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) , active(U12(tt(), V1, V2)) -> mark(U13(isNatKind(V2), V1, V2)) , active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) , active(U13(tt(), V1, V2)) -> mark(U14(isNatKind(V2), V1, V2)) , active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) , active(U14(tt(), V1, V2)) -> mark(U15(isNat(V1), V2)) , active(U15(X1, X2)) -> U15(active(X1), X2) , active(U15(tt(), V2)) -> mark(U16(isNat(V2))) , active(U16(X)) -> U16(active(X)) , active(U16(tt())) -> mark(tt()) , active(U21(X1, X2)) -> U21(active(X1), X2) , active(U21(tt(), V1)) -> mark(U22(isNatKind(V1), V1)) , active(U22(X1, X2)) -> U22(active(X1), X2) , active(U22(tt(), V1)) -> mark(U23(isNat(V1))) , active(U23(X)) -> U23(active(X)) , active(U23(tt())) -> mark(tt()) , active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) , active(U31(tt(), V1, V2)) -> mark(U32(isNatKind(V1), V1, V2)) , active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) , active(U32(tt(), V1, V2)) -> mark(U33(isNatKind(V2), V1, V2)) , active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) , active(U33(tt(), V1, V2)) -> mark(U34(isNatKind(V2), V1, V2)) , active(U34(X1, X2, X3)) -> U34(active(X1), X2, X3) , active(U34(tt(), V1, V2)) -> mark(U35(isNat(V1), V2)) , active(U35(X1, X2)) -> U35(active(X1), X2) , active(U35(tt(), V2)) -> mark(U36(isNat(V2))) , active(U36(X)) -> U36(active(X)) , active(U36(tt())) -> mark(tt()) , active(U41(X1, X2)) -> U41(active(X1), X2) , active(U41(tt(), V2)) -> mark(U42(isNatKind(V2))) , active(U42(X)) -> U42(active(X)) , active(U42(tt())) -> mark(tt()) , active(U51(X)) -> U51(active(X)) , active(U51(tt())) -> mark(tt()) , active(U61(X1, X2)) -> U61(active(X1), X2) , active(U61(tt(), V2)) -> mark(U62(isNatKind(V2))) , active(U62(X)) -> U62(active(X)) , active(U62(tt())) -> mark(tt()) , active(U71(X1, X2)) -> U71(active(X1), X2) , active(U71(tt(), N)) -> mark(U72(isNatKind(N), N)) , active(U72(X1, X2)) -> U72(active(X1), X2) , active(U72(tt(), N)) -> mark(N) , active(U81(X1, X2, X3)) -> U81(active(X1), X2, X3) , active(U81(tt(), M, N)) -> mark(U82(isNatKind(M), M, N)) , active(U82(X1, X2, X3)) -> U82(active(X1), X2, X3) , active(U82(tt(), M, N)) -> mark(U83(isNat(N), M, N)) , active(U83(X1, X2, X3)) -> U83(active(X1), X2, X3) , active(U83(tt(), M, N)) -> mark(U84(isNatKind(N), M, N)) , active(U84(X1, X2, X3)) -> U84(active(X1), X2, X3) , active(U84(tt(), M, N)) -> mark(s(plus(N, M))) , active(s(X)) -> s(active(X)) , active(U91(X1, X2)) -> U91(active(X1), X2) , active(U91(tt(), N)) -> mark(U92(isNatKind(N))) , active(U92(X)) -> U92(active(X)) , active(U92(tt())) -> mark(0()) , U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) , U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) , U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) , U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) , isNatKind(ok(X)) -> ok(isNatKind(X)) , U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) , U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) , isNat(ok(X)) -> ok(isNat(X)) , U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) , U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) , plus(X1, mark(X2)) -> mark(plus(X1, X2)) , plus(mark(X1), X2) -> mark(plus(X1, X2)) , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) , x(X1, mark(X2)) -> mark(x(X1, X2)) , x(mark(X1), X2) -> mark(x(X1, X2)) , x(ok(X1), ok(X2)) -> ok(x(X1, X2)) , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) , U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) , U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) , U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) , U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) , U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) , U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) , U15(mark(X1), X2) -> mark(U15(X1, X2)) , U15(ok(X1), ok(X2)) -> ok(U15(X1, X2)) , U16(mark(X)) -> mark(U16(X)) , U16(ok(X)) -> ok(U16(X)) , U21(mark(X1), X2) -> mark(U21(X1, X2)) , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)) , U22(mark(X1), X2) -> mark(U22(X1, X2)) , U22(ok(X1), ok(X2)) -> ok(U22(X1, X2)) , U23(mark(X)) -> mark(U23(X)) , U23(ok(X)) -> ok(U23(X)) , U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) , U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) , U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) , U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) , U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) , U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) , U34(mark(X1), X2, X3) -> mark(U34(X1, X2, X3)) , U34(ok(X1), ok(X2), ok(X3)) -> ok(U34(X1, X2, X3)) , U35(mark(X1), X2) -> mark(U35(X1, X2)) , U35(ok(X1), ok(X2)) -> ok(U35(X1, X2)) , U36(mark(X)) -> mark(U36(X)) , U36(ok(X)) -> ok(U36(X)) , U41(mark(X1), X2) -> mark(U41(X1, X2)) , U41(ok(X1), ok(X2)) -> ok(U41(X1, X2)) , U42(mark(X)) -> mark(U42(X)) , U42(ok(X)) -> ok(U42(X)) , U51(mark(X)) -> mark(U51(X)) , U51(ok(X)) -> ok(U51(X)) , U61(mark(X1), X2) -> mark(U61(X1, X2)) , U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) , U62(mark(X)) -> mark(U62(X)) , U62(ok(X)) -> ok(U62(X)) , U71(mark(X1), X2) -> mark(U71(X1, X2)) , U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) , U72(mark(X1), X2) -> mark(U72(X1, X2)) , U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) , U81(mark(X1), X2, X3) -> mark(U81(X1, X2, X3)) , U81(ok(X1), ok(X2), ok(X3)) -> ok(U81(X1, X2, X3)) , U82(mark(X1), X2, X3) -> mark(U82(X1, X2, X3)) , U82(ok(X1), ok(X2), ok(X3)) -> ok(U82(X1, X2, X3)) , U83(mark(X1), X2, X3) -> mark(U83(X1, X2, X3)) , U83(ok(X1), ok(X2), ok(X3)) -> ok(U83(X1, X2, X3)) , U84(mark(X1), X2, X3) -> mark(U84(X1, X2, X3)) , U84(ok(X1), ok(X2), ok(X3)) -> ok(U84(X1, X2, X3)) , s(mark(X)) -> mark(s(X)) , s(ok(X)) -> ok(s(X)) , U91(mark(X1), X2) -> mark(U91(X1, X2)) , U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) , U92(mark(X)) -> mark(U92(X)) , U92(ok(X)) -> ok(U92(X)) , proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) , proper(tt()) -> ok(tt()) , proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) , proper(isNatKind(X)) -> isNatKind(proper(X)) , proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) , proper(isNat(X)) -> isNat(proper(X)) , proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) , proper(x(X1, X2)) -> x(proper(X1), proper(X2)) , proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) , proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) , proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) , proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) , proper(U15(X1, X2)) -> U15(proper(X1), proper(X2)) , proper(U16(X)) -> U16(proper(X)) , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)) , proper(U22(X1, X2)) -> U22(proper(X1), proper(X2)) , proper(U23(X)) -> U23(proper(X)) , proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) , proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) , proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) , proper(U34(X1, X2, X3)) -> U34(proper(X1), proper(X2), proper(X3)) , proper(U35(X1, X2)) -> U35(proper(X1), proper(X2)) , proper(U36(X)) -> U36(proper(X)) , proper(U41(X1, X2)) -> U41(proper(X1), proper(X2)) , proper(U42(X)) -> U42(proper(X)) , proper(U51(X)) -> U51(proper(X)) , proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) , proper(U62(X)) -> U62(proper(X)) , proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) , proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) , proper(U81(X1, X2, X3)) -> U81(proper(X1), proper(X2), proper(X3)) , proper(U82(X1, X2, X3)) -> U82(proper(X1), proper(X2), proper(X3)) , proper(U83(X1, X2, X3)) -> U83(proper(X1), proper(X2), proper(X3)) , proper(U84(X1, X2, X3)) -> U84(proper(X1), proper(X2), proper(X3)) , proper(s(X)) -> s(proper(X)) , proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) , proper(U92(X)) -> U92(proper(X)) , proper(0()) -> ok(0()) , top(mark(X)) -> top(proper(X)) , top(ok(X)) -> top(active(X)) } Weak DPs: { proper^#(tt()) -> c_157() , proper^#(0()) -> c_194() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..