- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__U101(tt,M,N) -> a__U102(a__isNatKind(M),M,N) [2] a__U102(tt,M,N) -> a__U103(a__isNat(N),M,N) [3] a__U103(tt,M,N) -> a__U104(a__isNatKind(N),M,N) [4] a__U104(tt,M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) [5] a__U11(tt,V1,V2) -> a__U12(a__isNatKind(V1),V1,V2) [6] a__U12(tt,V1,V2) -> a__U13(a__isNatKind(V2),V1,V2) [7] a__U13(tt,V1,V2) -> a__U14(a__isNatKind(V2),V1,V2) [8] a__U14(tt,V1,V2) -> a__U15(a__isNat(V1),V2) [9] a__U15(tt,V2) -> a__U16(a__isNat(V2)) [10] a__U16(tt) -> tt [11] a__U21(tt,V1) -> a__U22(a__isNatKind(V1),V1) [12] a__U22(tt,V1) -> a__U23(a__isNat(V1)) [13] a__U23(tt) -> tt [14] a__U31(tt,V1,V2) -> a__U32(a__isNatKind(V1),V1,V2) [15] a__U32(tt,V1,V2) -> a__U33(a__isNatKind(V2),V1,V2) [16] a__U33(tt,V1,V2) -> a__U34(a__isNatKind(V2),V1,V2) [17] a__U34(tt,V1,V2) -> a__U35(a__isNat(V1),V2) [18] a__U35(tt,V2) -> a__U36(a__isNat(V2)) [19] a__U36(tt) -> tt [20] a__U41(tt,V2) -> a__U42(a__isNatKind(V2)) [21] a__U42(tt) -> tt [22] a__U51(tt) -> tt [23] a__U61(tt,V2) -> a__U62(a__isNatKind(V2)) [24] a__U62(tt) -> tt [25] a__U71(tt,N) -> a__U72(a__isNatKind(N),N) [26] a__U72(tt,N) -> mark(N) [27] a__U81(tt,M,N) -> a__U82(a__isNatKind(M),M,N) [28] a__U82(tt,M,N) -> a__U83(a__isNat(N),M,N) [29] a__U83(tt,M,N) -> a__U84(a__isNatKind(N),M,N) [30] a__U84(tt,M,N) -> s(a__plus(mark(N),mark(M))) [31] a__U91(tt,N) -> a__U92(a__isNatKind(N)) [32] a__U92(tt) -> 0 [33] a__isNat(0) -> tt [34] a__isNat(plus(V1,V2)) -> a__U11(a__isNatKind(V1),V1,V2) [35] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) [36] a__isNat(x(V1,V2)) -> a__U31(a__isNatKind(V1),V1,V2) [37] a__isNatKind(0) -> tt [38] a__isNatKind(plus(V1,V2)) -> a__U41(a__isNatKind(V1),V2) [39] a__isNatKind(s(V1)) -> a__U51(a__isNatKind(V1)) [40] a__isNatKind(x(V1,V2)) -> a__U61(a__isNatKind(V1),V2) [41] a__plus(N,0) -> a__U71(a__isNat(N),N) [42] a__plus(N,s(M)) -> a__U81(a__isNat(M),M,N) [43] a__x(N,0) -> a__U91(a__isNat(N),N) [44] a__x(N,s(M)) -> a__U101(a__isNat(M),M,N) [45] mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) [46] mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) [47] mark(isNatKind(X)) -> a__isNatKind(X) [48] mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) [49] mark(isNat(X)) -> a__isNat(X) [50] mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) [51] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) [52] mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) [53] mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) [54] mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3) [55] mark(U13(X1,X2,X3)) -> a__U13(mark(X1),X2,X3) [56] mark(U14(X1,X2,X3)) -> a__U14(mark(X1),X2,X3) [57] mark(U15(X1,X2)) -> a__U15(mark(X1),X2) [58] mark(U16(X)) -> a__U16(mark(X)) [59] mark(U21(X1,X2)) -> a__U21(mark(X1),X2) [60] mark(U22(X1,X2)) -> a__U22(mark(X1),X2) [61] mark(U23(X)) -> a__U23(mark(X)) [62] mark(U31(X1,X2,X3)) -> a__U31(mark(X1),X2,X3) [63] mark(U32(X1,X2,X3)) -> a__U32(mark(X1),X2,X3) [64] mark(U33(X1,X2,X3)) -> a__U33(mark(X1),X2,X3) [65] mark(U34(X1,X2,X3)) -> a__U34(mark(X1),X2,X3) [66] mark(U35(X1,X2)) -> a__U35(mark(X1),X2) [67] mark(U36(X)) -> a__U36(mark(X)) [68] mark(U41(X1,X2)) -> a__U41(mark(X1),X2) [69] mark(U42(X)) -> a__U42(mark(X)) [70] mark(U51(X)) -> a__U51(mark(X)) [71] mark(U61(X1,X2)) -> a__U61(mark(X1),X2) [72] mark(U62(X)) -> a__U62(mark(X)) [73] mark(U71(X1,X2)) -> a__U71(mark(X1),X2) [74] mark(U72(X1,X2)) -> a__U72(mark(X1),X2) [75] mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) [76] mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) [77] mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) [78] mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) [79] mark(U91(X1,X2)) -> a__U91(mark(X1),X2) [80] mark(U92(X)) -> a__U92(mark(X)) [81] mark(tt) -> tt [82] mark(s(X)) -> s(mark(X)) [83] mark(0) -> 0 [84] a__U101(X1,X2,X3) -> U101(X1,X2,X3) [85] a__U102(X1,X2,X3) -> U102(X1,X2,X3) [86] a__isNatKind(X) -> isNatKind(X) [87] a__U103(X1,X2,X3) -> U103(X1,X2,X3) [88] a__isNat(X) -> isNat(X) [89] a__U104(X1,X2,X3) -> U104(X1,X2,X3) [90] a__plus(X1,X2) -> plus(X1,X2) [91] a__x(X1,X2) -> x(X1,X2) [92] a__U11(X1,X2,X3) -> U11(X1,X2,X3) [93] a__U12(X1,X2,X3) -> U12(X1,X2,X3) [94] a__U13(X1,X2,X3) -> U13(X1,X2,X3) [95] a__U14(X1,X2,X3) -> U14(X1,X2,X3) [96] a__U15(X1,X2) -> U15(X1,X2) [97] a__U16(X) -> U16(X) [98] a__U21(X1,X2) -> U21(X1,X2) [99] a__U22(X1,X2) -> U22(X1,X2) [100] a__U23(X) -> U23(X) [101] a__U31(X1,X2,X3) -> U31(X1,X2,X3) [102] a__U32(X1,X2,X3) -> U32(X1,X2,X3) [103] a__U33(X1,X2,X3) -> U33(X1,X2,X3) [104] a__U34(X1,X2,X3) -> U34(X1,X2,X3) [105] a__U35(X1,X2) -> U35(X1,X2) [106] a__U36(X) -> U36(X) [107] a__U41(X1,X2) -> U41(X1,X2) [108] a__U42(X) -> U42(X) [109] a__U51(X) -> U51(X) [110] a__U61(X1,X2) -> U61(X1,X2) [111] a__U62(X) -> U62(X) [112] a__U71(X1,X2) -> U71(X1,X2) [113] a__U72(X1,X2) -> U72(X1,X2) [114] a__U81(X1,X2,X3) -> U81(X1,X2,X3) [115] a__U82(X1,X2,X3) -> U82(X1,X2,X3) [116] a__U83(X1,X2,X3) -> U83(X1,X2,X3) [117] a__U84(X1,X2,X3) -> U84(X1,X2,X3) [118] a__U91(X1,X2) -> U91(X1,X2) [119] a__U92(X) -> U92(X) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) ; a__U102(X1,X2,X3) >= U102(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) ; a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) ; a__U101(X1,X2,X3) >= U101(X1,X2,X3) ; a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) ; a__U103(X1,X2,X3) >= U103(X1,X2,X3) ; a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) ; a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) ; a__isNat(X) >= isNat(X) ; a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ; a__U104(X1,X2,X3) >= U104(X1,X2,X3) ; a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) ; a__plus(N,0) >= a__U71(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) ; a__x(N,0) >= a__U91(a__isNat(N),N) ; a__x(X1,X2) >= x(X1,X2) ; mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ; mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) ; mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) ; mark(isNat(X)) >= a__isNat(X) ; mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) ; mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) ; mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) ; mark(U15(X1,X2)) >= a__U15(mark(X1),X2) ; mark(U16(X)) >= a__U16(mark(X)) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U22(X1,X2)) >= a__U22(mark(X1),X2) ; mark(U23(X)) >= a__U23(mark(X)) ; mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) ; mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) ; mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) ; mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) ; mark(U35(X1,X2)) >= a__U35(mark(X1),X2) ; mark(U36(X)) >= a__U36(mark(X)) ; mark(U41(X1,X2)) >= a__U41(mark(X1),X2) ; mark(U42(X)) >= a__U42(mark(X)) ; mark(U51(X)) >= a__U51(mark(X)) ; mark(U61(X1,X2)) >= a__U61(mark(X1),X2) ; mark(U62(X)) >= a__U62(mark(X)) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U72(X1,X2)) >= a__U72(mark(X1),X2) ; mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) ; mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) ; mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) ; mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) ; mark(U91(X1,X2)) >= a__U91(mark(X1),X2) ; mark(U92(X)) >= a__U92(mark(X)) ; a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) ; a__U11(X1,X2,X3) >= U11(X1,X2,X3) ; a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) ; a__U13(X1,X2,X3) >= U13(X1,X2,X3) ; a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) ; a__U14(X1,X2,X3) >= U14(X1,X2,X3) ; a__U15(tt,V2) >= a__U16(a__isNat(V2)) ; a__U15(X1,X2) >= U15(X1,X2) ; a__U16(tt) >= tt ; a__U16(X) >= U16(X) ; a__U22(tt,V1) >= a__U23(a__isNat(V1)) ; a__U22(X1,X2) >= U22(X1,X2) ; a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U23(tt) >= tt ; a__U23(X) >= U23(X) ; a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) ; a__U32(X1,X2,X3) >= U32(X1,X2,X3) ; a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) ; a__U31(X1,X2,X3) >= U31(X1,X2,X3) ; a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) ; a__U33(X1,X2,X3) >= U33(X1,X2,X3) ; a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) ; a__U34(X1,X2,X3) >= U34(X1,X2,X3) ; a__U35(tt,V2) >= a__U36(a__isNat(V2)) ; a__U35(X1,X2) >= U35(X1,X2) ; a__U36(tt) >= tt ; a__U36(X) >= U36(X) ; a__U42(tt) >= tt ; a__U42(X) >= U42(X) ; a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) ; a__U41(X1,X2) >= U41(X1,X2) ; a__U51(tt) >= tt ; a__U51(X) >= U51(X) ; a__U62(tt) >= tt ; a__U62(X) >= U62(X) ; a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) ; a__U61(X1,X2) >= U61(X1,X2) ; a__U72(tt,N) >= mark(N) ; a__U72(X1,X2) >= U72(X1,X2) ; a__U71(tt,N) >= a__U72(a__isNatKind(N),N) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) ; a__U82(X1,X2,X3) >= U82(X1,X2,X3) ; a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) ; a__U81(X1,X2,X3) >= U81(X1,X2,X3) ; a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) ; a__U83(X1,X2,X3) >= U83(X1,X2,X3) ; a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U84(X1,X2,X3) >= U84(X1,X2,X3) ; a__U92(tt) >= 0 ; a__U92(X) >= U92(X) ; a__U91(tt,N) >= a__U92(a__isNatKind(N)) ; a__U91(X1,X2) >= U91(X1,X2) ; Marked_a__U84(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) ; Marked_a__U84(tt,M,N) >= Marked_mark(M) ; Marked_a__U84(tt,M,N) >= Marked_mark(N) ; Marked_a__U83(tt,M,N) >= Marked_a__U84(a__isNatKind(N),M,N) ; Marked_a__U82(tt,M,N) >= Marked_a__U83(a__isNat(N),M,N) ; Marked_a__U81(tt,M,N) >= Marked_a__U82(a__isNatKind(M),M,N) ; Marked_a__U72(tt,N) >= Marked_mark(N) ; Marked_a__U71(tt,N) >= Marked_a__U72(a__isNatKind(N),N) ; Marked_a__x(N,s(M)) >= Marked_a__U101(a__isNat(M),M,N) ; Marked_a__plus(N,s(M)) >= Marked_a__U81(a__isNat(M),M,N) ; Marked_a__plus(N,0) >= Marked_a__U71(a__isNat(N),N) ; Marked_a__U104(tt,M,N) >= Marked_a__x(mark(N),mark(M)) ; Marked_a__U104(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ; Marked_a__U104(tt,M,N) >= Marked_mark(M) ; Marked_a__U104(tt,M,N) >= Marked_mark(N) ; Marked_a__U103(tt,M,N) >= Marked_a__U104(a__isNatKind(N),M,N) ; Marked_a__U102(tt,M,N) >= Marked_a__U103(a__isNat(N),M,N) ; Marked_a__U101(tt,M,N) >= Marked_a__U102(a__isNatKind(M),M,N) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(x(X1,X2)) >= Marked_a__x(mark(X1),mark(X2)) ; Marked_mark(x(X1,X2)) >= Marked_mark(X1) ; Marked_mark(x(X1,X2)) >= Marked_mark(X2) ; Marked_mark(U101(X1,X2,X3)) >= Marked_a__U101(mark(X1),X2,X3) ; Marked_mark(U101(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U102(X1,X2,X3)) >= Marked_a__U102(mark(X1),X2,X3) ; Marked_mark(U102(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U103(X1,X2,X3)) >= Marked_a__U103(mark(X1),X2,X3) ; Marked_mark(U103(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U104(X1,X2,X3)) >= Marked_a__U104(mark(X1),X2,X3) ; Marked_mark(U104(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U13(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U14(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U15(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U16(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U22(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U23(X)) >= Marked_mark(X) ; Marked_mark(U31(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U32(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U33(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U34(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U35(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U36(X)) >= Marked_mark(X) ; Marked_mark(U41(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U42(X)) >= Marked_mark(X) ; Marked_mark(U51(X)) >= Marked_mark(X) ; Marked_mark(U61(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U62(X)) >= Marked_mark(X) ; Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) ; Marked_mark(U71(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U72(X1,X2)) >= Marked_a__U72(mark(X1),X2) ; Marked_mark(U72(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U81(X1,X2,X3)) >= Marked_a__U81(mark(X1),X2,X3) ; Marked_mark(U81(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U82(X1,X2,X3)) >= Marked_a__U82(mark(X1),X2,X3) ; Marked_mark(U82(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U83(X1,X2,X3)) >= Marked_a__U83(mark(X1),X2,X3) ; Marked_mark(U83(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U84(X1,X2,X3)) >= Marked_a__U84(mark(X1),X2,X3) ; Marked_mark(U84(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U91(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U92(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__U84(tt,M,N) > Marked_a__plus(mark(N),mark(M)) ; } { Marked_a__U84(tt,M,N) > Marked_mark(M) ; } { Marked_a__U84(tt,M,N) > Marked_mark(N) ; } { Marked_a__U83(tt,M,N) > Marked_a__U84(a__isNatKind(N),M,N) ; } { Marked_a__U82(tt,M,N) > Marked_a__U83(a__isNat(N),M,N) ; } { Marked_a__U81(tt,M,N) > Marked_a__U82(a__isNatKind(M),M,N) ; } { Marked_a__U72(tt,N) > Marked_mark(N) ; } { Marked_a__U71(tt,N) > Marked_a__U72(a__isNatKind(N),N) ; } { Marked_a__x(N,s(M)) > Marked_a__U101(a__isNat(M),M,N) ; } { Marked_a__plus(N,s(M)) > Marked_a__U81(a__isNat(M),M,N) ; } { Marked_a__plus(N,0) > Marked_a__U71(a__isNat(N),N) ; } { Marked_a__U104(tt,M,N) > Marked_a__x(mark(N),mark(M)) ; } { Marked_a__U104(tt,M,N) > Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ; } { Marked_a__U104(tt,M,N) > Marked_mark(M) ; } { Marked_a__U104(tt,M,N) > Marked_mark(N) ; } { Marked_a__U103(tt,M,N) > Marked_a__U104(a__isNatKind(N),M,N) ; } { Marked_a__U102(tt,M,N) > Marked_a__U103(a__isNat(N),M,N) ; } { Marked_a__U101(tt,M,N) > Marked_a__U102(a__isNatKind(M),M,N) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(plus(X1,X2)) > Marked_a__plus(mark(X1),mark(X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(x(X1,X2)) > Marked_a__x(mark(X1),mark(X2)) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(U101(X1,X2,X3)) > Marked_a__U101(mark(X1),X2,X3) ; } { Marked_mark(U101(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U102(X1,X2,X3)) > Marked_a__U102(mark(X1),X2,X3) ; } { Marked_mark(U102(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U103(X1,X2,X3)) > Marked_a__U103(mark(X1),X2,X3) ; } { Marked_mark(U103(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U104(X1,X2,X3)) > Marked_a__U104(mark(X1),X2,X3) ; } { Marked_mark(U104(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U13(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U14(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U15(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U16(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U22(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U23(X)) > Marked_mark(X) ; } { Marked_mark(U31(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U32(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U33(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U34(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U35(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U36(X)) > Marked_mark(X) ; } { Marked_mark(U41(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U42(X)) > Marked_mark(X) ; } { Marked_mark(U51(X)) > Marked_mark(X) ; } { Marked_mark(U61(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U62(X)) > Marked_mark(X) ; } { Marked_mark(U71(X1,X2)) > Marked_a__U71(mark(X1),X2) ; } { Marked_mark(U71(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U72(X1,X2)) > Marked_a__U72(mark(X1),X2) ; } { Marked_mark(U72(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U81(X1,X2,X3)) > Marked_a__U81(mark(X1),X2,X3) ; } { Marked_mark(U81(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U82(X1,X2,X3)) > Marked_a__U82(mark(X1),X2,X3) ; } { Marked_mark(U82(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U83(X1,X2,X3)) > Marked_a__U83(mark(X1),X2,X3) ; } { Marked_mark(U83(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U84(X1,X2,X3)) > Marked_a__U84(mark(X1),X2,X3) ; } { Marked_mark(U84(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U91(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U92(X)) > Marked_mark(X) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) constraint: a__U102(X1,X2,X3) >= U102(X1,X2,X3) constraint: a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) constraint: a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) constraint: a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) constraint: a__U101(X1,X2,X3) >= U101(X1,X2,X3) constraint: a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) constraint: a__U103(X1,X2,X3) >= U103(X1,X2,X3) constraint: a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) constraint: a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) constraint: a__isNat(X) >= isNat(X) constraint: a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) constraint: a__U104(X1,X2,X3) >= U104(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U71(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) constraint: a__x(N,0) >= a__U91(a__isNat(N),N) constraint: a__x(X1,X2) >= x(X1,X2) constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) constraint: mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) constraint: mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) constraint: mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) constraint: mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) constraint: mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) constraint: mark(U15(X1,X2)) >= a__U15(mark(X1),X2) constraint: mark(U16(X)) >= a__U16(mark(X)) constraint: mark(U21(X1,X2)) >= a__U21(mark(X1),X2) constraint: mark(U22(X1,X2)) >= a__U22(mark(X1),X2) constraint: mark(U23(X)) >= a__U23(mark(X)) constraint: mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) constraint: mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) constraint: mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) constraint: mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) constraint: mark(U35(X1,X2)) >= a__U35(mark(X1),X2) constraint: mark(U36(X)) >= a__U36(mark(X)) constraint: mark(U41(X1,X2)) >= a__U41(mark(X1),X2) constraint: mark(U42(X)) >= a__U42(mark(X)) constraint: mark(U51(X)) >= a__U51(mark(X)) constraint: mark(U61(X1,X2)) >= a__U61(mark(X1),X2) constraint: mark(U62(X)) >= a__U62(mark(X)) constraint: mark(U71(X1,X2)) >= a__U71(mark(X1),X2) constraint: mark(U72(X1,X2)) >= a__U72(mark(X1),X2) constraint: mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) constraint: mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) constraint: mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) constraint: mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) constraint: mark(U91(X1,X2)) >= a__U91(mark(X1),X2) constraint: mark(U92(X)) >= a__U92(mark(X)) constraint: a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) constraint: a__U12(X1,X2,X3) >= U12(X1,X2,X3) constraint: a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) constraint: a__U11(X1,X2,X3) >= U11(X1,X2,X3) constraint: a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) constraint: a__U13(X1,X2,X3) >= U13(X1,X2,X3) constraint: a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) constraint: a__U14(X1,X2,X3) >= U14(X1,X2,X3) constraint: a__U15(tt,V2) >= a__U16(a__isNat(V2)) constraint: a__U15(X1,X2) >= U15(X1,X2) constraint: a__U16(tt) >= tt constraint: a__U16(X) >= U16(X) constraint: a__U22(tt,V1) >= a__U23(a__isNat(V1)) constraint: a__U22(X1,X2) >= U22(X1,X2) constraint: a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) constraint: a__U21(X1,X2) >= U21(X1,X2) constraint: a__U23(tt) >= tt constraint: a__U23(X) >= U23(X) constraint: a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) constraint: a__U32(X1,X2,X3) >= U32(X1,X2,X3) constraint: a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) constraint: a__U31(X1,X2,X3) >= U31(X1,X2,X3) constraint: a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) constraint: a__U33(X1,X2,X3) >= U33(X1,X2,X3) constraint: a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) constraint: a__U34(X1,X2,X3) >= U34(X1,X2,X3) constraint: a__U35(tt,V2) >= a__U36(a__isNat(V2)) constraint: a__U35(X1,X2) >= U35(X1,X2) constraint: a__U36(tt) >= tt constraint: a__U36(X) >= U36(X) constraint: a__U42(tt) >= tt constraint: a__U42(X) >= U42(X) constraint: a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) constraint: a__U41(X1,X2) >= U41(X1,X2) constraint: a__U51(tt) >= tt constraint: a__U51(X) >= U51(X) constraint: a__U62(tt) >= tt constraint: a__U62(X) >= U62(X) constraint: a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) constraint: a__U61(X1,X2) >= U61(X1,X2) constraint: a__U72(tt,N) >= mark(N) constraint: a__U72(X1,X2) >= U72(X1,X2) constraint: a__U71(tt,N) >= a__U72(a__isNatKind(N),N) constraint: a__U71(X1,X2) >= U71(X1,X2) constraint: a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) constraint: a__U82(X1,X2,X3) >= U82(X1,X2,X3) constraint: a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) constraint: a__U81(X1,X2,X3) >= U81(X1,X2,X3) constraint: a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) constraint: a__U83(X1,X2,X3) >= U83(X1,X2,X3) constraint: a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U84(X1,X2,X3) >= U84(X1,X2,X3) constraint: a__U92(tt) >= 0 constraint: a__U92(X) >= U92(X) constraint: a__U91(tt,N) >= a__U92(a__isNatKind(N)) constraint: a__U91(X1,X2) >= U91(X1,X2) constraint: Marked_a__U84(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) constraint: Marked_a__U84(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U84(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U83(tt,M,N) >= Marked_a__U84(a__isNatKind(N),M,N) constraint: Marked_a__U82(tt,M,N) >= Marked_a__U83(a__isNat(N),M,N) constraint: Marked_a__U81(tt,M,N) >= Marked_a__U82(a__isNatKind(M),M,N) constraint: Marked_a__U72(tt,N) >= Marked_mark(N) constraint: Marked_a__U71(tt,N) >= Marked_a__U72(a__isNatKind(N),N) constraint: Marked_a__x(N,s(M)) >= Marked_a__U101(a__isNat(M),M,N) constraint: Marked_a__plus(N,s(M)) >= Marked_a__U81(a__isNat(M),M,N) constraint: Marked_a__plus(N,0) >= Marked_a__U71(a__isNat(N),N) constraint: Marked_a__U104(tt,M,N) >= Marked_a__x(mark(N),mark(M)) constraint: Marked_a__U104(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)), mark(N)) constraint: Marked_a__U104(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U104(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U103(tt,M,N) >= Marked_a__U104(a__isNatKind(N),M,N) constraint: Marked_a__U102(tt,M,N) >= Marked_a__U103(a__isNat(N),M,N) constraint: Marked_a__U101(tt,M,N) >= Marked_a__U102(a__isNatKind(M),M,N) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(x(X1,X2)) >= Marked_a__x(mark(X1),mark(X2)) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(U101(X1,X2,X3)) >= Marked_a__U101(mark(X1),X2,X3) constraint: Marked_mark(U101(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U102(X1,X2,X3)) >= Marked_a__U102(mark(X1),X2,X3) constraint: Marked_mark(U102(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U103(X1,X2,X3)) >= Marked_a__U103(mark(X1),X2,X3) constraint: Marked_mark(U103(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U104(X1,X2,X3)) >= Marked_a__U104(mark(X1),X2,X3) constraint: Marked_mark(U104(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U13(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U14(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U15(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U16(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U22(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U23(X)) >= Marked_mark(X) constraint: Marked_mark(U31(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U32(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U33(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U34(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U35(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U36(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U42(X)) >= Marked_mark(X) constraint: Marked_mark(U51(X)) >= Marked_mark(X) constraint: Marked_mark(U61(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U62(X)) >= Marked_mark(X) constraint: Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) constraint: Marked_mark(U71(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U72(X1,X2)) >= Marked_a__U72(mark(X1),X2) constraint: Marked_mark(U72(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U81(X1,X2,X3)) >= Marked_a__U81(mark(X1),X2,X3) constraint: Marked_mark(U81(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U82(X1,X2,X3)) >= Marked_a__U82(mark(X1),X2,X3) constraint: Marked_mark(U82(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U83(X1,X2,X3)) >= Marked_a__U83(mark(X1),X2,X3) constraint: Marked_mark(U83(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U84(X1,X2,X3)) >= Marked_a__U84(mark(X1),X2,X3) constraint: Marked_mark(U84(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U91(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U92(X)) >= Marked_mark(X) APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) ; a__U102(X1,X2,X3) >= U102(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) ; a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) ; a__U101(X1,X2,X3) >= U101(X1,X2,X3) ; a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) ; a__U103(X1,X2,X3) >= U103(X1,X2,X3) ; a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) ; a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) ; a__isNat(X) >= isNat(X) ; a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ; a__U104(X1,X2,X3) >= U104(X1,X2,X3) ; a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) ; a__plus(N,0) >= a__U71(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) ; a__x(N,0) >= a__U91(a__isNat(N),N) ; a__x(X1,X2) >= x(X1,X2) ; mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ; mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) ; mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) ; mark(isNat(X)) >= a__isNat(X) ; mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) ; mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) ; mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) ; mark(U15(X1,X2)) >= a__U15(mark(X1),X2) ; mark(U16(X)) >= a__U16(mark(X)) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U22(X1,X2)) >= a__U22(mark(X1),X2) ; mark(U23(X)) >= a__U23(mark(X)) ; mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) ; mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) ; mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) ; mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) ; mark(U35(X1,X2)) >= a__U35(mark(X1),X2) ; mark(U36(X)) >= a__U36(mark(X)) ; mark(U41(X1,X2)) >= a__U41(mark(X1),X2) ; mark(U42(X)) >= a__U42(mark(X)) ; mark(U51(X)) >= a__U51(mark(X)) ; mark(U61(X1,X2)) >= a__U61(mark(X1),X2) ; mark(U62(X)) >= a__U62(mark(X)) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U72(X1,X2)) >= a__U72(mark(X1),X2) ; mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) ; mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) ; mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) ; mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) ; mark(U91(X1,X2)) >= a__U91(mark(X1),X2) ; mark(U92(X)) >= a__U92(mark(X)) ; a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) ; a__U11(X1,X2,X3) >= U11(X1,X2,X3) ; a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) ; a__U13(X1,X2,X3) >= U13(X1,X2,X3) ; a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) ; a__U14(X1,X2,X3) >= U14(X1,X2,X3) ; a__U15(tt,V2) >= a__U16(a__isNat(V2)) ; a__U15(X1,X2) >= U15(X1,X2) ; a__U16(tt) >= tt ; a__U16(X) >= U16(X) ; a__U22(tt,V1) >= a__U23(a__isNat(V1)) ; a__U22(X1,X2) >= U22(X1,X2) ; a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U23(tt) >= tt ; a__U23(X) >= U23(X) ; a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) ; a__U32(X1,X2,X3) >= U32(X1,X2,X3) ; a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) ; a__U31(X1,X2,X3) >= U31(X1,X2,X3) ; a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) ; a__U33(X1,X2,X3) >= U33(X1,X2,X3) ; a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) ; a__U34(X1,X2,X3) >= U34(X1,X2,X3) ; a__U35(tt,V2) >= a__U36(a__isNat(V2)) ; a__U35(X1,X2) >= U35(X1,X2) ; a__U36(tt) >= tt ; a__U36(X) >= U36(X) ; a__U42(tt) >= tt ; a__U42(X) >= U42(X) ; a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) ; a__U41(X1,X2) >= U41(X1,X2) ; a__U51(tt) >= tt ; a__U51(X) >= U51(X) ; a__U62(tt) >= tt ; a__U62(X) >= U62(X) ; a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) ; a__U61(X1,X2) >= U61(X1,X2) ; a__U72(tt,N) >= mark(N) ; a__U72(X1,X2) >= U72(X1,X2) ; a__U71(tt,N) >= a__U72(a__isNatKind(N),N) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) ; a__U82(X1,X2,X3) >= U82(X1,X2,X3) ; a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) ; a__U81(X1,X2,X3) >= U81(X1,X2,X3) ; a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) ; a__U83(X1,X2,X3) >= U83(X1,X2,X3) ; a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U84(X1,X2,X3) >= U84(X1,X2,X3) ; a__U92(tt) >= 0 ; a__U92(X) >= U92(X) ; a__U91(tt,N) >= a__U92(a__isNatKind(N)) ; a__U91(X1,X2) >= U91(X1,X2) ; Marked_a__U35(tt,V2) >= Marked_a__isNat(V2) ; Marked_a__U34(tt,V1,V2) >= Marked_a__U35(a__isNat(V1),V2) ; Marked_a__U34(tt,V1,V2) >= Marked_a__isNat(V1) ; Marked_a__U33(tt,V1,V2) >= Marked_a__U34(a__isNatKind(V2),V1,V2) ; Marked_a__U32(tt,V1,V2) >= Marked_a__U33(a__isNatKind(V2),V1,V2) ; Marked_a__U31(tt,V1,V2) >= Marked_a__U32(a__isNatKind(V1),V1,V2) ; Marked_a__U22(tt,V1) >= Marked_a__isNat(V1) ; Marked_a__U21(tt,V1) >= Marked_a__U22(a__isNatKind(V1),V1) ; Marked_a__U15(tt,V2) >= Marked_a__isNat(V2) ; Marked_a__U14(tt,V1,V2) >= Marked_a__U15(a__isNat(V1),V2) ; Marked_a__U14(tt,V1,V2) >= Marked_a__isNat(V1) ; Marked_a__U13(tt,V1,V2) >= Marked_a__U14(a__isNatKind(V2),V1,V2) ; Marked_a__U12(tt,V1,V2) >= Marked_a__U13(a__isNatKind(V2),V1,V2) ; Marked_a__U11(tt,V1,V2) >= Marked_a__U12(a__isNatKind(V1),V1,V2) ; Marked_a__isNat(s(V1)) >= Marked_a__U21(a__isNatKind(V1),V1) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__U11(a__isNatKind(V1),V1,V2) ; Marked_a__isNat(x(V1,V2)) >= Marked_a__U31(a__isNatKind(V1),V1,V2) ; } + Disjunctions:{ { Marked_a__U35(tt,V2) > Marked_a__isNat(V2) ; } { Marked_a__U34(tt,V1,V2) > Marked_a__U35(a__isNat(V1),V2) ; } { Marked_a__U34(tt,V1,V2) > Marked_a__isNat(V1) ; } { Marked_a__U33(tt,V1,V2) > Marked_a__U34(a__isNatKind(V2),V1,V2) ; } { Marked_a__U32(tt,V1,V2) > Marked_a__U33(a__isNatKind(V2),V1,V2) ; } { Marked_a__U31(tt,V1,V2) > Marked_a__U32(a__isNatKind(V1),V1,V2) ; } { Marked_a__U22(tt,V1) > Marked_a__isNat(V1) ; } { Marked_a__U21(tt,V1) > Marked_a__U22(a__isNatKind(V1),V1) ; } { Marked_a__U15(tt,V2) > Marked_a__isNat(V2) ; } { Marked_a__U14(tt,V1,V2) > Marked_a__U15(a__isNat(V1),V2) ; } { Marked_a__U14(tt,V1,V2) > Marked_a__isNat(V1) ; } { Marked_a__U13(tt,V1,V2) > Marked_a__U14(a__isNatKind(V2),V1,V2) ; } { Marked_a__U12(tt,V1,V2) > Marked_a__U13(a__isNatKind(V2),V1,V2) ; } { Marked_a__U11(tt,V1,V2) > Marked_a__U12(a__isNatKind(V1),V1,V2) ; } { Marked_a__isNat(s(V1)) > Marked_a__U21(a__isNatKind(V1),V1) ; } { Marked_a__isNat(plus(V1,V2)) > Marked_a__U11(a__isNatKind(V1),V1,V2) ; } { Marked_a__isNat(x(V1,V2)) > Marked_a__U31(a__isNatKind(V1),V1,V2) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) constraint: a__U102(X1,X2,X3) >= U102(X1,X2,X3) constraint: a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) constraint: a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) constraint: a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) constraint: a__U101(X1,X2,X3) >= U101(X1,X2,X3) constraint: a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) constraint: a__U103(X1,X2,X3) >= U103(X1,X2,X3) constraint: a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) constraint: a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) constraint: a__isNat(X) >= isNat(X) constraint: a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) constraint: a__U104(X1,X2,X3) >= U104(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U71(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) constraint: a__x(N,0) >= a__U91(a__isNat(N),N) constraint: a__x(X1,X2) >= x(X1,X2) constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) constraint: mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) constraint: mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) constraint: mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) constraint: mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) constraint: mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) constraint: mark(U15(X1,X2)) >= a__U15(mark(X1),X2) constraint: mark(U16(X)) >= a__U16(mark(X)) constraint: mark(U21(X1,X2)) >= a__U21(mark(X1),X2) constraint: mark(U22(X1,X2)) >= a__U22(mark(X1),X2) constraint: mark(U23(X)) >= a__U23(mark(X)) constraint: mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) constraint: mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) constraint: mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) constraint: mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) constraint: mark(U35(X1,X2)) >= a__U35(mark(X1),X2) constraint: mark(U36(X)) >= a__U36(mark(X)) constraint: mark(U41(X1,X2)) >= a__U41(mark(X1),X2) constraint: mark(U42(X)) >= a__U42(mark(X)) constraint: mark(U51(X)) >= a__U51(mark(X)) constraint: mark(U61(X1,X2)) >= a__U61(mark(X1),X2) constraint: mark(U62(X)) >= a__U62(mark(X)) constraint: mark(U71(X1,X2)) >= a__U71(mark(X1),X2) constraint: mark(U72(X1,X2)) >= a__U72(mark(X1),X2) constraint: mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) constraint: mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) constraint: mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) constraint: mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) constraint: mark(U91(X1,X2)) >= a__U91(mark(X1),X2) constraint: mark(U92(X)) >= a__U92(mark(X)) constraint: a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) constraint: a__U12(X1,X2,X3) >= U12(X1,X2,X3) constraint: a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) constraint: a__U11(X1,X2,X3) >= U11(X1,X2,X3) constraint: a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) constraint: a__U13(X1,X2,X3) >= U13(X1,X2,X3) constraint: a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) constraint: a__U14(X1,X2,X3) >= U14(X1,X2,X3) constraint: a__U15(tt,V2) >= a__U16(a__isNat(V2)) constraint: a__U15(X1,X2) >= U15(X1,X2) constraint: a__U16(tt) >= tt constraint: a__U16(X) >= U16(X) constraint: a__U22(tt,V1) >= a__U23(a__isNat(V1)) constraint: a__U22(X1,X2) >= U22(X1,X2) constraint: a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) constraint: a__U21(X1,X2) >= U21(X1,X2) constraint: a__U23(tt) >= tt constraint: a__U23(X) >= U23(X) constraint: a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) constraint: a__U32(X1,X2,X3) >= U32(X1,X2,X3) constraint: a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) constraint: a__U31(X1,X2,X3) >= U31(X1,X2,X3) constraint: a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) constraint: a__U33(X1,X2,X3) >= U33(X1,X2,X3) constraint: a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) constraint: a__U34(X1,X2,X3) >= U34(X1,X2,X3) constraint: a__U35(tt,V2) >= a__U36(a__isNat(V2)) constraint: a__U35(X1,X2) >= U35(X1,X2) constraint: a__U36(tt) >= tt constraint: a__U36(X) >= U36(X) constraint: a__U42(tt) >= tt constraint: a__U42(X) >= U42(X) constraint: a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) constraint: a__U41(X1,X2) >= U41(X1,X2) constraint: a__U51(tt) >= tt constraint: a__U51(X) >= U51(X) constraint: a__U62(tt) >= tt constraint: a__U62(X) >= U62(X) constraint: a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) constraint: a__U61(X1,X2) >= U61(X1,X2) constraint: a__U72(tt,N) >= mark(N) constraint: a__U72(X1,X2) >= U72(X1,X2) constraint: a__U71(tt,N) >= a__U72(a__isNatKind(N),N) constraint: a__U71(X1,X2) >= U71(X1,X2) constraint: a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) constraint: a__U82(X1,X2,X3) >= U82(X1,X2,X3) constraint: a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) constraint: a__U81(X1,X2,X3) >= U81(X1,X2,X3) constraint: a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) constraint: a__U83(X1,X2,X3) >= U83(X1,X2,X3) constraint: a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U84(X1,X2,X3) >= U84(X1,X2,X3) constraint: a__U92(tt) >= 0 constraint: a__U92(X) >= U92(X) constraint: a__U91(tt,N) >= a__U92(a__isNatKind(N)) constraint: a__U91(X1,X2) >= U91(X1,X2) constraint: Marked_a__U35(tt,V2) >= Marked_a__isNat(V2) constraint: Marked_a__U34(tt,V1,V2) >= Marked_a__U35(a__isNat(V1),V2) constraint: Marked_a__U34(tt,V1,V2) >= Marked_a__isNat(V1) constraint: Marked_a__U33(tt,V1,V2) >= Marked_a__U34(a__isNatKind(V2),V1,V2) constraint: Marked_a__U32(tt,V1,V2) >= Marked_a__U33(a__isNatKind(V2),V1,V2) constraint: Marked_a__U31(tt,V1,V2) >= Marked_a__U32(a__isNatKind(V1),V1,V2) constraint: Marked_a__U22(tt,V1) >= Marked_a__isNat(V1) constraint: Marked_a__U21(tt,V1) >= Marked_a__U22(a__isNatKind(V1),V1) constraint: Marked_a__U15(tt,V2) >= Marked_a__isNat(V2) constraint: Marked_a__U14(tt,V1,V2) >= Marked_a__U15(a__isNat(V1),V2) constraint: Marked_a__U14(tt,V1,V2) >= Marked_a__isNat(V1) constraint: Marked_a__U13(tt,V1,V2) >= Marked_a__U14(a__isNatKind(V2),V1,V2) constraint: Marked_a__U12(tt,V1,V2) >= Marked_a__U13(a__isNatKind(V2),V1,V2) constraint: Marked_a__U11(tt,V1,V2) >= Marked_a__U12(a__isNatKind(V1),V1,V2) constraint: Marked_a__isNat(s(V1)) >= Marked_a__U21(a__isNatKind(V1),V1) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__U11(a__isNatKind(V1), V1,V2) constraint: Marked_a__isNat(x(V1,V2)) >= Marked_a__U31(a__isNatKind(V1),V1,V2) APPLY CRITERIA (Subterm criterion) ST: Marked_a__U61 -> 2 Marked_a__isNatKind -> 1 Marked_a__U41 -> 2 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) ; a__U102(X1,X2,X3) >= U102(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) ; a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) ; a__U101(X1,X2,X3) >= U101(X1,X2,X3) ; a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) ; a__U103(X1,X2,X3) >= U103(X1,X2,X3) ; a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) ; a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) ; a__isNat(X) >= isNat(X) ; a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ; a__U104(X1,X2,X3) >= U104(X1,X2,X3) ; a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) ; a__plus(N,0) >= a__U71(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) ; a__x(N,0) >= a__U91(a__isNat(N),N) ; a__x(X1,X2) >= x(X1,X2) ; mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ; mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) ; mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) ; mark(isNat(X)) >= a__isNat(X) ; mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) ; mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) ; mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) ; mark(U15(X1,X2)) >= a__U15(mark(X1),X2) ; mark(U16(X)) >= a__U16(mark(X)) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U22(X1,X2)) >= a__U22(mark(X1),X2) ; mark(U23(X)) >= a__U23(mark(X)) ; mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) ; mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) ; mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) ; mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) ; mark(U35(X1,X2)) >= a__U35(mark(X1),X2) ; mark(U36(X)) >= a__U36(mark(X)) ; mark(U41(X1,X2)) >= a__U41(mark(X1),X2) ; mark(U42(X)) >= a__U42(mark(X)) ; mark(U51(X)) >= a__U51(mark(X)) ; mark(U61(X1,X2)) >= a__U61(mark(X1),X2) ; mark(U62(X)) >= a__U62(mark(X)) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U72(X1,X2)) >= a__U72(mark(X1),X2) ; mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) ; mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) ; mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) ; mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) ; mark(U91(X1,X2)) >= a__U91(mark(X1),X2) ; mark(U92(X)) >= a__U92(mark(X)) ; a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) ; a__U11(X1,X2,X3) >= U11(X1,X2,X3) ; a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) ; a__U13(X1,X2,X3) >= U13(X1,X2,X3) ; a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) ; a__U14(X1,X2,X3) >= U14(X1,X2,X3) ; a__U15(tt,V2) >= a__U16(a__isNat(V2)) ; a__U15(X1,X2) >= U15(X1,X2) ; a__U16(tt) >= tt ; a__U16(X) >= U16(X) ; a__U22(tt,V1) >= a__U23(a__isNat(V1)) ; a__U22(X1,X2) >= U22(X1,X2) ; a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U23(tt) >= tt ; a__U23(X) >= U23(X) ; a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) ; a__U32(X1,X2,X3) >= U32(X1,X2,X3) ; a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) ; a__U31(X1,X2,X3) >= U31(X1,X2,X3) ; a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) ; a__U33(X1,X2,X3) >= U33(X1,X2,X3) ; a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) ; a__U34(X1,X2,X3) >= U34(X1,X2,X3) ; a__U35(tt,V2) >= a__U36(a__isNat(V2)) ; a__U35(X1,X2) >= U35(X1,X2) ; a__U36(tt) >= tt ; a__U36(X) >= U36(X) ; a__U42(tt) >= tt ; a__U42(X) >= U42(X) ; a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) ; a__U41(X1,X2) >= U41(X1,X2) ; a__U51(tt) >= tt ; a__U51(X) >= U51(X) ; a__U62(tt) >= tt ; a__U62(X) >= U62(X) ; a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) ; a__U61(X1,X2) >= U61(X1,X2) ; a__U72(tt,N) >= mark(N) ; a__U72(X1,X2) >= U72(X1,X2) ; a__U71(tt,N) >= a__U72(a__isNatKind(N),N) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) ; a__U82(X1,X2,X3) >= U82(X1,X2,X3) ; a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) ; a__U81(X1,X2,X3) >= U81(X1,X2,X3) ; a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) ; a__U83(X1,X2,X3) >= U83(X1,X2,X3) ; a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U84(X1,X2,X3) >= U84(X1,X2,X3) ; a__U92(tt) >= 0 ; a__U92(X) >= U92(X) ; a__U91(tt,N) >= a__U92(a__isNatKind(N)) ; a__U91(X1,X2) >= U91(X1,X2) ; Marked_a__U72(tt,N) >= Marked_mark(N) ; Marked_a__U71(tt,N) >= Marked_a__U72(a__isNatKind(N),N) ; Marked_a__plus(N,0) >= Marked_a__U71(a__isNat(N),N) ; Marked_a__U104(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ; Marked_a__U104(tt,M,N) >= Marked_mark(M) ; Marked_a__U104(tt,M,N) >= Marked_mark(N) ; Marked_a__U103(tt,M,N) >= Marked_a__U104(a__isNatKind(N),M,N) ; Marked_a__U102(tt,M,N) >= Marked_a__U103(a__isNat(N),M,N) ; Marked_a__U101(tt,M,N) >= Marked_a__U102(a__isNatKind(M),M,N) ; Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(x(X1,X2)) >= Marked_mark(X1) ; Marked_mark(x(X1,X2)) >= Marked_mark(X2) ; Marked_mark(U101(X1,X2,X3)) >= Marked_a__U101(mark(X1),X2,X3) ; Marked_mark(U101(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U102(X1,X2,X3)) >= Marked_a__U102(mark(X1),X2,X3) ; Marked_mark(U102(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U103(X1,X2,X3)) >= Marked_a__U103(mark(X1),X2,X3) ; Marked_mark(U103(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U104(X1,X2,X3)) >= Marked_a__U104(mark(X1),X2,X3) ; Marked_mark(U104(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U13(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U14(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U15(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U16(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U22(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U23(X)) >= Marked_mark(X) ; Marked_mark(U31(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U32(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U33(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U34(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U35(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U36(X)) >= Marked_mark(X) ; Marked_mark(U41(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U42(X)) >= Marked_mark(X) ; Marked_mark(U51(X)) >= Marked_mark(X) ; Marked_mark(U61(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U62(X)) >= Marked_mark(X) ; Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) ; Marked_mark(U71(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U72(X1,X2)) >= Marked_a__U72(mark(X1),X2) ; Marked_mark(U72(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U91(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U92(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__U72(tt,N) > Marked_mark(N) ; } { Marked_a__U71(tt,N) > Marked_a__U72(a__isNatKind(N),N) ; } { Marked_a__plus(N,0) > Marked_a__U71(a__isNat(N),N) ; } { Marked_a__U104(tt,M,N) > Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ; } { Marked_a__U104(tt,M,N) > Marked_mark(M) ; } { Marked_a__U104(tt,M,N) > Marked_mark(N) ; } { Marked_a__U103(tt,M,N) > Marked_a__U104(a__isNatKind(N),M,N) ; } { Marked_a__U102(tt,M,N) > Marked_a__U103(a__isNat(N),M,N) ; } { Marked_a__U101(tt,M,N) > Marked_a__U102(a__isNatKind(M),M,N) ; } { Marked_mark(plus(X1,X2)) > Marked_a__plus(mark(X1),mark(X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(U101(X1,X2,X3)) > Marked_a__U101(mark(X1),X2,X3) ; } { Marked_mark(U101(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U102(X1,X2,X3)) > Marked_a__U102(mark(X1),X2,X3) ; } { Marked_mark(U102(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U103(X1,X2,X3)) > Marked_a__U103(mark(X1),X2,X3) ; } { Marked_mark(U103(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U104(X1,X2,X3)) > Marked_a__U104(mark(X1),X2,X3) ; } { Marked_mark(U104(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U13(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U14(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U15(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U16(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U22(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U23(X)) > Marked_mark(X) ; } { Marked_mark(U31(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U32(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U33(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U34(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U35(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U36(X)) > Marked_mark(X) ; } { Marked_mark(U41(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U42(X)) > Marked_mark(X) ; } { Marked_mark(U51(X)) > Marked_mark(X) ; } { Marked_mark(U61(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U62(X)) > Marked_mark(X) ; } { Marked_mark(U71(X1,X2)) > Marked_a__U71(mark(X1),X2) ; } { Marked_mark(U71(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U72(X1,X2)) > Marked_a__U72(mark(X1),X2) ; } { Marked_mark(U72(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U91(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U92(X)) > Marked_mark(X) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) constraint: a__U102(X1,X2,X3) >= U102(X1,X2,X3) constraint: a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) constraint: a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) constraint: a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) constraint: a__U101(X1,X2,X3) >= U101(X1,X2,X3) constraint: a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) constraint: a__U103(X1,X2,X3) >= U103(X1,X2,X3) constraint: a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) constraint: a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) constraint: a__isNat(X) >= isNat(X) constraint: a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) constraint: a__U104(X1,X2,X3) >= U104(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U71(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) constraint: a__x(N,0) >= a__U91(a__isNat(N),N) constraint: a__x(X1,X2) >= x(X1,X2) constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) constraint: mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) constraint: mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) constraint: mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) constraint: mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) constraint: mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) constraint: mark(U15(X1,X2)) >= a__U15(mark(X1),X2) constraint: mark(U16(X)) >= a__U16(mark(X)) constraint: mark(U21(X1,X2)) >= a__U21(mark(X1),X2) constraint: mark(U22(X1,X2)) >= a__U22(mark(X1),X2) constraint: mark(U23(X)) >= a__U23(mark(X)) constraint: mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) constraint: mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) constraint: mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) constraint: mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) constraint: mark(U35(X1,X2)) >= a__U35(mark(X1),X2) constraint: mark(U36(X)) >= a__U36(mark(X)) constraint: mark(U41(X1,X2)) >= a__U41(mark(X1),X2) constraint: mark(U42(X)) >= a__U42(mark(X)) constraint: mark(U51(X)) >= a__U51(mark(X)) constraint: mark(U61(X1,X2)) >= a__U61(mark(X1),X2) constraint: mark(U62(X)) >= a__U62(mark(X)) constraint: mark(U71(X1,X2)) >= a__U71(mark(X1),X2) constraint: mark(U72(X1,X2)) >= a__U72(mark(X1),X2) constraint: mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) constraint: mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) constraint: mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) constraint: mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) constraint: mark(U91(X1,X2)) >= a__U91(mark(X1),X2) constraint: mark(U92(X)) >= a__U92(mark(X)) constraint: a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) constraint: a__U12(X1,X2,X3) >= U12(X1,X2,X3) constraint: a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) constraint: a__U11(X1,X2,X3) >= U11(X1,X2,X3) constraint: a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) constraint: a__U13(X1,X2,X3) >= U13(X1,X2,X3) constraint: a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) constraint: a__U14(X1,X2,X3) >= U14(X1,X2,X3) constraint: a__U15(tt,V2) >= a__U16(a__isNat(V2)) constraint: a__U15(X1,X2) >= U15(X1,X2) constraint: a__U16(tt) >= tt constraint: a__U16(X) >= U16(X) constraint: a__U22(tt,V1) >= a__U23(a__isNat(V1)) constraint: a__U22(X1,X2) >= U22(X1,X2) constraint: a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) constraint: a__U21(X1,X2) >= U21(X1,X2) constraint: a__U23(tt) >= tt constraint: a__U23(X) >= U23(X) constraint: a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) constraint: a__U32(X1,X2,X3) >= U32(X1,X2,X3) constraint: a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) constraint: a__U31(X1,X2,X3) >= U31(X1,X2,X3) constraint: a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) constraint: a__U33(X1,X2,X3) >= U33(X1,X2,X3) constraint: a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) constraint: a__U34(X1,X2,X3) >= U34(X1,X2,X3) constraint: a__U35(tt,V2) >= a__U36(a__isNat(V2)) constraint: a__U35(X1,X2) >= U35(X1,X2) constraint: a__U36(tt) >= tt constraint: a__U36(X) >= U36(X) constraint: a__U42(tt) >= tt constraint: a__U42(X) >= U42(X) constraint: a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) constraint: a__U41(X1,X2) >= U41(X1,X2) constraint: a__U51(tt) >= tt constraint: a__U51(X) >= U51(X) constraint: a__U62(tt) >= tt constraint: a__U62(X) >= U62(X) constraint: a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) constraint: a__U61(X1,X2) >= U61(X1,X2) constraint: a__U72(tt,N) >= mark(N) constraint: a__U72(X1,X2) >= U72(X1,X2) constraint: a__U71(tt,N) >= a__U72(a__isNatKind(N),N) constraint: a__U71(X1,X2) >= U71(X1,X2) constraint: a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) constraint: a__U82(X1,X2,X3) >= U82(X1,X2,X3) constraint: a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) constraint: a__U81(X1,X2,X3) >= U81(X1,X2,X3) constraint: a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) constraint: a__U83(X1,X2,X3) >= U83(X1,X2,X3) constraint: a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U84(X1,X2,X3) >= U84(X1,X2,X3) constraint: a__U92(tt) >= 0 constraint: a__U92(X) >= U92(X) constraint: a__U91(tt,N) >= a__U92(a__isNatKind(N)) constraint: a__U91(X1,X2) >= U91(X1,X2) constraint: Marked_a__U72(tt,N) >= Marked_mark(N) constraint: Marked_a__U71(tt,N) >= Marked_a__U72(a__isNatKind(N),N) constraint: Marked_a__plus(N,0) >= Marked_a__U71(a__isNat(N),N) constraint: Marked_a__U104(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)), mark(N)) constraint: Marked_a__U104(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U104(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U103(tt,M,N) >= Marked_a__U104(a__isNatKind(N),M,N) constraint: Marked_a__U102(tt,M,N) >= Marked_a__U103(a__isNat(N),M,N) constraint: Marked_a__U101(tt,M,N) >= Marked_a__U102(a__isNatKind(M),M,N) constraint: Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(U101(X1,X2,X3)) >= Marked_a__U101(mark(X1),X2,X3) constraint: Marked_mark(U101(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U102(X1,X2,X3)) >= Marked_a__U102(mark(X1),X2,X3) constraint: Marked_mark(U102(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U103(X1,X2,X3)) >= Marked_a__U103(mark(X1),X2,X3) constraint: Marked_mark(U103(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U104(X1,X2,X3)) >= Marked_a__U104(mark(X1),X2,X3) constraint: Marked_mark(U104(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U13(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U14(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U15(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U16(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U22(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U23(X)) >= Marked_mark(X) constraint: Marked_mark(U31(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U32(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U33(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U34(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U35(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U36(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U42(X)) >= Marked_mark(X) constraint: Marked_mark(U51(X)) >= Marked_mark(X) constraint: Marked_mark(U61(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U62(X)) >= Marked_mark(X) constraint: Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) constraint: Marked_mark(U71(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U72(X1,X2)) >= Marked_a__U72(mark(X1),X2) constraint: Marked_mark(U72(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U91(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U92(X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) ; a__U102(X1,X2,X3) >= U102(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) ; a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) ; a__U101(X1,X2,X3) >= U101(X1,X2,X3) ; a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) ; a__U103(X1,X2,X3) >= U103(X1,X2,X3) ; a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) ; a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) ; a__isNat(X) >= isNat(X) ; a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ; a__U104(X1,X2,X3) >= U104(X1,X2,X3) ; a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) ; a__plus(N,0) >= a__U71(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) ; a__x(N,0) >= a__U91(a__isNat(N),N) ; a__x(X1,X2) >= x(X1,X2) ; mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ; mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) ; mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) ; mark(isNat(X)) >= a__isNat(X) ; mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) ; mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) ; mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) ; mark(U15(X1,X2)) >= a__U15(mark(X1),X2) ; mark(U16(X)) >= a__U16(mark(X)) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U22(X1,X2)) >= a__U22(mark(X1),X2) ; mark(U23(X)) >= a__U23(mark(X)) ; mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) ; mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) ; mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) ; mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) ; mark(U35(X1,X2)) >= a__U35(mark(X1),X2) ; mark(U36(X)) >= a__U36(mark(X)) ; mark(U41(X1,X2)) >= a__U41(mark(X1),X2) ; mark(U42(X)) >= a__U42(mark(X)) ; mark(U51(X)) >= a__U51(mark(X)) ; mark(U61(X1,X2)) >= a__U61(mark(X1),X2) ; mark(U62(X)) >= a__U62(mark(X)) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U72(X1,X2)) >= a__U72(mark(X1),X2) ; mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) ; mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) ; mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) ; mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) ; mark(U91(X1,X2)) >= a__U91(mark(X1),X2) ; mark(U92(X)) >= a__U92(mark(X)) ; a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) ; a__U11(X1,X2,X3) >= U11(X1,X2,X3) ; a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) ; a__U13(X1,X2,X3) >= U13(X1,X2,X3) ; a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) ; a__U14(X1,X2,X3) >= U14(X1,X2,X3) ; a__U15(tt,V2) >= a__U16(a__isNat(V2)) ; a__U15(X1,X2) >= U15(X1,X2) ; a__U16(tt) >= tt ; a__U16(X) >= U16(X) ; a__U22(tt,V1) >= a__U23(a__isNat(V1)) ; a__U22(X1,X2) >= U22(X1,X2) ; a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U23(tt) >= tt ; a__U23(X) >= U23(X) ; a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) ; a__U32(X1,X2,X3) >= U32(X1,X2,X3) ; a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) ; a__U31(X1,X2,X3) >= U31(X1,X2,X3) ; a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) ; a__U33(X1,X2,X3) >= U33(X1,X2,X3) ; a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) ; a__U34(X1,X2,X3) >= U34(X1,X2,X3) ; a__U35(tt,V2) >= a__U36(a__isNat(V2)) ; a__U35(X1,X2) >= U35(X1,X2) ; a__U36(tt) >= tt ; a__U36(X) >= U36(X) ; a__U42(tt) >= tt ; a__U42(X) >= U42(X) ; a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) ; a__U41(X1,X2) >= U41(X1,X2) ; a__U51(tt) >= tt ; a__U51(X) >= U51(X) ; a__U62(tt) >= tt ; a__U62(X) >= U62(X) ; a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) ; a__U61(X1,X2) >= U61(X1,X2) ; a__U72(tt,N) >= mark(N) ; a__U72(X1,X2) >= U72(X1,X2) ; a__U71(tt,N) >= a__U72(a__isNatKind(N),N) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) ; a__U82(X1,X2,X3) >= U82(X1,X2,X3) ; a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) ; a__U81(X1,X2,X3) >= U81(X1,X2,X3) ; a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) ; a__U83(X1,X2,X3) >= U83(X1,X2,X3) ; a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U84(X1,X2,X3) >= U84(X1,X2,X3) ; a__U92(tt) >= 0 ; a__U92(X) >= U92(X) ; a__U91(tt,N) >= a__U92(a__isNatKind(N)) ; a__U91(X1,X2) >= U91(X1,X2) ; Marked_a__U72(tt,N) >= Marked_mark(N) ; Marked_a__U71(tt,N) >= Marked_a__U72(a__isNatKind(N),N) ; Marked_a__plus(N,0) >= Marked_a__U71(a__isNat(N),N) ; Marked_a__U104(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ; Marked_a__U104(tt,M,N) >= Marked_mark(M) ; Marked_a__U104(tt,M,N) >= Marked_mark(N) ; Marked_a__U103(tt,M,N) >= Marked_a__U104(a__isNatKind(N),M,N) ; Marked_a__U102(tt,M,N) >= Marked_a__U103(a__isNat(N),M,N) ; Marked_a__U101(tt,M,N) >= Marked_a__U102(a__isNatKind(M),M,N) ; Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(x(X1,X2)) >= Marked_mark(X1) ; Marked_mark(x(X1,X2)) >= Marked_mark(X2) ; Marked_mark(U101(X1,X2,X3)) >= Marked_a__U101(mark(X1),X2,X3) ; Marked_mark(U101(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U102(X1,X2,X3)) >= Marked_a__U102(mark(X1),X2,X3) ; Marked_mark(U102(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U103(X1,X2,X3)) >= Marked_a__U103(mark(X1),X2,X3) ; Marked_mark(U103(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U104(X1,X2,X3)) >= Marked_a__U104(mark(X1),X2,X3) ; Marked_mark(U104(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U13(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U14(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U15(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U16(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U22(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U23(X)) >= Marked_mark(X) ; Marked_mark(U31(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U32(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U33(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U34(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U35(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U36(X)) >= Marked_mark(X) ; Marked_mark(U41(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U42(X)) >= Marked_mark(X) ; Marked_mark(U51(X)) >= Marked_mark(X) ; Marked_mark(U61(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U62(X)) >= Marked_mark(X) ; Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) ; Marked_mark(U71(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U72(X1,X2)) >= Marked_a__U72(mark(X1),X2) ; Marked_mark(U72(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__U72(tt,N) > Marked_mark(N) ; } { Marked_a__U71(tt,N) > Marked_a__U72(a__isNatKind(N),N) ; } { Marked_a__plus(N,0) > Marked_a__U71(a__isNat(N),N) ; } { Marked_a__U104(tt,M,N) > Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ; } { Marked_a__U104(tt,M,N) > Marked_mark(M) ; } { Marked_a__U104(tt,M,N) > Marked_mark(N) ; } { Marked_a__U103(tt,M,N) > Marked_a__U104(a__isNatKind(N),M,N) ; } { Marked_a__U102(tt,M,N) > Marked_a__U103(a__isNat(N),M,N) ; } { Marked_a__U101(tt,M,N) > Marked_a__U102(a__isNatKind(M),M,N) ; } { Marked_mark(plus(X1,X2)) > Marked_a__plus(mark(X1),mark(X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(U101(X1,X2,X3)) > Marked_a__U101(mark(X1),X2,X3) ; } { Marked_mark(U101(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U102(X1,X2,X3)) > Marked_a__U102(mark(X1),X2,X3) ; } { Marked_mark(U102(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U103(X1,X2,X3)) > Marked_a__U103(mark(X1),X2,X3) ; } { Marked_mark(U103(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U104(X1,X2,X3)) > Marked_a__U104(mark(X1),X2,X3) ; } { Marked_mark(U104(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U13(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U14(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U15(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U16(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U22(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U23(X)) > Marked_mark(X) ; } { Marked_mark(U31(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U32(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U33(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U34(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U35(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U36(X)) > Marked_mark(X) ; } { Marked_mark(U41(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U42(X)) > Marked_mark(X) ; } { Marked_mark(U51(X)) > Marked_mark(X) ; } { Marked_mark(U61(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U62(X)) > Marked_mark(X) ; } { Marked_mark(U71(X1,X2)) > Marked_a__U71(mark(X1),X2) ; } { Marked_mark(U71(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U72(X1,X2)) > Marked_a__U72(mark(X1),X2) ; } { Marked_mark(U72(X1,X2)) > Marked_mark(X1) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) constraint: a__U102(X1,X2,X3) >= U102(X1,X2,X3) constraint: a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) constraint: a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) constraint: a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) constraint: a__U101(X1,X2,X3) >= U101(X1,X2,X3) constraint: a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) constraint: a__U103(X1,X2,X3) >= U103(X1,X2,X3) constraint: a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) constraint: a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) constraint: a__isNat(X) >= isNat(X) constraint: a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) constraint: a__U104(X1,X2,X3) >= U104(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U71(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) constraint: a__x(N,0) >= a__U91(a__isNat(N),N) constraint: a__x(X1,X2) >= x(X1,X2) constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) constraint: mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) constraint: mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) constraint: mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) constraint: mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) constraint: mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) constraint: mark(U15(X1,X2)) >= a__U15(mark(X1),X2) constraint: mark(U16(X)) >= a__U16(mark(X)) constraint: mark(U21(X1,X2)) >= a__U21(mark(X1),X2) constraint: mark(U22(X1,X2)) >= a__U22(mark(X1),X2) constraint: mark(U23(X)) >= a__U23(mark(X)) constraint: mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) constraint: mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) constraint: mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) constraint: mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) constraint: mark(U35(X1,X2)) >= a__U35(mark(X1),X2) constraint: mark(U36(X)) >= a__U36(mark(X)) constraint: mark(U41(X1,X2)) >= a__U41(mark(X1),X2) constraint: mark(U42(X)) >= a__U42(mark(X)) constraint: mark(U51(X)) >= a__U51(mark(X)) constraint: mark(U61(X1,X2)) >= a__U61(mark(X1),X2) constraint: mark(U62(X)) >= a__U62(mark(X)) constraint: mark(U71(X1,X2)) >= a__U71(mark(X1),X2) constraint: mark(U72(X1,X2)) >= a__U72(mark(X1),X2) constraint: mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) constraint: mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) constraint: mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) constraint: mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) constraint: mark(U91(X1,X2)) >= a__U91(mark(X1),X2) constraint: mark(U92(X)) >= a__U92(mark(X)) constraint: a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) constraint: a__U12(X1,X2,X3) >= U12(X1,X2,X3) constraint: a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) constraint: a__U11(X1,X2,X3) >= U11(X1,X2,X3) constraint: a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) constraint: a__U13(X1,X2,X3) >= U13(X1,X2,X3) constraint: a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) constraint: a__U14(X1,X2,X3) >= U14(X1,X2,X3) constraint: a__U15(tt,V2) >= a__U16(a__isNat(V2)) constraint: a__U15(X1,X2) >= U15(X1,X2) constraint: a__U16(tt) >= tt constraint: a__U16(X) >= U16(X) constraint: a__U22(tt,V1) >= a__U23(a__isNat(V1)) constraint: a__U22(X1,X2) >= U22(X1,X2) constraint: a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) constraint: a__U21(X1,X2) >= U21(X1,X2) constraint: a__U23(tt) >= tt constraint: a__U23(X) >= U23(X) constraint: a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) constraint: a__U32(X1,X2,X3) >= U32(X1,X2,X3) constraint: a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) constraint: a__U31(X1,X2,X3) >= U31(X1,X2,X3) constraint: a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) constraint: a__U33(X1,X2,X3) >= U33(X1,X2,X3) constraint: a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) constraint: a__U34(X1,X2,X3) >= U34(X1,X2,X3) constraint: a__U35(tt,V2) >= a__U36(a__isNat(V2)) constraint: a__U35(X1,X2) >= U35(X1,X2) constraint: a__U36(tt) >= tt constraint: a__U36(X) >= U36(X) constraint: a__U42(tt) >= tt constraint: a__U42(X) >= U42(X) constraint: a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) constraint: a__U41(X1,X2) >= U41(X1,X2) constraint: a__U51(tt) >= tt constraint: a__U51(X) >= U51(X) constraint: a__U62(tt) >= tt constraint: a__U62(X) >= U62(X) constraint: a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) constraint: a__U61(X1,X2) >= U61(X1,X2) constraint: a__U72(tt,N) >= mark(N) constraint: a__U72(X1,X2) >= U72(X1,X2) constraint: a__U71(tt,N) >= a__U72(a__isNatKind(N),N) constraint: a__U71(X1,X2) >= U71(X1,X2) constraint: a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) constraint: a__U82(X1,X2,X3) >= U82(X1,X2,X3) constraint: a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) constraint: a__U81(X1,X2,X3) >= U81(X1,X2,X3) constraint: a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) constraint: a__U83(X1,X2,X3) >= U83(X1,X2,X3) constraint: a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U84(X1,X2,X3) >= U84(X1,X2,X3) constraint: a__U92(tt) >= 0 constraint: a__U92(X) >= U92(X) constraint: a__U91(tt,N) >= a__U92(a__isNatKind(N)) constraint: a__U91(X1,X2) >= U91(X1,X2) constraint: Marked_a__U72(tt,N) >= Marked_mark(N) constraint: Marked_a__U71(tt,N) >= Marked_a__U72(a__isNatKind(N),N) constraint: Marked_a__plus(N,0) >= Marked_a__U71(a__isNat(N),N) constraint: Marked_a__U104(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)), mark(N)) constraint: Marked_a__U104(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U104(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U103(tt,M,N) >= Marked_a__U104(a__isNatKind(N),M,N) constraint: Marked_a__U102(tt,M,N) >= Marked_a__U103(a__isNat(N),M,N) constraint: Marked_a__U101(tt,M,N) >= Marked_a__U102(a__isNatKind(M),M,N) constraint: Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(U101(X1,X2,X3)) >= Marked_a__U101(mark(X1),X2,X3) constraint: Marked_mark(U101(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U102(X1,X2,X3)) >= Marked_a__U102(mark(X1),X2,X3) constraint: Marked_mark(U102(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U103(X1,X2,X3)) >= Marked_a__U103(mark(X1),X2,X3) constraint: Marked_mark(U103(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U104(X1,X2,X3)) >= Marked_a__U104(mark(X1),X2,X3) constraint: Marked_mark(U104(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U13(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U14(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U15(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U16(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U22(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U23(X)) >= Marked_mark(X) constraint: Marked_mark(U31(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U32(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U33(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U34(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U35(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U36(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U42(X)) >= Marked_mark(X) constraint: Marked_mark(U51(X)) >= Marked_mark(X) constraint: Marked_mark(U61(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U62(X)) >= Marked_mark(X) constraint: Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) constraint: Marked_mark(U71(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U72(X1,X2)) >= Marked_a__U72(mark(X1),X2) constraint: Marked_mark(U72(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) ; a__U102(X1,X2,X3) >= U102(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) ; a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) ; a__U101(X1,X2,X3) >= U101(X1,X2,X3) ; a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) ; a__U103(X1,X2,X3) >= U103(X1,X2,X3) ; a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) ; a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) ; a__isNat(X) >= isNat(X) ; a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ; a__U104(X1,X2,X3) >= U104(X1,X2,X3) ; a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) ; a__plus(N,0) >= a__U71(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) ; a__x(N,0) >= a__U91(a__isNat(N),N) ; a__x(X1,X2) >= x(X1,X2) ; mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ; mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) ; mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) ; mark(isNat(X)) >= a__isNat(X) ; mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) ; mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) ; mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) ; mark(U15(X1,X2)) >= a__U15(mark(X1),X2) ; mark(U16(X)) >= a__U16(mark(X)) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U22(X1,X2)) >= a__U22(mark(X1),X2) ; mark(U23(X)) >= a__U23(mark(X)) ; mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) ; mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) ; mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) ; mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) ; mark(U35(X1,X2)) >= a__U35(mark(X1),X2) ; mark(U36(X)) >= a__U36(mark(X)) ; mark(U41(X1,X2)) >= a__U41(mark(X1),X2) ; mark(U42(X)) >= a__U42(mark(X)) ; mark(U51(X)) >= a__U51(mark(X)) ; mark(U61(X1,X2)) >= a__U61(mark(X1),X2) ; mark(U62(X)) >= a__U62(mark(X)) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U72(X1,X2)) >= a__U72(mark(X1),X2) ; mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) ; mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) ; mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) ; mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) ; mark(U91(X1,X2)) >= a__U91(mark(X1),X2) ; mark(U92(X)) >= a__U92(mark(X)) ; a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) ; a__U11(X1,X2,X3) >= U11(X1,X2,X3) ; a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) ; a__U13(X1,X2,X3) >= U13(X1,X2,X3) ; a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) ; a__U14(X1,X2,X3) >= U14(X1,X2,X3) ; a__U15(tt,V2) >= a__U16(a__isNat(V2)) ; a__U15(X1,X2) >= U15(X1,X2) ; a__U16(tt) >= tt ; a__U16(X) >= U16(X) ; a__U22(tt,V1) >= a__U23(a__isNat(V1)) ; a__U22(X1,X2) >= U22(X1,X2) ; a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U23(tt) >= tt ; a__U23(X) >= U23(X) ; a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) ; a__U32(X1,X2,X3) >= U32(X1,X2,X3) ; a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) ; a__U31(X1,X2,X3) >= U31(X1,X2,X3) ; a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) ; a__U33(X1,X2,X3) >= U33(X1,X2,X3) ; a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) ; a__U34(X1,X2,X3) >= U34(X1,X2,X3) ; a__U35(tt,V2) >= a__U36(a__isNat(V2)) ; a__U35(X1,X2) >= U35(X1,X2) ; a__U36(tt) >= tt ; a__U36(X) >= U36(X) ; a__U42(tt) >= tt ; a__U42(X) >= U42(X) ; a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) ; a__U41(X1,X2) >= U41(X1,X2) ; a__U51(tt) >= tt ; a__U51(X) >= U51(X) ; a__U62(tt) >= tt ; a__U62(X) >= U62(X) ; a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) ; a__U61(X1,X2) >= U61(X1,X2) ; a__U72(tt,N) >= mark(N) ; a__U72(X1,X2) >= U72(X1,X2) ; a__U71(tt,N) >= a__U72(a__isNatKind(N),N) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) ; a__U82(X1,X2,X3) >= U82(X1,X2,X3) ; a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) ; a__U81(X1,X2,X3) >= U81(X1,X2,X3) ; a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) ; a__U83(X1,X2,X3) >= U83(X1,X2,X3) ; a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U84(X1,X2,X3) >= U84(X1,X2,X3) ; a__U92(tt) >= 0 ; a__U92(X) >= U92(X) ; a__U91(tt,N) >= a__U92(a__isNatKind(N)) ; a__U91(X1,X2) >= U91(X1,X2) ; Marked_a__U72(tt,N) >= Marked_mark(N) ; Marked_a__U71(tt,N) >= Marked_a__U72(a__isNatKind(N),N) ; Marked_a__plus(N,0) >= Marked_a__U71(a__isNat(N),N) ; Marked_a__U104(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ; Marked_a__U104(tt,M,N) >= Marked_mark(M) ; Marked_a__U104(tt,M,N) >= Marked_mark(N) ; Marked_a__U103(tt,M,N) >= Marked_a__U104(a__isNatKind(N),M,N) ; Marked_a__U102(tt,M,N) >= Marked_a__U103(a__isNat(N),M,N) ; Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(x(X1,X2)) >= Marked_mark(X1) ; Marked_mark(x(X1,X2)) >= Marked_mark(X2) ; Marked_mark(U102(X1,X2,X3)) >= Marked_a__U102(mark(X1),X2,X3) ; Marked_mark(U102(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U103(X1,X2,X3)) >= Marked_a__U103(mark(X1),X2,X3) ; Marked_mark(U103(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U104(X1,X2,X3)) >= Marked_a__U104(mark(X1),X2,X3) ; Marked_mark(U104(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U13(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U14(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U15(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U16(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U22(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U23(X)) >= Marked_mark(X) ; Marked_mark(U31(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U32(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U33(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U34(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U35(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U36(X)) >= Marked_mark(X) ; Marked_mark(U41(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U42(X)) >= Marked_mark(X) ; Marked_mark(U51(X)) >= Marked_mark(X) ; Marked_mark(U61(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U62(X)) >= Marked_mark(X) ; Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) ; Marked_mark(U71(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U72(X1,X2)) >= Marked_a__U72(mark(X1),X2) ; Marked_mark(U72(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__U72(tt,N) > Marked_mark(N) ; } { Marked_a__U71(tt,N) > Marked_a__U72(a__isNatKind(N),N) ; } { Marked_a__plus(N,0) > Marked_a__U71(a__isNat(N),N) ; } { Marked_a__U104(tt,M,N) > Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ; } { Marked_a__U104(tt,M,N) > Marked_mark(M) ; } { Marked_a__U104(tt,M,N) > Marked_mark(N) ; } { Marked_a__U103(tt,M,N) > Marked_a__U104(a__isNatKind(N),M,N) ; } { Marked_a__U102(tt,M,N) > Marked_a__U103(a__isNat(N),M,N) ; } { Marked_mark(plus(X1,X2)) > Marked_a__plus(mark(X1),mark(X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(U102(X1,X2,X3)) > Marked_a__U102(mark(X1),X2,X3) ; } { Marked_mark(U102(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U103(X1,X2,X3)) > Marked_a__U103(mark(X1),X2,X3) ; } { Marked_mark(U103(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U104(X1,X2,X3)) > Marked_a__U104(mark(X1),X2,X3) ; } { Marked_mark(U104(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U13(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U14(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U15(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U16(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U22(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U23(X)) > Marked_mark(X) ; } { Marked_mark(U31(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U32(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U33(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U34(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U35(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U36(X)) > Marked_mark(X) ; } { Marked_mark(U41(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U42(X)) > Marked_mark(X) ; } { Marked_mark(U51(X)) > Marked_mark(X) ; } { Marked_mark(U61(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U62(X)) > Marked_mark(X) ; } { Marked_mark(U71(X1,X2)) > Marked_a__U71(mark(X1),X2) ; } { Marked_mark(U71(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U72(X1,X2)) > Marked_a__U72(mark(X1),X2) ; } { Marked_mark(U72(X1,X2)) > Marked_mark(X1) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) constraint: a__U102(X1,X2,X3) >= U102(X1,X2,X3) constraint: a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) constraint: a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) constraint: a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) constraint: a__U101(X1,X2,X3) >= U101(X1,X2,X3) constraint: a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) constraint: a__U103(X1,X2,X3) >= U103(X1,X2,X3) constraint: a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) constraint: a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) constraint: a__isNat(X) >= isNat(X) constraint: a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) constraint: a__U104(X1,X2,X3) >= U104(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U71(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) constraint: a__x(N,0) >= a__U91(a__isNat(N),N) constraint: a__x(X1,X2) >= x(X1,X2) constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) constraint: mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) constraint: mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) constraint: mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) constraint: mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) constraint: mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) constraint: mark(U15(X1,X2)) >= a__U15(mark(X1),X2) constraint: mark(U16(X)) >= a__U16(mark(X)) constraint: mark(U21(X1,X2)) >= a__U21(mark(X1),X2) constraint: mark(U22(X1,X2)) >= a__U22(mark(X1),X2) constraint: mark(U23(X)) >= a__U23(mark(X)) constraint: mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) constraint: mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) constraint: mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) constraint: mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) constraint: mark(U35(X1,X2)) >= a__U35(mark(X1),X2) constraint: mark(U36(X)) >= a__U36(mark(X)) constraint: mark(U41(X1,X2)) >= a__U41(mark(X1),X2) constraint: mark(U42(X)) >= a__U42(mark(X)) constraint: mark(U51(X)) >= a__U51(mark(X)) constraint: mark(U61(X1,X2)) >= a__U61(mark(X1),X2) constraint: mark(U62(X)) >= a__U62(mark(X)) constraint: mark(U71(X1,X2)) >= a__U71(mark(X1),X2) constraint: mark(U72(X1,X2)) >= a__U72(mark(X1),X2) constraint: mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) constraint: mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) constraint: mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) constraint: mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) constraint: mark(U91(X1,X2)) >= a__U91(mark(X1),X2) constraint: mark(U92(X)) >= a__U92(mark(X)) constraint: a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) constraint: a__U12(X1,X2,X3) >= U12(X1,X2,X3) constraint: a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) constraint: a__U11(X1,X2,X3) >= U11(X1,X2,X3) constraint: a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) constraint: a__U13(X1,X2,X3) >= U13(X1,X2,X3) constraint: a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) constraint: a__U14(X1,X2,X3) >= U14(X1,X2,X3) constraint: a__U15(tt,V2) >= a__U16(a__isNat(V2)) constraint: a__U15(X1,X2) >= U15(X1,X2) constraint: a__U16(tt) >= tt constraint: a__U16(X) >= U16(X) constraint: a__U22(tt,V1) >= a__U23(a__isNat(V1)) constraint: a__U22(X1,X2) >= U22(X1,X2) constraint: a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) constraint: a__U21(X1,X2) >= U21(X1,X2) constraint: a__U23(tt) >= tt constraint: a__U23(X) >= U23(X) constraint: a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) constraint: a__U32(X1,X2,X3) >= U32(X1,X2,X3) constraint: a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) constraint: a__U31(X1,X2,X3) >= U31(X1,X2,X3) constraint: a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) constraint: a__U33(X1,X2,X3) >= U33(X1,X2,X3) constraint: a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) constraint: a__U34(X1,X2,X3) >= U34(X1,X2,X3) constraint: a__U35(tt,V2) >= a__U36(a__isNat(V2)) constraint: a__U35(X1,X2) >= U35(X1,X2) constraint: a__U36(tt) >= tt constraint: a__U36(X) >= U36(X) constraint: a__U42(tt) >= tt constraint: a__U42(X) >= U42(X) constraint: a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) constraint: a__U41(X1,X2) >= U41(X1,X2) constraint: a__U51(tt) >= tt constraint: a__U51(X) >= U51(X) constraint: a__U62(tt) >= tt constraint: a__U62(X) >= U62(X) constraint: a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) constraint: a__U61(X1,X2) >= U61(X1,X2) constraint: a__U72(tt,N) >= mark(N) constraint: a__U72(X1,X2) >= U72(X1,X2) constraint: a__U71(tt,N) >= a__U72(a__isNatKind(N),N) constraint: a__U71(X1,X2) >= U71(X1,X2) constraint: a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) constraint: a__U82(X1,X2,X3) >= U82(X1,X2,X3) constraint: a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) constraint: a__U81(X1,X2,X3) >= U81(X1,X2,X3) constraint: a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) constraint: a__U83(X1,X2,X3) >= U83(X1,X2,X3) constraint: a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U84(X1,X2,X3) >= U84(X1,X2,X3) constraint: a__U92(tt) >= 0 constraint: a__U92(X) >= U92(X) constraint: a__U91(tt,N) >= a__U92(a__isNatKind(N)) constraint: a__U91(X1,X2) >= U91(X1,X2) constraint: Marked_a__U72(tt,N) >= Marked_mark(N) constraint: Marked_a__U71(tt,N) >= Marked_a__U72(a__isNatKind(N),N) constraint: Marked_a__plus(N,0) >= Marked_a__U71(a__isNat(N),N) constraint: Marked_a__U104(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)), mark(N)) constraint: Marked_a__U104(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U104(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U103(tt,M,N) >= Marked_a__U104(a__isNatKind(N),M,N) constraint: Marked_a__U102(tt,M,N) >= Marked_a__U103(a__isNat(N),M,N) constraint: Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(U102(X1,X2,X3)) >= Marked_a__U102(mark(X1),X2,X3) constraint: Marked_mark(U102(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U103(X1,X2,X3)) >= Marked_a__U103(mark(X1),X2,X3) constraint: Marked_mark(U103(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U104(X1,X2,X3)) >= Marked_a__U104(mark(X1),X2,X3) constraint: Marked_mark(U104(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U13(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U14(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U15(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U16(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U22(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U23(X)) >= Marked_mark(X) constraint: Marked_mark(U31(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U32(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U33(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U34(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U35(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U36(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U42(X)) >= Marked_mark(X) constraint: Marked_mark(U51(X)) >= Marked_mark(X) constraint: Marked_mark(U61(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U62(X)) >= Marked_mark(X) constraint: Marked_mark(U71(X1,X2)) >= Marked_a__U71(mark(X1),X2) constraint: Marked_mark(U71(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U72(X1,X2)) >= Marked_a__U72(mark(X1),X2) constraint: Marked_mark(U72(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) ; a__U102(X1,X2,X3) >= U102(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) ; a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) ; a__U101(X1,X2,X3) >= U101(X1,X2,X3) ; a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) ; a__U103(X1,X2,X3) >= U103(X1,X2,X3) ; a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) ; a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) ; a__isNat(X) >= isNat(X) ; a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ; a__U104(X1,X2,X3) >= U104(X1,X2,X3) ; a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) ; a__plus(N,0) >= a__U71(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) ; a__x(N,0) >= a__U91(a__isNat(N),N) ; a__x(X1,X2) >= x(X1,X2) ; mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ; mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) ; mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) ; mark(isNat(X)) >= a__isNat(X) ; mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) ; mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) ; mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) ; mark(U15(X1,X2)) >= a__U15(mark(X1),X2) ; mark(U16(X)) >= a__U16(mark(X)) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U22(X1,X2)) >= a__U22(mark(X1),X2) ; mark(U23(X)) >= a__U23(mark(X)) ; mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) ; mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) ; mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) ; mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) ; mark(U35(X1,X2)) >= a__U35(mark(X1),X2) ; mark(U36(X)) >= a__U36(mark(X)) ; mark(U41(X1,X2)) >= a__U41(mark(X1),X2) ; mark(U42(X)) >= a__U42(mark(X)) ; mark(U51(X)) >= a__U51(mark(X)) ; mark(U61(X1,X2)) >= a__U61(mark(X1),X2) ; mark(U62(X)) >= a__U62(mark(X)) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U72(X1,X2)) >= a__U72(mark(X1),X2) ; mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) ; mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) ; mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) ; mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) ; mark(U91(X1,X2)) >= a__U91(mark(X1),X2) ; mark(U92(X)) >= a__U92(mark(X)) ; a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) ; a__U11(X1,X2,X3) >= U11(X1,X2,X3) ; a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) ; a__U13(X1,X2,X3) >= U13(X1,X2,X3) ; a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) ; a__U14(X1,X2,X3) >= U14(X1,X2,X3) ; a__U15(tt,V2) >= a__U16(a__isNat(V2)) ; a__U15(X1,X2) >= U15(X1,X2) ; a__U16(tt) >= tt ; a__U16(X) >= U16(X) ; a__U22(tt,V1) >= a__U23(a__isNat(V1)) ; a__U22(X1,X2) >= U22(X1,X2) ; a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U23(tt) >= tt ; a__U23(X) >= U23(X) ; a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) ; a__U32(X1,X2,X3) >= U32(X1,X2,X3) ; a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) ; a__U31(X1,X2,X3) >= U31(X1,X2,X3) ; a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) ; a__U33(X1,X2,X3) >= U33(X1,X2,X3) ; a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) ; a__U34(X1,X2,X3) >= U34(X1,X2,X3) ; a__U35(tt,V2) >= a__U36(a__isNat(V2)) ; a__U35(X1,X2) >= U35(X1,X2) ; a__U36(tt) >= tt ; a__U36(X) >= U36(X) ; a__U42(tt) >= tt ; a__U42(X) >= U42(X) ; a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) ; a__U41(X1,X2) >= U41(X1,X2) ; a__U51(tt) >= tt ; a__U51(X) >= U51(X) ; a__U62(tt) >= tt ; a__U62(X) >= U62(X) ; a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) ; a__U61(X1,X2) >= U61(X1,X2) ; a__U72(tt,N) >= mark(N) ; a__U72(X1,X2) >= U72(X1,X2) ; a__U71(tt,N) >= a__U72(a__isNatKind(N),N) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) ; a__U82(X1,X2,X3) >= U82(X1,X2,X3) ; a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) ; a__U81(X1,X2,X3) >= U81(X1,X2,X3) ; a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) ; a__U83(X1,X2,X3) >= U83(X1,X2,X3) ; a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U84(X1,X2,X3) >= U84(X1,X2,X3) ; a__U92(tt) >= 0 ; a__U92(X) >= U92(X) ; a__U91(tt,N) >= a__U92(a__isNatKind(N)) ; a__U91(X1,X2) >= U91(X1,X2) ; Marked_a__U72(tt,N) >= Marked_mark(N) ; Marked_a__U71(tt,N) >= Marked_a__U72(a__isNatKind(N),N) ; Marked_a__plus(N,0) >= Marked_a__U71(a__isNat(N),N) ; Marked_a__U104(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ; Marked_a__U104(tt,M,N) >= Marked_mark(M) ; Marked_a__U104(tt,M,N) >= Marked_mark(N) ; Marked_a__U103(tt,M,N) >= Marked_a__U104(a__isNatKind(N),M,N) ; Marked_a__U102(tt,M,N) >= Marked_a__U103(a__isNat(N),M,N) ; Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(x(X1,X2)) >= Marked_mark(X1) ; Marked_mark(x(X1,X2)) >= Marked_mark(X2) ; Marked_mark(U102(X1,X2,X3)) >= Marked_a__U102(mark(X1),X2,X3) ; Marked_mark(U102(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U103(X1,X2,X3)) >= Marked_a__U103(mark(X1),X2,X3) ; Marked_mark(U103(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U104(X1,X2,X3)) >= Marked_a__U104(mark(X1),X2,X3) ; Marked_mark(U104(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U13(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U14(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U15(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U16(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U22(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U23(X)) >= Marked_mark(X) ; Marked_mark(U31(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U32(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U33(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U34(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U35(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U36(X)) >= Marked_mark(X) ; Marked_mark(U41(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U42(X)) >= Marked_mark(X) ; Marked_mark(U51(X)) >= Marked_mark(X) ; Marked_mark(U61(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U62(X)) >= Marked_mark(X) ; Marked_mark(U72(X1,X2)) >= Marked_a__U72(mark(X1),X2) ; Marked_mark(U72(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__U72(tt,N) > Marked_mark(N) ; } { Marked_a__U71(tt,N) > Marked_a__U72(a__isNatKind(N),N) ; } { Marked_a__plus(N,0) > Marked_a__U71(a__isNat(N),N) ; } { Marked_a__U104(tt,M,N) > Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ; } { Marked_a__U104(tt,M,N) > Marked_mark(M) ; } { Marked_a__U104(tt,M,N) > Marked_mark(N) ; } { Marked_a__U103(tt,M,N) > Marked_a__U104(a__isNatKind(N),M,N) ; } { Marked_a__U102(tt,M,N) > Marked_a__U103(a__isNat(N),M,N) ; } { Marked_mark(plus(X1,X2)) > Marked_a__plus(mark(X1),mark(X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(U102(X1,X2,X3)) > Marked_a__U102(mark(X1),X2,X3) ; } { Marked_mark(U102(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U103(X1,X2,X3)) > Marked_a__U103(mark(X1),X2,X3) ; } { Marked_mark(U103(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U104(X1,X2,X3)) > Marked_a__U104(mark(X1),X2,X3) ; } { Marked_mark(U104(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U13(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U14(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U15(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U16(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U22(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U23(X)) > Marked_mark(X) ; } { Marked_mark(U31(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U32(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U33(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U34(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U35(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U36(X)) > Marked_mark(X) ; } { Marked_mark(U41(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U42(X)) > Marked_mark(X) ; } { Marked_mark(U51(X)) > Marked_mark(X) ; } { Marked_mark(U61(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U62(X)) > Marked_mark(X) ; } { Marked_mark(U72(X1,X2)) > Marked_a__U72(mark(X1),X2) ; } { Marked_mark(U72(X1,X2)) > Marked_mark(X1) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) constraint: a__U102(X1,X2,X3) >= U102(X1,X2,X3) constraint: a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) constraint: a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) constraint: a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) constraint: a__U101(X1,X2,X3) >= U101(X1,X2,X3) constraint: a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) constraint: a__U103(X1,X2,X3) >= U103(X1,X2,X3) constraint: a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) constraint: a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) constraint: a__isNat(X) >= isNat(X) constraint: a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) constraint: a__U104(X1,X2,X3) >= U104(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U71(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) constraint: a__x(N,0) >= a__U91(a__isNat(N),N) constraint: a__x(X1,X2) >= x(X1,X2) constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) constraint: mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) constraint: mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) constraint: mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) constraint: mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) constraint: mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) constraint: mark(U15(X1,X2)) >= a__U15(mark(X1),X2) constraint: mark(U16(X)) >= a__U16(mark(X)) constraint: mark(U21(X1,X2)) >= a__U21(mark(X1),X2) constraint: mark(U22(X1,X2)) >= a__U22(mark(X1),X2) constraint: mark(U23(X)) >= a__U23(mark(X)) constraint: mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) constraint: mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) constraint: mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) constraint: mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) constraint: mark(U35(X1,X2)) >= a__U35(mark(X1),X2) constraint: mark(U36(X)) >= a__U36(mark(X)) constraint: mark(U41(X1,X2)) >= a__U41(mark(X1),X2) constraint: mark(U42(X)) >= a__U42(mark(X)) constraint: mark(U51(X)) >= a__U51(mark(X)) constraint: mark(U61(X1,X2)) >= a__U61(mark(X1),X2) constraint: mark(U62(X)) >= a__U62(mark(X)) constraint: mark(U71(X1,X2)) >= a__U71(mark(X1),X2) constraint: mark(U72(X1,X2)) >= a__U72(mark(X1),X2) constraint: mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) constraint: mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) constraint: mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) constraint: mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) constraint: mark(U91(X1,X2)) >= a__U91(mark(X1),X2) constraint: mark(U92(X)) >= a__U92(mark(X)) constraint: a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) constraint: a__U12(X1,X2,X3) >= U12(X1,X2,X3) constraint: a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) constraint: a__U11(X1,X2,X3) >= U11(X1,X2,X3) constraint: a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) constraint: a__U13(X1,X2,X3) >= U13(X1,X2,X3) constraint: a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) constraint: a__U14(X1,X2,X3) >= U14(X1,X2,X3) constraint: a__U15(tt,V2) >= a__U16(a__isNat(V2)) constraint: a__U15(X1,X2) >= U15(X1,X2) constraint: a__U16(tt) >= tt constraint: a__U16(X) >= U16(X) constraint: a__U22(tt,V1) >= a__U23(a__isNat(V1)) constraint: a__U22(X1,X2) >= U22(X1,X2) constraint: a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) constraint: a__U21(X1,X2) >= U21(X1,X2) constraint: a__U23(tt) >= tt constraint: a__U23(X) >= U23(X) constraint: a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) constraint: a__U32(X1,X2,X3) >= U32(X1,X2,X3) constraint: a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) constraint: a__U31(X1,X2,X3) >= U31(X1,X2,X3) constraint: a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) constraint: a__U33(X1,X2,X3) >= U33(X1,X2,X3) constraint: a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) constraint: a__U34(X1,X2,X3) >= U34(X1,X2,X3) constraint: a__U35(tt,V2) >= a__U36(a__isNat(V2)) constraint: a__U35(X1,X2) >= U35(X1,X2) constraint: a__U36(tt) >= tt constraint: a__U36(X) >= U36(X) constraint: a__U42(tt) >= tt constraint: a__U42(X) >= U42(X) constraint: a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) constraint: a__U41(X1,X2) >= U41(X1,X2) constraint: a__U51(tt) >= tt constraint: a__U51(X) >= U51(X) constraint: a__U62(tt) >= tt constraint: a__U62(X) >= U62(X) constraint: a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) constraint: a__U61(X1,X2) >= U61(X1,X2) constraint: a__U72(tt,N) >= mark(N) constraint: a__U72(X1,X2) >= U72(X1,X2) constraint: a__U71(tt,N) >= a__U72(a__isNatKind(N),N) constraint: a__U71(X1,X2) >= U71(X1,X2) constraint: a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) constraint: a__U82(X1,X2,X3) >= U82(X1,X2,X3) constraint: a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) constraint: a__U81(X1,X2,X3) >= U81(X1,X2,X3) constraint: a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) constraint: a__U83(X1,X2,X3) >= U83(X1,X2,X3) constraint: a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U84(X1,X2,X3) >= U84(X1,X2,X3) constraint: a__U92(tt) >= 0 constraint: a__U92(X) >= U92(X) constraint: a__U91(tt,N) >= a__U92(a__isNatKind(N)) constraint: a__U91(X1,X2) >= U91(X1,X2) constraint: Marked_a__U72(tt,N) >= Marked_mark(N) constraint: Marked_a__U71(tt,N) >= Marked_a__U72(a__isNatKind(N),N) constraint: Marked_a__plus(N,0) >= Marked_a__U71(a__isNat(N),N) constraint: Marked_a__U104(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)), mark(N)) constraint: Marked_a__U104(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U104(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U103(tt,M,N) >= Marked_a__U104(a__isNatKind(N),M,N) constraint: Marked_a__U102(tt,M,N) >= Marked_a__U103(a__isNat(N),M,N) constraint: Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(U102(X1,X2,X3)) >= Marked_a__U102(mark(X1),X2,X3) constraint: Marked_mark(U102(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U103(X1,X2,X3)) >= Marked_a__U103(mark(X1),X2,X3) constraint: Marked_mark(U103(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U104(X1,X2,X3)) >= Marked_a__U104(mark(X1),X2,X3) constraint: Marked_mark(U104(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U13(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U14(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U15(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U16(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U22(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U23(X)) >= Marked_mark(X) constraint: Marked_mark(U31(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U32(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U33(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U34(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U35(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U36(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U42(X)) >= Marked_mark(X) constraint: Marked_mark(U51(X)) >= Marked_mark(X) constraint: Marked_mark(U61(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U62(X)) >= Marked_mark(X) constraint: Marked_mark(U72(X1,X2)) >= Marked_a__U72(mark(X1),X2) constraint: Marked_mark(U72(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) ; a__U102(X1,X2,X3) >= U102(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) ; a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) ; a__U101(X1,X2,X3) >= U101(X1,X2,X3) ; a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) ; a__U103(X1,X2,X3) >= U103(X1,X2,X3) ; a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) ; a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) ; a__isNat(X) >= isNat(X) ; a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) ; a__U104(X1,X2,X3) >= U104(X1,X2,X3) ; a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) ; a__plus(N,0) >= a__U71(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) ; a__x(N,0) >= a__U91(a__isNat(N),N) ; a__x(X1,X2) >= x(X1,X2) ; mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) ; mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) ; mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) ; mark(isNat(X)) >= a__isNat(X) ; mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) ; mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) ; mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) ; mark(U15(X1,X2)) >= a__U15(mark(X1),X2) ; mark(U16(X)) >= a__U16(mark(X)) ; mark(U21(X1,X2)) >= a__U21(mark(X1),X2) ; mark(U22(X1,X2)) >= a__U22(mark(X1),X2) ; mark(U23(X)) >= a__U23(mark(X)) ; mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) ; mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) ; mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) ; mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) ; mark(U35(X1,X2)) >= a__U35(mark(X1),X2) ; mark(U36(X)) >= a__U36(mark(X)) ; mark(U41(X1,X2)) >= a__U41(mark(X1),X2) ; mark(U42(X)) >= a__U42(mark(X)) ; mark(U51(X)) >= a__U51(mark(X)) ; mark(U61(X1,X2)) >= a__U61(mark(X1),X2) ; mark(U62(X)) >= a__U62(mark(X)) ; mark(U71(X1,X2)) >= a__U71(mark(X1),X2) ; mark(U72(X1,X2)) >= a__U72(mark(X1),X2) ; mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) ; mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) ; mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) ; mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) ; mark(U91(X1,X2)) >= a__U91(mark(X1),X2) ; mark(U92(X)) >= a__U92(mark(X)) ; a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) ; a__U11(X1,X2,X3) >= U11(X1,X2,X3) ; a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) ; a__U13(X1,X2,X3) >= U13(X1,X2,X3) ; a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) ; a__U14(X1,X2,X3) >= U14(X1,X2,X3) ; a__U15(tt,V2) >= a__U16(a__isNat(V2)) ; a__U15(X1,X2) >= U15(X1,X2) ; a__U16(tt) >= tt ; a__U16(X) >= U16(X) ; a__U22(tt,V1) >= a__U23(a__isNat(V1)) ; a__U22(X1,X2) >= U22(X1,X2) ; a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) ; a__U21(X1,X2) >= U21(X1,X2) ; a__U23(tt) >= tt ; a__U23(X) >= U23(X) ; a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) ; a__U32(X1,X2,X3) >= U32(X1,X2,X3) ; a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) ; a__U31(X1,X2,X3) >= U31(X1,X2,X3) ; a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) ; a__U33(X1,X2,X3) >= U33(X1,X2,X3) ; a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) ; a__U34(X1,X2,X3) >= U34(X1,X2,X3) ; a__U35(tt,V2) >= a__U36(a__isNat(V2)) ; a__U35(X1,X2) >= U35(X1,X2) ; a__U36(tt) >= tt ; a__U36(X) >= U36(X) ; a__U42(tt) >= tt ; a__U42(X) >= U42(X) ; a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) ; a__U41(X1,X2) >= U41(X1,X2) ; a__U51(tt) >= tt ; a__U51(X) >= U51(X) ; a__U62(tt) >= tt ; a__U62(X) >= U62(X) ; a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) ; a__U61(X1,X2) >= U61(X1,X2) ; a__U72(tt,N) >= mark(N) ; a__U72(X1,X2) >= U72(X1,X2) ; a__U71(tt,N) >= a__U72(a__isNatKind(N),N) ; a__U71(X1,X2) >= U71(X1,X2) ; a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) ; a__U82(X1,X2,X3) >= U82(X1,X2,X3) ; a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) ; a__U81(X1,X2,X3) >= U81(X1,X2,X3) ; a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) ; a__U83(X1,X2,X3) >= U83(X1,X2,X3) ; a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U84(X1,X2,X3) >= U84(X1,X2,X3) ; a__U92(tt) >= 0 ; a__U92(X) >= U92(X) ; a__U91(tt,N) >= a__U92(a__isNatKind(N)) ; a__U91(X1,X2) >= U91(X1,X2) ; Marked_a__U72(tt,N) >= Marked_mark(N) ; Marked_a__U71(tt,N) >= Marked_a__U72(a__isNatKind(N),N) ; Marked_a__plus(N,0) >= Marked_a__U71(a__isNat(N),N) ; Marked_a__U104(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ; Marked_a__U104(tt,M,N) >= Marked_mark(M) ; Marked_a__U104(tt,M,N) >= Marked_mark(N) ; Marked_a__U103(tt,M,N) >= Marked_a__U104(a__isNatKind(N),M,N) ; Marked_a__U102(tt,M,N) >= Marked_a__U103(a__isNat(N),M,N) ; Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(x(X1,X2)) >= Marked_mark(X1) ; Marked_mark(x(X1,X2)) >= Marked_mark(X2) ; Marked_mark(U102(X1,X2,X3)) >= Marked_a__U102(mark(X1),X2,X3) ; Marked_mark(U102(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U103(X1,X2,X3)) >= Marked_a__U103(mark(X1),X2,X3) ; Marked_mark(U103(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U104(X1,X2,X3)) >= Marked_a__U104(mark(X1),X2,X3) ; Marked_mark(U104(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U13(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U14(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U15(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U16(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U22(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U23(X)) >= Marked_mark(X) ; Marked_mark(U31(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U32(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U33(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U34(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U35(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U36(X)) >= Marked_mark(X) ; Marked_mark(U41(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U42(X)) >= Marked_mark(X) ; Marked_mark(U51(X)) >= Marked_mark(X) ; Marked_mark(U61(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U62(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__U72(tt,N) > Marked_mark(N) ; } { Marked_a__U71(tt,N) > Marked_a__U72(a__isNatKind(N),N) ; } { Marked_a__plus(N,0) > Marked_a__U71(a__isNat(N),N) ; } { Marked_a__U104(tt,M,N) > Marked_a__plus(a__x(mark(N),mark(M)),mark(N)) ; } { Marked_a__U104(tt,M,N) > Marked_mark(M) ; } { Marked_a__U104(tt,M,N) > Marked_mark(N) ; } { Marked_a__U103(tt,M,N) > Marked_a__U104(a__isNatKind(N),M,N) ; } { Marked_a__U102(tt,M,N) > Marked_a__U103(a__isNat(N),M,N) ; } { Marked_mark(plus(X1,X2)) > Marked_a__plus(mark(X1),mark(X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(U102(X1,X2,X3)) > Marked_a__U102(mark(X1),X2,X3) ; } { Marked_mark(U102(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U103(X1,X2,X3)) > Marked_a__U103(mark(X1),X2,X3) ; } { Marked_mark(U103(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U104(X1,X2,X3)) > Marked_a__U104(mark(X1),X2,X3) ; } { Marked_mark(U104(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U13(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U14(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U15(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U16(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U22(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U23(X)) > Marked_mark(X) ; } { Marked_mark(U31(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U32(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U33(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U34(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U35(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U36(X)) > Marked_mark(X) ; } { Marked_mark(U41(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U42(X)) > Marked_mark(X) ; } { Marked_mark(U51(X)) > Marked_mark(X) ; } { Marked_mark(U61(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U62(X)) > Marked_mark(X) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: a__U102(tt,M,N) >= a__U103(a__isNat(N),M,N) constraint: a__U102(X1,X2,X3) >= U102(X1,X2,X3) constraint: a__isNatKind(s(V1)) >= a__U51(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U41(a__isNatKind(V1),V2) constraint: a__isNatKind(x(V1,V2)) >= a__U61(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) constraint: a__U101(tt,M,N) >= a__U102(a__isNatKind(M),M,N) constraint: a__U101(X1,X2,X3) >= U101(X1,X2,X3) constraint: a__U103(tt,M,N) >= a__U104(a__isNatKind(N),M,N) constraint: a__U103(X1,X2,X3) >= U103(X1,X2,X3) constraint: a__isNat(s(V1)) >= a__U21(a__isNatKind(V1),V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__U11(a__isNatKind(V1),V1,V2) constraint: a__isNat(x(V1,V2)) >= a__U31(a__isNatKind(V1),V1,V2) constraint: a__isNat(X) >= isNat(X) constraint: a__U104(tt,M,N) >= a__plus(a__x(mark(N),mark(M)),mark(N)) constraint: a__U104(X1,X2,X3) >= U104(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U81(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U71(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__x(N,s(M)) >= a__U101(a__isNat(M),M,N) constraint: a__x(N,0) >= a__U91(a__isNat(N),N) constraint: a__x(X1,X2) >= x(X1,X2) constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(x(X1,X2)) >= a__x(mark(X1),mark(X2)) constraint: mark(U101(X1,X2,X3)) >= a__U101(mark(X1),X2,X3) constraint: mark(U102(X1,X2,X3)) >= a__U102(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) constraint: mark(U103(X1,X2,X3)) >= a__U103(mark(X1),X2,X3) constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(U104(X1,X2,X3)) >= a__U104(mark(X1),X2,X3) constraint: mark(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(U13(X1,X2,X3)) >= a__U13(mark(X1),X2,X3) constraint: mark(U14(X1,X2,X3)) >= a__U14(mark(X1),X2,X3) constraint: mark(U15(X1,X2)) >= a__U15(mark(X1),X2) constraint: mark(U16(X)) >= a__U16(mark(X)) constraint: mark(U21(X1,X2)) >= a__U21(mark(X1),X2) constraint: mark(U22(X1,X2)) >= a__U22(mark(X1),X2) constraint: mark(U23(X)) >= a__U23(mark(X)) constraint: mark(U31(X1,X2,X3)) >= a__U31(mark(X1),X2,X3) constraint: mark(U32(X1,X2,X3)) >= a__U32(mark(X1),X2,X3) constraint: mark(U33(X1,X2,X3)) >= a__U33(mark(X1),X2,X3) constraint: mark(U34(X1,X2,X3)) >= a__U34(mark(X1),X2,X3) constraint: mark(U35(X1,X2)) >= a__U35(mark(X1),X2) constraint: mark(U36(X)) >= a__U36(mark(X)) constraint: mark(U41(X1,X2)) >= a__U41(mark(X1),X2) constraint: mark(U42(X)) >= a__U42(mark(X)) constraint: mark(U51(X)) >= a__U51(mark(X)) constraint: mark(U61(X1,X2)) >= a__U61(mark(X1),X2) constraint: mark(U62(X)) >= a__U62(mark(X)) constraint: mark(U71(X1,X2)) >= a__U71(mark(X1),X2) constraint: mark(U72(X1,X2)) >= a__U72(mark(X1),X2) constraint: mark(U81(X1,X2,X3)) >= a__U81(mark(X1),X2,X3) constraint: mark(U82(X1,X2,X3)) >= a__U82(mark(X1),X2,X3) constraint: mark(U83(X1,X2,X3)) >= a__U83(mark(X1),X2,X3) constraint: mark(U84(X1,X2,X3)) >= a__U84(mark(X1),X2,X3) constraint: mark(U91(X1,X2)) >= a__U91(mark(X1),X2) constraint: mark(U92(X)) >= a__U92(mark(X)) constraint: a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) constraint: a__U12(X1,X2,X3) >= U12(X1,X2,X3) constraint: a__U11(tt,V1,V2) >= a__U12(a__isNatKind(V1),V1,V2) constraint: a__U11(X1,X2,X3) >= U11(X1,X2,X3) constraint: a__U13(tt,V1,V2) >= a__U14(a__isNatKind(V2),V1,V2) constraint: a__U13(X1,X2,X3) >= U13(X1,X2,X3) constraint: a__U14(tt,V1,V2) >= a__U15(a__isNat(V1),V2) constraint: a__U14(X1,X2,X3) >= U14(X1,X2,X3) constraint: a__U15(tt,V2) >= a__U16(a__isNat(V2)) constraint: a__U15(X1,X2) >= U15(X1,X2) constraint: a__U16(tt) >= tt constraint: a__U16(X) >= U16(X) constraint: a__U22(tt,V1) >= a__U23(a__isNat(V1)) constraint: a__U22(X1,X2) >= U22(X1,X2) constraint: a__U21(tt,V1) >= a__U22(a__isNatKind(V1),V1) constraint: a__U21(X1,X2) >= U21(X1,X2) constraint: a__U23(tt) >= tt constraint: a__U23(X) >= U23(X) constraint: a__U32(tt,V1,V2) >= a__U33(a__isNatKind(V2),V1,V2) constraint: a__U32(X1,X2,X3) >= U32(X1,X2,X3) constraint: a__U31(tt,V1,V2) >= a__U32(a__isNatKind(V1),V1,V2) constraint: a__U31(X1,X2,X3) >= U31(X1,X2,X3) constraint: a__U33(tt,V1,V2) >= a__U34(a__isNatKind(V2),V1,V2) constraint: a__U33(X1,X2,X3) >= U33(X1,X2,X3) constraint: a__U34(tt,V1,V2) >= a__U35(a__isNat(V1),V2) constraint: a__U34(X1,X2,X3) >= U34(X1,X2,X3) constraint: a__U35(tt,V2) >= a__U36(a__isNat(V2)) constraint: a__U35(X1,X2) >= U35(X1,X2) constraint: a__U36(tt) >= tt constraint: a__U36(X) >= U36(X) constraint: a__U42(tt) >= tt constraint: a__U42(X) >= U42(X) constraint: a__U41(tt,V2) >= a__U42(a__isNatKind(V2)) constraint: a__U41(X1,X2) >= U41(X1,X2) constraint: a__U51(tt) >= tt constraint: a__U51(X) >= U51(X) constraint: a__U62(tt) >= tt constraint: a__U62(X) >= U62(X) constraint: a__U61(tt,V2) >= a__U62(a__isNatKind(V2)) constraint: a__U61(X1,X2) >= U61(X1,X2) constraint: a__U72(tt,N) >= mark(N) constraint: a__U72(X1,X2) >= U72(X1,X2) constraint: a__U71(tt,N) >= a__U72(a__isNatKind(N),N) constraint: a__U71(X1,X2) >= U71(X1,X2) constraint: a__U82(tt,M,N) >= a__U83(a__isNat(N),M,N) constraint: a__U82(X1,X2,X3) >= U82(X1,X2,X3) constraint: a__U81(tt,M,N) >= a__U82(a__isNatKind(M),M,N) constraint: a__U81(X1,X2,X3) >= U81(X1,X2,X3) constraint: a__U83(tt,M,N) >= a__U84(a__isNatKind(N),M,N) constraint: a__U83(X1,X2,X3) >= U83(X1,X2,X3) constraint: a__U84(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U84(X1,X2,X3) >= U84(X1,X2,X3) constraint: a__U92(tt) >= 0 constraint: a__U92(X) >= U92(X) constraint: a__U91(tt,N) >= a__U92(a__isNatKind(N)) constraint: a__U91(X1,X2) >= U91(X1,X2) constraint: Marked_a__U72(tt,N) >= Marked_mark(N) constraint: Marked_a__U71(tt,N) >= Marked_a__U72(a__isNatKind(N),N) constraint: Marked_a__plus(N,0) >= Marked_a__U71(a__isNat(N),N) constraint: Marked_a__U104(tt,M,N) >= Marked_a__plus(a__x(mark(N),mark(M)), mark(N)) constraint: Marked_a__U104(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U104(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U103(tt,M,N) >= Marked_a__U104(a__isNatKind(N),M,N) constraint: Marked_a__U102(tt,M,N) >= Marked_a__U103(a__isNat(N),M,N) constraint: Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(U102(X1,X2,X3)) >= Marked_a__U102(mark(X1),X2,X3) constraint: Marked_mark(U102(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U103(X1,X2,X3)) >= Marked_a__U103(mark(X1),X2,X3) constraint: Marked_mark(U103(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U104(X1,X2,X3)) >= Marked_a__U104(mark(X1),X2,X3) constraint: Marked_mark(U104(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U13(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U14(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U15(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U16(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U22(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U23(X)) >= Marked_mark(X) constraint: Marked_mark(U31(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U32(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U33(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U34(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U35(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U36(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U42(X)) >= Marked_mark(X) constraint: Marked_mark(U51(X)) >= Marked_mark(X) constraint: Marked_mark(U61(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U62(X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> -->