- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__U11(tt,V1,V2) -> a__U12(a__isNatKind(V1),V1,V2) [2] a__U12(tt,V1,V2) -> a__U13(a__isNatKind(V2),V1,V2) [3] a__U13(tt,V1,V2) -> a__U14(a__isNatKind(V2),V1,V2) [4] a__U14(tt,V1,V2) -> a__U15(a__isNat(V1),V2) [5] a__U15(tt,V2) -> a__U16(a__isNat(V2)) [6] a__U16(tt) -> tt [7] a__U21(tt,V1) -> a__U22(a__isNatKind(V1),V1) [8] a__U22(tt,V1) -> a__U23(a__isNat(V1)) [9] a__U23(tt) -> tt [10] a__U31(tt,V2) -> a__U32(a__isNatKind(V2)) [11] a__U32(tt) -> tt [12] a__U41(tt) -> tt [13] a__U51(tt,N) -> a__U52(a__isNatKind(N),N) [14] a__U52(tt,N) -> mark(N) [15] a__U61(tt,M,N) -> a__U62(a__isNatKind(M),M,N) [16] a__U62(tt,M,N) -> a__U63(a__isNat(N),M,N) [17] a__U63(tt,M,N) -> a__U64(a__isNatKind(N),M,N) [18] a__U64(tt,M,N) -> s(a__plus(mark(N),mark(M))) [19] a__isNat(0) -> tt [20] a__isNat(plus(V1,V2)) -> a__U11(a__isNatKind(V1),V1,V2) [21] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) [22] a__isNatKind(0) -> tt [23] a__isNatKind(plus(V1,V2)) -> a__U31(a__isNatKind(V1),V2) [24] a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1)) [25] a__plus(N,0) -> a__U51(a__isNat(N),N) [26] a__plus(N,s(M)) -> a__U61(a__isNat(M),M,N) [27] mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) [28] mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3) [29] mark(isNatKind(X)) -> a__isNatKind(X) [30] mark(U13(X1,X2,X3)) -> a__U13(mark(X1),X2,X3) [31] mark(U14(X1,X2,X3)) -> a__U14(mark(X1),X2,X3) [32] mark(U15(X1,X2)) -> a__U15(mark(X1),X2) [33] mark(isNat(X)) -> a__isNat(X) [34] mark(U16(X)) -> a__U16(mark(X)) [35] mark(U21(X1,X2)) -> a__U21(mark(X1),X2) [36] mark(U22(X1,X2)) -> a__U22(mark(X1),X2) [37] mark(U23(X)) -> a__U23(mark(X)) [38] mark(U31(X1,X2)) -> a__U31(mark(X1),X2) [39] mark(U32(X)) -> a__U32(mark(X)) [40] mark(U41(X)) -> a__U41(mark(X)) [41] mark(U51(X1,X2)) -> a__U51(mark(X1),X2) [42] mark(U52(X1,X2)) -> a__U52(mark(X1),X2) [43] mark(U61(X1,X2,X3)) -> a__U61(mark(X1),X2,X3) [44] mark(U62(X1,X2,X3)) -> a__U62(mark(X1),X2,X3) [45] mark(U63(X1,X2,X3)) -> a__U63(mark(X1),X2,X3) [46] mark(U64(X1,X2,X3)) -> a__U64(mark(X1),X2,X3) [47] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) [48] mark(tt) -> tt [49] mark(s(X)) -> s(mark(X)) [50] mark(0) -> 0 [51] a__U11(X1,X2,X3) -> U11(X1,X2,X3) [52] a__U12(X1,X2,X3) -> U12(X1,X2,X3) [53] a__isNatKind(X) -> isNatKind(X) [54] a__U13(X1,X2,X3) -> U13(X1,X2,X3) [55] a__U14(X1,X2,X3) -> U14(X1,X2,X3) [56] a__U15(X1,X2) -> U15(X1,X2) [57] a__isNat(X) -> isNat(X) [58] a__U16(X) -> U16(X) [59] a__U21(X1,X2) -> U21(X1,X2) [60] a__U22(X1,X2) -> U22(X1,X2) [61] a__U23(X) -> U23(X) [62] a__U31(X1,X2) -> U31(X1,X2) [63] a__U32(X) -> U32(X) [64] a__U41(X) -> U41(X) [65] a__U51(X1,X2) -> U51(X1,X2) [66] a__U52(X1,X2) -> U52(X1,X2) [67] a__U61(X1,X2,X3) -> U61(X1,X2,X3) [68] a__U62(X1,X2,X3) -> U62(X1,X2,X3) [69] a__U63(X1,X2,X3) -> U63(X1,X2,X3) [70] a__U64(X1,X2,X3) -> U64(X1,X2,X3) [71] a__plus(X1,X2) -> plus(X1,X2) 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__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; 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__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) >= isNat(X) ; 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) >= tt ; a__U32(X) >= U32(X) ; a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U41(tt) >= tt ; a__U41(X) >= U41(X) ; a__U52(tt,N) >= mark(N) ; a__U52(X1,X2) >= U52(X1,X2) ; a__U51(tt,N) >= a__U52(a__isNatKind(N),N) ; a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; 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(isNat(X)) >= a__isNat(X) ; 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)) >= a__U31(mark(X1),X2) ; mark(U32(X)) >= a__U32(mark(X)) ; mark(U41(X)) >= a__U41(mark(X)) ; mark(U51(X1,X2)) >= a__U51(mark(X1),X2) ; mark(U52(X1,X2)) >= a__U52(mark(X1),X2) ; mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) ; mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) ; mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) ; mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) ; a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) ; a__U62(X1,X2,X3) >= U62(X1,X2,X3) ; a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) ; a__U61(X1,X2,X3) >= U61(X1,X2,X3) ; a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) ; a__U63(X1,X2,X3) >= U63(X1,X2,X3) ; a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U64(X1,X2,X3) >= U64(X1,X2,X3) ; a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) ; a__plus(N,0) >= a__U51(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; Marked_a__plus(N,s(M)) >= Marked_a__U61(a__isNat(M),M,N) ; Marked_a__plus(N,0) >= Marked_a__U51(a__isNat(N),N) ; Marked_a__U64(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) ; Marked_a__U64(tt,M,N) >= Marked_mark(N) ; Marked_a__U64(tt,M,N) >= Marked_mark(M) ; Marked_a__U63(tt,M,N) >= Marked_a__U64(a__isNatKind(N),M,N) ; Marked_a__U62(tt,M,N) >= Marked_a__U63(a__isNat(N),M,N) ; Marked_a__U61(tt,M,N) >= Marked_a__U62(a__isNatKind(M),M,N) ; Marked_a__U52(tt,N) >= Marked_mark(N) ; Marked_a__U51(tt,N) >= Marked_a__U52(a__isNatKind(N),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(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)) >= Marked_mark(X1) ; Marked_mark(U32(X)) >= Marked_mark(X) ; Marked_mark(U41(X)) >= Marked_mark(X) ; Marked_mark(U51(X1,X2)) >= Marked_a__U51(mark(X1),X2) ; Marked_mark(U51(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) ; Marked_mark(U52(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U61(X1,X2,X3)) >= Marked_a__U61(mark(X1),X2,X3) ; Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U62(X1,X2,X3)) >= Marked_a__U62(mark(X1),X2,X3) ; Marked_mark(U62(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U63(X1,X2,X3)) >= Marked_a__U63(mark(X1),X2,X3) ; Marked_mark(U63(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U64(X1,X2,X3)) >= Marked_a__U64(mark(X1),X2,X3) ; Marked_mark(U64(X1,X2,X3)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__plus(N,s(M)) > Marked_a__U61(a__isNat(M),M,N) ; } { Marked_a__plus(N,0) > Marked_a__U51(a__isNat(N),N) ; } { Marked_a__U64(tt,M,N) > Marked_a__plus(mark(N),mark(M)) ; } { Marked_a__U64(tt,M,N) > Marked_mark(N) ; } { Marked_a__U64(tt,M,N) > Marked_mark(M) ; } { Marked_a__U63(tt,M,N) > Marked_a__U64(a__isNatKind(N),M,N) ; } { Marked_a__U62(tt,M,N) > Marked_a__U63(a__isNat(N),M,N) ; } { Marked_a__U61(tt,M,N) > Marked_a__U62(a__isNatKind(M),M,N) ; } { Marked_a__U52(tt,N) > Marked_mark(N) ; } { Marked_a__U51(tt,N) > Marked_a__U52(a__isNatKind(N),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(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)) > Marked_mark(X1) ; } { Marked_mark(U32(X)) > Marked_mark(X) ; } { Marked_mark(U41(X)) > Marked_mark(X) ; } { Marked_mark(U51(X1,X2)) > Marked_a__U51(mark(X1),X2) ; } { Marked_mark(U51(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U52(X1,X2)) > Marked_a__U52(mark(X1),X2) ; } { Marked_mark(U52(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_a__U61(mark(X1),X2,X3) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U62(X1,X2,X3)) > Marked_a__U62(mark(X1),X2,X3) ; } { Marked_mark(U62(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U63(X1,X2,X3)) > Marked_a__U63(mark(X1),X2,X3) ; } { Marked_mark(U63(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U64(X1,X2,X3)) > Marked_a__U64(mark(X1),X2,X3) ; } { Marked_mark(U64(X1,X2,X3)) > 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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === 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__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) 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__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) >= isNat(X) 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) >= tt constraint: a__U32(X) >= U32(X) constraint: a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) constraint: a__U31(X1,X2) >= U31(X1,X2) constraint: a__U41(tt) >= tt constraint: a__U41(X) >= U41(X) constraint: a__U52(tt,N) >= mark(N) constraint: a__U52(X1,X2) >= U52(X1,X2) constraint: a__U51(tt,N) >= a__U52(a__isNatKind(N),N) constraint: a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) 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(isNat(X)) >= a__isNat(X) 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)) >= a__U31(mark(X1),X2) constraint: mark(U32(X)) >= a__U32(mark(X)) constraint: mark(U41(X)) >= a__U41(mark(X)) constraint: mark(U51(X1,X2)) >= a__U51(mark(X1),X2) constraint: mark(U52(X1,X2)) >= a__U52(mark(X1),X2) constraint: mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) constraint: mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) constraint: mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) constraint: mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) constraint: a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) constraint: a__U62(X1,X2,X3) >= U62(X1,X2,X3) constraint: a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) constraint: a__U61(X1,X2,X3) >= U61(X1,X2,X3) constraint: a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) constraint: a__U63(X1,X2,X3) >= U63(X1,X2,X3) constraint: a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U64(X1,X2,X3) >= U64(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U51(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: Marked_a__plus(N,s(M)) >= Marked_a__U61(a__isNat(M),M,N) constraint: Marked_a__plus(N,0) >= Marked_a__U51(a__isNat(N),N) constraint: Marked_a__U64(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) constraint: Marked_a__U64(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U64(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U63(tt,M,N) >= Marked_a__U64(a__isNatKind(N),M,N) constraint: Marked_a__U62(tt,M,N) >= Marked_a__U63(a__isNat(N),M,N) constraint: Marked_a__U61(tt,M,N) >= Marked_a__U62(a__isNatKind(M),M,N) constraint: Marked_a__U52(tt,N) >= Marked_mark(N) constraint: Marked_a__U51(tt,N) >= Marked_a__U52(a__isNatKind(N),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(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)) >= Marked_mark(X1) constraint: Marked_mark(U32(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X)) >= Marked_mark(X) constraint: Marked_mark(U51(X1,X2)) >= Marked_a__U51(mark(X1),X2) constraint: Marked_mark(U51(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) constraint: Marked_mark(U52(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_a__U61(mark(X1),X2,X3) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U62(X1,X2,X3)) >= Marked_a__U62(mark(X1),X2,X3) constraint: Marked_mark(U62(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U63(X1,X2,X3)) >= Marked_a__U63(mark(X1),X2,X3) constraint: Marked_mark(U63(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U64(X1,X2,X3)) >= Marked_a__U64(mark(X1),X2,X3) constraint: Marked_mark(U64(X1,X2,X3)) >= Marked_mark(X1) APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; 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__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) >= isNat(X) ; 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) >= tt ; a__U32(X) >= U32(X) ; a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U41(tt) >= tt ; a__U41(X) >= U41(X) ; a__U52(tt,N) >= mark(N) ; a__U52(X1,X2) >= U52(X1,X2) ; a__U51(tt,N) >= a__U52(a__isNatKind(N),N) ; a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; 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(isNat(X)) >= a__isNat(X) ; 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)) >= a__U31(mark(X1),X2) ; mark(U32(X)) >= a__U32(mark(X)) ; mark(U41(X)) >= a__U41(mark(X)) ; mark(U51(X1,X2)) >= a__U51(mark(X1),X2) ; mark(U52(X1,X2)) >= a__U52(mark(X1),X2) ; mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) ; mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) ; mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) ; mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) ; a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) ; a__U62(X1,X2,X3) >= U62(X1,X2,X3) ; a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) ; a__U61(X1,X2,X3) >= U61(X1,X2,X3) ; a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) ; a__U63(X1,X2,X3) >= U63(X1,X2,X3) ; a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U64(X1,X2,X3) >= U64(X1,X2,X3) ; a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) ; a__plus(N,0) >= a__U51(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; Marked_a__U22(tt,V1) >= Marked_a__isNat(V1) ; Marked_a__U21(tt,V1) >= Marked_a__U22(a__isNatKind(V1),V1) ; 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__U15(tt,V2) >= Marked_a__isNat(V2) ; Marked_a__U14(tt,V1,V2) >= Marked_a__isNat(V1) ; Marked_a__U14(tt,V1,V2) >= Marked_a__U15(a__isNat(V1),V2) ; 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) ; } + Disjunctions:{ { Marked_a__U22(tt,V1) > Marked_a__isNat(V1) ; } { Marked_a__U21(tt,V1) > Marked_a__U22(a__isNatKind(V1),V1) ; } { 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__U15(tt,V2) > Marked_a__isNat(V2) ; } { Marked_a__U14(tt,V1,V2) > Marked_a__isNat(V1) ; } { Marked_a__U14(tt,V1,V2) > Marked_a__U15(a__isNat(V1),V2) ; } { 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) ; } } === 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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === 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__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) 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__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) >= isNat(X) 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) >= tt constraint: a__U32(X) >= U32(X) constraint: a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) constraint: a__U31(X1,X2) >= U31(X1,X2) constraint: a__U41(tt) >= tt constraint: a__U41(X) >= U41(X) constraint: a__U52(tt,N) >= mark(N) constraint: a__U52(X1,X2) >= U52(X1,X2) constraint: a__U51(tt,N) >= a__U52(a__isNatKind(N),N) constraint: a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) 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(isNat(X)) >= a__isNat(X) 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)) >= a__U31(mark(X1),X2) constraint: mark(U32(X)) >= a__U32(mark(X)) constraint: mark(U41(X)) >= a__U41(mark(X)) constraint: mark(U51(X1,X2)) >= a__U51(mark(X1),X2) constraint: mark(U52(X1,X2)) >= a__U52(mark(X1),X2) constraint: mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) constraint: mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) constraint: mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) constraint: mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) constraint: a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) constraint: a__U62(X1,X2,X3) >= U62(X1,X2,X3) constraint: a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) constraint: a__U61(X1,X2,X3) >= U61(X1,X2,X3) constraint: a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) constraint: a__U63(X1,X2,X3) >= U63(X1,X2,X3) constraint: a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U64(X1,X2,X3) >= U64(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U51(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) 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__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__U15(tt,V2) >= Marked_a__isNat(V2) constraint: Marked_a__U14(tt,V1,V2) >= Marked_a__isNat(V1) constraint: Marked_a__U14(tt,V1,V2) >= Marked_a__U15(a__isNat(V1),V2) 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) APPLY CRITERIA (Subterm criterion) ST: Marked_a__isNatKind -> 1 Marked_a__U31 -> 2 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; 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__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) >= isNat(X) ; 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) >= tt ; a__U32(X) >= U32(X) ; a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U41(tt) >= tt ; a__U41(X) >= U41(X) ; a__U52(tt,N) >= mark(N) ; a__U52(X1,X2) >= U52(X1,X2) ; a__U51(tt,N) >= a__U52(a__isNatKind(N),N) ; a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; 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(isNat(X)) >= a__isNat(X) ; 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)) >= a__U31(mark(X1),X2) ; mark(U32(X)) >= a__U32(mark(X)) ; mark(U41(X)) >= a__U41(mark(X)) ; mark(U51(X1,X2)) >= a__U51(mark(X1),X2) ; mark(U52(X1,X2)) >= a__U52(mark(X1),X2) ; mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) ; mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) ; mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) ; mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) ; a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) ; a__U62(X1,X2,X3) >= U62(X1,X2,X3) ; a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) ; a__U61(X1,X2,X3) >= U61(X1,X2,X3) ; a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) ; a__U63(X1,X2,X3) >= U63(X1,X2,X3) ; a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U64(X1,X2,X3) >= U64(X1,X2,X3) ; a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) ; a__plus(N,0) >= a__U51(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; Marked_a__plus(N,s(M)) >= Marked_a__U61(a__isNat(M),M,N) ; Marked_a__U64(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) ; Marked_a__U64(tt,M,N) >= Marked_mark(N) ; Marked_a__U64(tt,M,N) >= Marked_mark(M) ; Marked_a__U63(tt,M,N) >= Marked_a__U64(a__isNatKind(N),M,N) ; Marked_a__U62(tt,M,N) >= Marked_a__U63(a__isNat(N),M,N) ; Marked_a__U61(tt,M,N) >= Marked_a__U62(a__isNatKind(M),M,N) ; Marked_a__U52(tt,N) >= Marked_mark(N) ; Marked_a__U51(tt,N) >= Marked_a__U52(a__isNatKind(N),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(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)) >= Marked_mark(X1) ; Marked_mark(U32(X)) >= Marked_mark(X) ; Marked_mark(U41(X)) >= Marked_mark(X) ; Marked_mark(U51(X1,X2)) >= Marked_a__U51(mark(X1),X2) ; Marked_mark(U51(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) ; Marked_mark(U52(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U61(X1,X2,X3)) >= Marked_a__U61(mark(X1),X2,X3) ; Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U62(X1,X2,X3)) >= Marked_a__U62(mark(X1),X2,X3) ; Marked_mark(U62(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U63(X1,X2,X3)) >= Marked_a__U63(mark(X1),X2,X3) ; Marked_mark(U63(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U64(X1,X2,X3)) >= Marked_a__U64(mark(X1),X2,X3) ; Marked_mark(U64(X1,X2,X3)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__plus(N,s(M)) > Marked_a__U61(a__isNat(M),M,N) ; } { Marked_a__U64(tt,M,N) > Marked_a__plus(mark(N),mark(M)) ; } { Marked_a__U64(tt,M,N) > Marked_mark(N) ; } { Marked_a__U64(tt,M,N) > Marked_mark(M) ; } { Marked_a__U63(tt,M,N) > Marked_a__U64(a__isNatKind(N),M,N) ; } { Marked_a__U62(tt,M,N) > Marked_a__U63(a__isNat(N),M,N) ; } { Marked_a__U61(tt,M,N) > Marked_a__U62(a__isNatKind(M),M,N) ; } { Marked_a__U52(tt,N) > Marked_mark(N) ; } { Marked_a__U51(tt,N) > Marked_a__U52(a__isNatKind(N),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(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)) > Marked_mark(X1) ; } { Marked_mark(U32(X)) > Marked_mark(X) ; } { Marked_mark(U41(X)) > Marked_mark(X) ; } { Marked_mark(U51(X1,X2)) > Marked_a__U51(mark(X1),X2) ; } { Marked_mark(U51(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U52(X1,X2)) > Marked_a__U52(mark(X1),X2) ; } { Marked_mark(U52(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_a__U61(mark(X1),X2,X3) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U62(X1,X2,X3)) > Marked_a__U62(mark(X1),X2,X3) ; } { Marked_mark(U62(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U63(X1,X2,X3)) > Marked_a__U63(mark(X1),X2,X3) ; } { Marked_mark(U63(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U64(X1,X2,X3)) > Marked_a__U64(mark(X1),X2,X3) ; } { Marked_mark(U64(X1,X2,X3)) > 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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === 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__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) 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__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) >= isNat(X) 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) >= tt constraint: a__U32(X) >= U32(X) constraint: a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) constraint: a__U31(X1,X2) >= U31(X1,X2) constraint: a__U41(tt) >= tt constraint: a__U41(X) >= U41(X) constraint: a__U52(tt,N) >= mark(N) constraint: a__U52(X1,X2) >= U52(X1,X2) constraint: a__U51(tt,N) >= a__U52(a__isNatKind(N),N) constraint: a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) 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(isNat(X)) >= a__isNat(X) 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)) >= a__U31(mark(X1),X2) constraint: mark(U32(X)) >= a__U32(mark(X)) constraint: mark(U41(X)) >= a__U41(mark(X)) constraint: mark(U51(X1,X2)) >= a__U51(mark(X1),X2) constraint: mark(U52(X1,X2)) >= a__U52(mark(X1),X2) constraint: mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) constraint: mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) constraint: mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) constraint: mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) constraint: a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) constraint: a__U62(X1,X2,X3) >= U62(X1,X2,X3) constraint: a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) constraint: a__U61(X1,X2,X3) >= U61(X1,X2,X3) constraint: a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) constraint: a__U63(X1,X2,X3) >= U63(X1,X2,X3) constraint: a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U64(X1,X2,X3) >= U64(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U51(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: Marked_a__plus(N,s(M)) >= Marked_a__U61(a__isNat(M),M,N) constraint: Marked_a__U64(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) constraint: Marked_a__U64(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U64(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U63(tt,M,N) >= Marked_a__U64(a__isNatKind(N),M,N) constraint: Marked_a__U62(tt,M,N) >= Marked_a__U63(a__isNat(N),M,N) constraint: Marked_a__U61(tt,M,N) >= Marked_a__U62(a__isNatKind(M),M,N) constraint: Marked_a__U52(tt,N) >= Marked_mark(N) constraint: Marked_a__U51(tt,N) >= Marked_a__U52(a__isNatKind(N),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(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)) >= Marked_mark(X1) constraint: Marked_mark(U32(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X)) >= Marked_mark(X) constraint: Marked_mark(U51(X1,X2)) >= Marked_a__U51(mark(X1),X2) constraint: Marked_mark(U51(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) constraint: Marked_mark(U52(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_a__U61(mark(X1),X2,X3) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U62(X1,X2,X3)) >= Marked_a__U62(mark(X1),X2,X3) constraint: Marked_mark(U62(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U63(X1,X2,X3)) >= Marked_a__U63(mark(X1),X2,X3) constraint: Marked_mark(U63(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U64(X1,X2,X3)) >= Marked_a__U64(mark(X1),X2,X3) constraint: Marked_mark(U64(X1,X2,X3)) >= 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__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; 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__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) >= isNat(X) ; 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) >= tt ; a__U32(X) >= U32(X) ; a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U41(tt) >= tt ; a__U41(X) >= U41(X) ; a__U52(tt,N) >= mark(N) ; a__U52(X1,X2) >= U52(X1,X2) ; a__U51(tt,N) >= a__U52(a__isNatKind(N),N) ; a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; 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(isNat(X)) >= a__isNat(X) ; 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)) >= a__U31(mark(X1),X2) ; mark(U32(X)) >= a__U32(mark(X)) ; mark(U41(X)) >= a__U41(mark(X)) ; mark(U51(X1,X2)) >= a__U51(mark(X1),X2) ; mark(U52(X1,X2)) >= a__U52(mark(X1),X2) ; mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) ; mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) ; mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) ; mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) ; a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) ; a__U62(X1,X2,X3) >= U62(X1,X2,X3) ; a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) ; a__U61(X1,X2,X3) >= U61(X1,X2,X3) ; a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) ; a__U63(X1,X2,X3) >= U63(X1,X2,X3) ; a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U64(X1,X2,X3) >= U64(X1,X2,X3) ; a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) ; a__plus(N,0) >= a__U51(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; Marked_a__plus(N,s(M)) >= Marked_a__U61(a__isNat(M),M,N) ; Marked_a__U64(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) ; Marked_a__U64(tt,M,N) >= Marked_mark(N) ; Marked_a__U64(tt,M,N) >= Marked_mark(M) ; Marked_a__U63(tt,M,N) >= Marked_a__U64(a__isNatKind(N),M,N) ; Marked_a__U62(tt,M,N) >= Marked_a__U63(a__isNat(N),M,N) ; Marked_a__U61(tt,M,N) >= Marked_a__U62(a__isNatKind(M),M,N) ; Marked_a__U52(tt,N) >= Marked_mark(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(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)) >= Marked_mark(X1) ; Marked_mark(U32(X)) >= Marked_mark(X) ; Marked_mark(U41(X)) >= Marked_mark(X) ; Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) ; Marked_mark(U52(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U61(X1,X2,X3)) >= Marked_a__U61(mark(X1),X2,X3) ; Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U62(X1,X2,X3)) >= Marked_a__U62(mark(X1),X2,X3) ; Marked_mark(U62(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U63(X1,X2,X3)) >= Marked_a__U63(mark(X1),X2,X3) ; Marked_mark(U63(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U64(X1,X2,X3)) >= Marked_a__U64(mark(X1),X2,X3) ; Marked_mark(U64(X1,X2,X3)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__plus(N,s(M)) > Marked_a__U61(a__isNat(M),M,N) ; } { Marked_a__U64(tt,M,N) > Marked_a__plus(mark(N),mark(M)) ; } { Marked_a__U64(tt,M,N) > Marked_mark(N) ; } { Marked_a__U64(tt,M,N) > Marked_mark(M) ; } { Marked_a__U63(tt,M,N) > Marked_a__U64(a__isNatKind(N),M,N) ; } { Marked_a__U62(tt,M,N) > Marked_a__U63(a__isNat(N),M,N) ; } { Marked_a__U61(tt,M,N) > Marked_a__U62(a__isNatKind(M),M,N) ; } { Marked_a__U52(tt,N) > Marked_mark(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(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)) > Marked_mark(X1) ; } { Marked_mark(U32(X)) > Marked_mark(X) ; } { Marked_mark(U41(X)) > Marked_mark(X) ; } { Marked_mark(U52(X1,X2)) > Marked_a__U52(mark(X1),X2) ; } { Marked_mark(U52(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_a__U61(mark(X1),X2,X3) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U62(X1,X2,X3)) > Marked_a__U62(mark(X1),X2,X3) ; } { Marked_mark(U62(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U63(X1,X2,X3)) > Marked_a__U63(mark(X1),X2,X3) ; } { Marked_mark(U63(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U64(X1,X2,X3)) > Marked_a__U64(mark(X1),X2,X3) ; } { Marked_mark(U64(X1,X2,X3)) > 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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === 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__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) 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__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) >= isNat(X) 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) >= tt constraint: a__U32(X) >= U32(X) constraint: a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) constraint: a__U31(X1,X2) >= U31(X1,X2) constraint: a__U41(tt) >= tt constraint: a__U41(X) >= U41(X) constraint: a__U52(tt,N) >= mark(N) constraint: a__U52(X1,X2) >= U52(X1,X2) constraint: a__U51(tt,N) >= a__U52(a__isNatKind(N),N) constraint: a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) 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(isNat(X)) >= a__isNat(X) 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)) >= a__U31(mark(X1),X2) constraint: mark(U32(X)) >= a__U32(mark(X)) constraint: mark(U41(X)) >= a__U41(mark(X)) constraint: mark(U51(X1,X2)) >= a__U51(mark(X1),X2) constraint: mark(U52(X1,X2)) >= a__U52(mark(X1),X2) constraint: mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) constraint: mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) constraint: mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) constraint: mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) constraint: a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) constraint: a__U62(X1,X2,X3) >= U62(X1,X2,X3) constraint: a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) constraint: a__U61(X1,X2,X3) >= U61(X1,X2,X3) constraint: a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) constraint: a__U63(X1,X2,X3) >= U63(X1,X2,X3) constraint: a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U64(X1,X2,X3) >= U64(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U51(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: Marked_a__plus(N,s(M)) >= Marked_a__U61(a__isNat(M),M,N) constraint: Marked_a__U64(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) constraint: Marked_a__U64(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U64(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U63(tt,M,N) >= Marked_a__U64(a__isNatKind(N),M,N) constraint: Marked_a__U62(tt,M,N) >= Marked_a__U63(a__isNat(N),M,N) constraint: Marked_a__U61(tt,M,N) >= Marked_a__U62(a__isNatKind(M),M,N) constraint: Marked_a__U52(tt,N) >= Marked_mark(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(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)) >= Marked_mark(X1) constraint: Marked_mark(U32(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X)) >= Marked_mark(X) constraint: Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) constraint: Marked_mark(U52(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_a__U61(mark(X1),X2,X3) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U62(X1,X2,X3)) >= Marked_a__U62(mark(X1),X2,X3) constraint: Marked_mark(U62(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U63(X1,X2,X3)) >= Marked_a__U63(mark(X1),X2,X3) constraint: Marked_mark(U63(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U64(X1,X2,X3)) >= Marked_a__U64(mark(X1),X2,X3) constraint: Marked_mark(U64(X1,X2,X3)) >= 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__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; 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__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) >= isNat(X) ; 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) >= tt ; a__U32(X) >= U32(X) ; a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U41(tt) >= tt ; a__U41(X) >= U41(X) ; a__U52(tt,N) >= mark(N) ; a__U52(X1,X2) >= U52(X1,X2) ; a__U51(tt,N) >= a__U52(a__isNatKind(N),N) ; a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; 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(isNat(X)) >= a__isNat(X) ; 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)) >= a__U31(mark(X1),X2) ; mark(U32(X)) >= a__U32(mark(X)) ; mark(U41(X)) >= a__U41(mark(X)) ; mark(U51(X1,X2)) >= a__U51(mark(X1),X2) ; mark(U52(X1,X2)) >= a__U52(mark(X1),X2) ; mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) ; mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) ; mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) ; mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) ; a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) ; a__U62(X1,X2,X3) >= U62(X1,X2,X3) ; a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) ; a__U61(X1,X2,X3) >= U61(X1,X2,X3) ; a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) ; a__U63(X1,X2,X3) >= U63(X1,X2,X3) ; a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U64(X1,X2,X3) >= U64(X1,X2,X3) ; a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) ; a__plus(N,0) >= a__U51(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; Marked_a__U64(tt,M,N) >= Marked_mark(N) ; Marked_a__U64(tt,M,N) >= Marked_mark(M) ; Marked_a__U63(tt,M,N) >= Marked_a__U64(a__isNatKind(N),M,N) ; Marked_a__U62(tt,M,N) >= Marked_a__U63(a__isNat(N),M,N) ; Marked_a__U61(tt,M,N) >= Marked_a__U62(a__isNatKind(M),M,N) ; Marked_a__U52(tt,N) >= Marked_mark(N) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; 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)) >= Marked_mark(X1) ; Marked_mark(U32(X)) >= Marked_mark(X) ; Marked_mark(U41(X)) >= Marked_mark(X) ; Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) ; Marked_mark(U52(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U61(X1,X2,X3)) >= Marked_a__U61(mark(X1),X2,X3) ; Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U62(X1,X2,X3)) >= Marked_a__U62(mark(X1),X2,X3) ; Marked_mark(U62(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U63(X1,X2,X3)) >= Marked_a__U63(mark(X1),X2,X3) ; Marked_mark(U63(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U64(X1,X2,X3)) >= Marked_a__U64(mark(X1),X2,X3) ; Marked_mark(U64(X1,X2,X3)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__U64(tt,M,N) > Marked_mark(N) ; } { Marked_a__U64(tt,M,N) > Marked_mark(M) ; } { Marked_a__U63(tt,M,N) > Marked_a__U64(a__isNatKind(N),M,N) ; } { Marked_a__U62(tt,M,N) > Marked_a__U63(a__isNat(N),M,N) ; } { Marked_a__U61(tt,M,N) > Marked_a__U62(a__isNatKind(M),M,N) ; } { Marked_a__U52(tt,N) > Marked_mark(N) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { 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)) > Marked_mark(X1) ; } { Marked_mark(U32(X)) > Marked_mark(X) ; } { Marked_mark(U41(X)) > Marked_mark(X) ; } { Marked_mark(U52(X1,X2)) > Marked_a__U52(mark(X1),X2) ; } { Marked_mark(U52(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_a__U61(mark(X1),X2,X3) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U62(X1,X2,X3)) > Marked_a__U62(mark(X1),X2,X3) ; } { Marked_mark(U62(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U63(X1,X2,X3)) > Marked_a__U63(mark(X1),X2,X3) ; } { Marked_mark(U63(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U64(X1,X2,X3)) > Marked_a__U64(mark(X1),X2,X3) ; } { Marked_mark(U64(X1,X2,X3)) > 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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === 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__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) 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__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) >= isNat(X) 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) >= tt constraint: a__U32(X) >= U32(X) constraint: a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) constraint: a__U31(X1,X2) >= U31(X1,X2) constraint: a__U41(tt) >= tt constraint: a__U41(X) >= U41(X) constraint: a__U52(tt,N) >= mark(N) constraint: a__U52(X1,X2) >= U52(X1,X2) constraint: a__U51(tt,N) >= a__U52(a__isNatKind(N),N) constraint: a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) 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(isNat(X)) >= a__isNat(X) 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)) >= a__U31(mark(X1),X2) constraint: mark(U32(X)) >= a__U32(mark(X)) constraint: mark(U41(X)) >= a__U41(mark(X)) constraint: mark(U51(X1,X2)) >= a__U51(mark(X1),X2) constraint: mark(U52(X1,X2)) >= a__U52(mark(X1),X2) constraint: mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) constraint: mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) constraint: mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) constraint: mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) constraint: a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) constraint: a__U62(X1,X2,X3) >= U62(X1,X2,X3) constraint: a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) constraint: a__U61(X1,X2,X3) >= U61(X1,X2,X3) constraint: a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) constraint: a__U63(X1,X2,X3) >= U63(X1,X2,X3) constraint: a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U64(X1,X2,X3) >= U64(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U51(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: Marked_a__U64(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U64(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U63(tt,M,N) >= Marked_a__U64(a__isNatKind(N),M,N) constraint: Marked_a__U62(tt,M,N) >= Marked_a__U63(a__isNat(N),M,N) constraint: Marked_a__U61(tt,M,N) >= Marked_a__U62(a__isNatKind(M),M,N) constraint: Marked_a__U52(tt,N) >= Marked_mark(N) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) 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)) >= Marked_mark(X1) constraint: Marked_mark(U32(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X)) >= Marked_mark(X) constraint: Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) constraint: Marked_mark(U52(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_a__U61(mark(X1),X2,X3) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U62(X1,X2,X3)) >= Marked_a__U62(mark(X1),X2,X3) constraint: Marked_mark(U62(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U63(X1,X2,X3)) >= Marked_a__U63(mark(X1),X2,X3) constraint: Marked_mark(U63(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U64(X1,X2,X3)) >= Marked_a__U64(mark(X1),X2,X3) constraint: Marked_mark(U64(X1,X2,X3)) >= 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__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; 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__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) >= isNat(X) ; 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) >= tt ; a__U32(X) >= U32(X) ; a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U41(tt) >= tt ; a__U41(X) >= U41(X) ; a__U52(tt,N) >= mark(N) ; a__U52(X1,X2) >= U52(X1,X2) ; a__U51(tt,N) >= a__U52(a__isNatKind(N),N) ; a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; 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(isNat(X)) >= a__isNat(X) ; 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)) >= a__U31(mark(X1),X2) ; mark(U32(X)) >= a__U32(mark(X)) ; mark(U41(X)) >= a__U41(mark(X)) ; mark(U51(X1,X2)) >= a__U51(mark(X1),X2) ; mark(U52(X1,X2)) >= a__U52(mark(X1),X2) ; mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) ; mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) ; mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) ; mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) ; a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) ; a__U62(X1,X2,X3) >= U62(X1,X2,X3) ; a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) ; a__U61(X1,X2,X3) >= U61(X1,X2,X3) ; a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) ; a__U63(X1,X2,X3) >= U63(X1,X2,X3) ; a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U64(X1,X2,X3) >= U64(X1,X2,X3) ; a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) ; a__plus(N,0) >= a__U51(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; Marked_a__U64(tt,M,N) >= Marked_mark(N) ; Marked_a__U64(tt,M,N) >= Marked_mark(M) ; Marked_a__U63(tt,M,N) >= Marked_a__U64(a__isNatKind(N),M,N) ; Marked_a__U62(tt,M,N) >= Marked_a__U63(a__isNat(N),M,N) ; Marked_a__U52(tt,N) >= Marked_mark(N) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; 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)) >= Marked_mark(X1) ; Marked_mark(U32(X)) >= Marked_mark(X) ; Marked_mark(U41(X)) >= Marked_mark(X) ; Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) ; Marked_mark(U52(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U62(X1,X2,X3)) >= Marked_a__U62(mark(X1),X2,X3) ; Marked_mark(U62(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U63(X1,X2,X3)) >= Marked_a__U63(mark(X1),X2,X3) ; Marked_mark(U63(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U64(X1,X2,X3)) >= Marked_a__U64(mark(X1),X2,X3) ; Marked_mark(U64(X1,X2,X3)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__U64(tt,M,N) > Marked_mark(N) ; } { Marked_a__U64(tt,M,N) > Marked_mark(M) ; } { Marked_a__U63(tt,M,N) > Marked_a__U64(a__isNatKind(N),M,N) ; } { Marked_a__U62(tt,M,N) > Marked_a__U63(a__isNat(N),M,N) ; } { Marked_a__U52(tt,N) > Marked_mark(N) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { 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)) > Marked_mark(X1) ; } { Marked_mark(U32(X)) > Marked_mark(X) ; } { Marked_mark(U41(X)) > Marked_mark(X) ; } { Marked_mark(U52(X1,X2)) > Marked_a__U52(mark(X1),X2) ; } { Marked_mark(U52(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U62(X1,X2,X3)) > Marked_a__U62(mark(X1),X2,X3) ; } { Marked_mark(U62(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U63(X1,X2,X3)) > Marked_a__U63(mark(X1),X2,X3) ; } { Marked_mark(U63(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U64(X1,X2,X3)) > Marked_a__U64(mark(X1),X2,X3) ; } { Marked_mark(U64(X1,X2,X3)) > 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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === 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__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) 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__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) >= isNat(X) 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) >= tt constraint: a__U32(X) >= U32(X) constraint: a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) constraint: a__U31(X1,X2) >= U31(X1,X2) constraint: a__U41(tt) >= tt constraint: a__U41(X) >= U41(X) constraint: a__U52(tt,N) >= mark(N) constraint: a__U52(X1,X2) >= U52(X1,X2) constraint: a__U51(tt,N) >= a__U52(a__isNatKind(N),N) constraint: a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) 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(isNat(X)) >= a__isNat(X) 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)) >= a__U31(mark(X1),X2) constraint: mark(U32(X)) >= a__U32(mark(X)) constraint: mark(U41(X)) >= a__U41(mark(X)) constraint: mark(U51(X1,X2)) >= a__U51(mark(X1),X2) constraint: mark(U52(X1,X2)) >= a__U52(mark(X1),X2) constraint: mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) constraint: mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) constraint: mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) constraint: mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) constraint: a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) constraint: a__U62(X1,X2,X3) >= U62(X1,X2,X3) constraint: a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) constraint: a__U61(X1,X2,X3) >= U61(X1,X2,X3) constraint: a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) constraint: a__U63(X1,X2,X3) >= U63(X1,X2,X3) constraint: a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U64(X1,X2,X3) >= U64(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U51(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: Marked_a__U64(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U64(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U63(tt,M,N) >= Marked_a__U64(a__isNatKind(N),M,N) constraint: Marked_a__U62(tt,M,N) >= Marked_a__U63(a__isNat(N),M,N) constraint: Marked_a__U52(tt,N) >= Marked_mark(N) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) 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)) >= Marked_mark(X1) constraint: Marked_mark(U32(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X)) >= Marked_mark(X) constraint: Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) constraint: Marked_mark(U52(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U62(X1,X2,X3)) >= Marked_a__U62(mark(X1),X2,X3) constraint: Marked_mark(U62(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U63(X1,X2,X3)) >= Marked_a__U63(mark(X1),X2,X3) constraint: Marked_mark(U63(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U64(X1,X2,X3)) >= Marked_a__U64(mark(X1),X2,X3) constraint: Marked_mark(U64(X1,X2,X3)) >= 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__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; 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__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) >= isNat(X) ; 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) >= tt ; a__U32(X) >= U32(X) ; a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U41(tt) >= tt ; a__U41(X) >= U41(X) ; a__U52(tt,N) >= mark(N) ; a__U52(X1,X2) >= U52(X1,X2) ; a__U51(tt,N) >= a__U52(a__isNatKind(N),N) ; a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; 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(isNat(X)) >= a__isNat(X) ; 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)) >= a__U31(mark(X1),X2) ; mark(U32(X)) >= a__U32(mark(X)) ; mark(U41(X)) >= a__U41(mark(X)) ; mark(U51(X1,X2)) >= a__U51(mark(X1),X2) ; mark(U52(X1,X2)) >= a__U52(mark(X1),X2) ; mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) ; mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) ; mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) ; mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) ; a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) ; a__U62(X1,X2,X3) >= U62(X1,X2,X3) ; a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) ; a__U61(X1,X2,X3) >= U61(X1,X2,X3) ; a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) ; a__U63(X1,X2,X3) >= U63(X1,X2,X3) ; a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U64(X1,X2,X3) >= U64(X1,X2,X3) ; a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) ; a__plus(N,0) >= a__U51(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; Marked_a__U64(tt,M,N) >= Marked_mark(N) ; Marked_a__U64(tt,M,N) >= Marked_mark(M) ; Marked_a__U63(tt,M,N) >= Marked_a__U64(a__isNatKind(N),M,N) ; Marked_a__U52(tt,N) >= Marked_mark(N) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; 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)) >= Marked_mark(X1) ; Marked_mark(U32(X)) >= Marked_mark(X) ; Marked_mark(U41(X)) >= Marked_mark(X) ; Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) ; Marked_mark(U52(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U62(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U63(X1,X2,X3)) >= Marked_a__U63(mark(X1),X2,X3) ; Marked_mark(U63(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U64(X1,X2,X3)) >= Marked_a__U64(mark(X1),X2,X3) ; Marked_mark(U64(X1,X2,X3)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__U64(tt,M,N) > Marked_mark(N) ; } { Marked_a__U64(tt,M,N) > Marked_mark(M) ; } { Marked_a__U63(tt,M,N) > Marked_a__U64(a__isNatKind(N),M,N) ; } { Marked_a__U52(tt,N) > Marked_mark(N) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { 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)) > Marked_mark(X1) ; } { Marked_mark(U32(X)) > Marked_mark(X) ; } { Marked_mark(U41(X)) > Marked_mark(X) ; } { Marked_mark(U52(X1,X2)) > Marked_a__U52(mark(X1),X2) ; } { Marked_mark(U52(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U61(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U62(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U63(X1,X2,X3)) > Marked_a__U63(mark(X1),X2,X3) ; } { Marked_mark(U63(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U64(X1,X2,X3)) > Marked_a__U64(mark(X1),X2,X3) ; } { Marked_mark(U64(X1,X2,X3)) > 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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === 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__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) 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__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) >= isNat(X) 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) >= tt constraint: a__U32(X) >= U32(X) constraint: a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) constraint: a__U31(X1,X2) >= U31(X1,X2) constraint: a__U41(tt) >= tt constraint: a__U41(X) >= U41(X) constraint: a__U52(tt,N) >= mark(N) constraint: a__U52(X1,X2) >= U52(X1,X2) constraint: a__U51(tt,N) >= a__U52(a__isNatKind(N),N) constraint: a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) 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(isNat(X)) >= a__isNat(X) 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)) >= a__U31(mark(X1),X2) constraint: mark(U32(X)) >= a__U32(mark(X)) constraint: mark(U41(X)) >= a__U41(mark(X)) constraint: mark(U51(X1,X2)) >= a__U51(mark(X1),X2) constraint: mark(U52(X1,X2)) >= a__U52(mark(X1),X2) constraint: mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) constraint: mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) constraint: mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) constraint: mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) constraint: a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) constraint: a__U62(X1,X2,X3) >= U62(X1,X2,X3) constraint: a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) constraint: a__U61(X1,X2,X3) >= U61(X1,X2,X3) constraint: a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) constraint: a__U63(X1,X2,X3) >= U63(X1,X2,X3) constraint: a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U64(X1,X2,X3) >= U64(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U51(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: Marked_a__U64(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U64(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U63(tt,M,N) >= Marked_a__U64(a__isNatKind(N),M,N) constraint: Marked_a__U52(tt,N) >= Marked_mark(N) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) 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)) >= Marked_mark(X1) constraint: Marked_mark(U32(X)) >= Marked_mark(X) constraint: Marked_mark(U41(X)) >= Marked_mark(X) constraint: Marked_mark(U52(X1,X2)) >= Marked_a__U52(mark(X1),X2) constraint: Marked_mark(U52(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U61(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U62(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U63(X1,X2,X3)) >= Marked_a__U63(mark(X1),X2,X3) constraint: Marked_mark(U63(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U64(X1,X2,X3)) >= Marked_a__U64(mark(X1),X2,X3) constraint: Marked_mark(U64(X1,X2,X3)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_mark -> 1 Marked_a__U52 -> 2 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__U12(tt,V1,V2) >= a__U13(a__isNatKind(V2),V1,V2) ; a__U12(X1,X2,X3) >= U12(X1,X2,X3) ; a__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) ; a__isNatKind(0) >= tt ; a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) ; a__isNatKind(X) >= isNatKind(X) ; 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__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) >= isNat(X) ; 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) >= tt ; a__U32(X) >= U32(X) ; a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) ; a__U31(X1,X2) >= U31(X1,X2) ; a__U41(tt) >= tt ; a__U41(X) >= U41(X) ; a__U52(tt,N) >= mark(N) ; a__U52(X1,X2) >= U52(X1,X2) ; a__U51(tt,N) >= a__U52(a__isNatKind(N),N) ; a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) ; mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) ; mark(isNatKind(X)) >= a__isNatKind(X) ; 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(isNat(X)) >= a__isNat(X) ; 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)) >= a__U31(mark(X1),X2) ; mark(U32(X)) >= a__U32(mark(X)) ; mark(U41(X)) >= a__U41(mark(X)) ; mark(U51(X1,X2)) >= a__U51(mark(X1),X2) ; mark(U52(X1,X2)) >= a__U52(mark(X1),X2) ; mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) ; mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) ; mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) ; mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) ; a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) ; a__U62(X1,X2,X3) >= U62(X1,X2,X3) ; a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) ; a__U61(X1,X2,X3) >= U61(X1,X2,X3) ; a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) ; a__U63(X1,X2,X3) >= U63(X1,X2,X3) ; a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U64(X1,X2,X3) >= U64(X1,X2,X3) ; a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) ; a__plus(N,0) >= a__U51(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__U11(a__isNatKind(V1),V1,V2) ; Marked_a__U15(tt,V2) >= Marked_a__isNat(V2) ; Marked_a__U14(tt,V1,V2) >= Marked_a__isNat(V1) ; Marked_a__U14(tt,V1,V2) >= Marked_a__U15(a__isNat(V1),V2) ; 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) ; } + Disjunctions:{ { Marked_a__isNat(plus(V1,V2)) > Marked_a__U11(a__isNatKind(V1),V1,V2) ; } { Marked_a__U15(tt,V2) > Marked_a__isNat(V2) ; } { Marked_a__U14(tt,V1,V2) > Marked_a__isNat(V1) ; } { Marked_a__U14(tt,V1,V2) > Marked_a__U15(a__isNat(V1),V2) ; } { 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) ; } } === 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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === 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__isNatKind(s(V1)) >= a__U41(a__isNatKind(V1)) constraint: a__isNatKind(0) >= tt constraint: a__isNatKind(plus(V1,V2)) >= a__U31(a__isNatKind(V1),V2) constraint: a__isNatKind(X) >= isNatKind(X) 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__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) >= isNat(X) 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) >= tt constraint: a__U32(X) >= U32(X) constraint: a__U31(tt,V2) >= a__U32(a__isNatKind(V2)) constraint: a__U31(X1,X2) >= U31(X1,X2) constraint: a__U41(tt) >= tt constraint: a__U41(X) >= U41(X) constraint: a__U52(tt,N) >= mark(N) constraint: a__U52(X1,X2) >= U52(X1,X2) constraint: a__U51(tt,N) >= a__U52(a__isNatKind(N),N) constraint: a__U51(X1,X2) >= U51(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(U11(X1,X2,X3)) >= a__U11(mark(X1),X2,X3) constraint: mark(U12(X1,X2,X3)) >= a__U12(mark(X1),X2,X3) constraint: mark(isNatKind(X)) >= a__isNatKind(X) 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(isNat(X)) >= a__isNat(X) 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)) >= a__U31(mark(X1),X2) constraint: mark(U32(X)) >= a__U32(mark(X)) constraint: mark(U41(X)) >= a__U41(mark(X)) constraint: mark(U51(X1,X2)) >= a__U51(mark(X1),X2) constraint: mark(U52(X1,X2)) >= a__U52(mark(X1),X2) constraint: mark(U61(X1,X2,X3)) >= a__U61(mark(X1),X2,X3) constraint: mark(U62(X1,X2,X3)) >= a__U62(mark(X1),X2,X3) constraint: mark(U63(X1,X2,X3)) >= a__U63(mark(X1),X2,X3) constraint: mark(U64(X1,X2,X3)) >= a__U64(mark(X1),X2,X3) constraint: a__U62(tt,M,N) >= a__U63(a__isNat(N),M,N) constraint: a__U62(X1,X2,X3) >= U62(X1,X2,X3) constraint: a__U61(tt,M,N) >= a__U62(a__isNatKind(M),M,N) constraint: a__U61(X1,X2,X3) >= U61(X1,X2,X3) constraint: a__U63(tt,M,N) >= a__U64(a__isNatKind(N),M,N) constraint: a__U63(X1,X2,X3) >= U63(X1,X2,X3) constraint: a__U64(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U64(X1,X2,X3) >= U64(X1,X2,X3) constraint: a__plus(N,s(M)) >= a__U61(a__isNat(M),M,N) constraint: a__plus(N,0) >= a__U51(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__U11(a__isNatKind(V1), V1,V2) constraint: Marked_a__U15(tt,V2) >= Marked_a__isNat(V2) constraint: Marked_a__U14(tt,V1,V2) >= Marked_a__isNat(V1) constraint: Marked_a__U14(tt,V1,V2) >= Marked_a__U15(a__isNat(V1),V2) 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) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] a__U11(tt,V1,V2) -> a__U12(a__isNatKind(V1),V1,V2) [2] a__U12(tt,V1,V2) -> a__U13(a__isNatKind(V2),V1,V2) [3] a__U13(tt,V1,V2) -> a__U14(a__isNatKind(V2),V1,V2) [4] a__U14(tt,V1,V2) -> a__U15(a__isNat(V1),V2) [5] a__U15(tt,V2) -> a__U16(a__isNat(V2)) [6] a__U16(tt) -> tt [7] a__U21(tt,V1) -> a__U22(a__isNatKind(V1),V1) [8] a__U22(tt,V1) -> a__U23(a__isNat(V1)) [9] a__U23(tt) -> tt [10] a__U31(tt,V2) -> a__U32(a__isNatKind(V2)) [11] a__U32(tt) -> tt [12] a__U41(tt) -> tt [13] a__U51(tt,N) -> a__U52(a__isNatKind(N),N) [14] a__U52(tt,N) -> mark(N) [15] a__U61(tt,M,N) -> a__U62(a__isNatKind(M),M,N) [16] a__U62(tt,M,N) -> a__U63(a__isNat(N),M,N) [17] a__U63(tt,M,N) -> a__U64(a__isNatKind(N),M,N) [18] a__U64(tt,M,N) -> s(a__plus(mark(N),mark(M))) [19] a__isNat(0) -> tt [20] a__isNat(plus(V1,V2)) -> a__U11(a__isNatKind(V1),V1,V2) [21] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) [22] a__isNatKind(0) -> tt [23] a__isNatKind(plus(V1,V2)) -> a__U31(a__isNatKind(V1),V2) [24] a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1)) [25] a__plus(N,0) -> a__U51(a__isNat(N),N) [26] a__plus(N,s(M)) -> a__U61(a__isNat(M),M,N) [27] mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) [28] mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3) [29] mark(isNatKind(X)) -> a__isNatKind(X) [30] mark(U13(X1,X2,X3)) -> a__U13(mark(X1),X2,X3) [31] mark(U14(X1,X2,X3)) -> a__U14(mark(X1),X2,X3) [32] mark(U15(X1,X2)) -> a__U15(mark(X1),X2) [33] mark(isNat(X)) -> a__isNat(X) [34] mark(U16(X)) -> a__U16(mark(X)) [35] mark(U21(X1,X2)) -> a__U21(mark(X1),X2) [36] mark(U22(X1,X2)) -> a__U22(mark(X1),X2) [37] mark(U23(X)) -> a__U23(mark(X)) [38] mark(U31(X1,X2)) -> a__U31(mark(X1),X2) [39] mark(U32(X)) -> a__U32(mark(X)) [40] mark(U41(X)) -> a__U41(mark(X)) [41] mark(U51(X1,X2)) -> a__U51(mark(X1),X2) [42] mark(U52(X1,X2)) -> a__U52(mark(X1),X2) [43] mark(U61(X1,X2,X3)) -> a__U61(mark(X1),X2,X3) [44] mark(U62(X1,X2,X3)) -> a__U62(mark(X1),X2,X3) [45] mark(U63(X1,X2,X3)) -> a__U63(mark(X1),X2,X3) [46] mark(U64(X1,X2,X3)) -> a__U64(mark(X1),X2,X3) [47] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) [48] mark(tt) -> tt [49] mark(s(X)) -> s(mark(X)) [50] mark(0) -> 0 [51] a__U11(X1,X2,X3) -> U11(X1,X2,X3) [52] a__U12(X1,X2,X3) -> U12(X1,X2,X3) [53] a__isNatKind(X) -> isNatKind(X) [54] a__U13(X1,X2,X3) -> U13(X1,X2,X3) [55] a__U14(X1,X2,X3) -> U14(X1,X2,X3) [56] a__U15(X1,X2) -> U15(X1,X2) [57] a__isNat(X) -> isNat(X) [58] a__U16(X) -> U16(X) [59] a__U21(X1,X2) -> U21(X1,X2) [60] a__U22(X1,X2) -> U22(X1,X2) [61] a__U23(X) -> U23(X) [62] a__U31(X1,X2) -> U31(X1,X2) [63] a__U32(X) -> U32(X) [64] a__U41(X) -> U41(X) [65] a__U51(X1,X2) -> U51(X1,X2) [66] a__U52(X1,X2) -> U52(X1,X2) [67] a__U61(X1,X2,X3) -> U61(X1,X2,X3) [68] a__U62(X1,X2,X3) -> U62(X1,X2,X3) [69] a__U63(X1,X2,X3) -> U63(X1,X2,X3) [70] a__U64(X1,X2,X3) -> U64(X1,X2,X3) [71] a__plus(X1,X2) -> plus(X1,X2) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ a__U12 ] (X0,X1,X2) = 1*X0; [ isNat ] (X0) = 0; [ a__U51 ] (X0,X1) = 1*X1 + 1*X0; [ Marked_a__U63 ] (X0,X1,X2) = 2*X2 + 2*X1; [ a__U16 ] (X0) = 2*X0; [ U51 ] (X0,X1) = 1*X1 + 1*X0; [ 0 ] () = 1; [ a__U13 ] (X0,X1,X2) = 2*X0; [ U23 ] (X0) = 2*X0; [ a__U63 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0; [ Marked_a__U51 ] (X0,X1) = 2*X1; [ a__U32 ] (X0) = 2*X0; [ U63 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0; [ isNatKind ] (X0) = 0; [ a__U11 ] (X0,X1,X2) = 2*X0; [ U21 ] (X0,X1) = 2*X0; [ a__U62 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1*X0; [ Marked_a__U61 ] (X0,X1,X2) = 2*X2 + 2*X1; [ a__U21 ] (X0,X1) = 2*X0; [ U61 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0; [ U11 ] (X0,X1,X2) = 2*X0; [ a__U15 ] (X0,X1) = 1*X0; [ U32 ] (X0) = 2*X0; [ s ] (X0) = 1*X0; [ a__U41 ] (X0) = 2*X0; [ Marked_a__plus ] (X0,X1) = 2*X1 + 2*X0; [ U14 ] (X0,X1,X2) = 1*X0; [ a__isNatKind ] (X0) = 0; [ U16 ] (X0) = 2*X0; [ mark ] (X0) = 1*X0; [ Marked_a__U62 ] (X0,X1,X2) = 2*X2 + 2*X1; [ a__U22 ] (X0,X1) = 1*X0; [ U52 ] (X0,X1) = 1*X1 + 1*X0; [ plus ] (X0,X1) = 1*X1 + 1*X0; [ a__U14 ] (X0,X1,X2) = 1*X0; [ U31 ] (X0,X1) = 1*X0; [ a__U64 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0; [ a__U31 ] (X0,X1) = 1*X0; [ U64 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0; [ U13 ] (X0,X1,X2) = 2*X0; [ tt ] () = 0; [ Marked_mark ] (X0) = 2*X0; [ U22 ] (X0,X1) = 1*X0; [ a__U61 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0; [ Marked_a__U52 ] (X0,X1) = 2*X1; [ a__U23 ] (X0) = 2*X0; [ U62 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1*X0; [ U12 ] (X0,X1,X2) = 1*X0; [ a__isNat ] (X0) = 0; [ U41 ] (X0) = 2*X0; [ a__plus ] (X0,X1) = 1*X1 + 1*X0; [ a__U52 ] (X0,X1) = 1*X1 + 1*X0; [ Marked_a__U64 ] (X0,X1,X2) = 2*X2 + 2*X1; [ U15 ] (X0,X1) = 1*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ a__U12 ] (X0,X1,X2) = 1*X0; [ isNat ] (X0) = 0; [ a__U51 ] (X0,X1) = 1*X1 + 2*X0 + 1; [ Marked_a__U63 ] (X0,X1,X2) = 2*X2 + 2*X1; [ a__U16 ] (X0) = 1*X0; [ U51 ] (X0,X1) = 1*X1 + 2*X0 + 1; [ 0 ] () = 1; [ a__U13 ] (X0,X1,X2) = 2*X0; [ U23 ] (X0) = 2*X0; [ a__U63 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1*X0; [ Marked_a__U51 ] (X0,X1) = 2*X1 + 2*X0; [ a__U32 ] (X0) = 1*X0; [ U63 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1*X0; [ isNatKind ] (X0) = 0; [ a__U11 ] (X0,X1,X2) = 2*X0; [ U21 ] (X0,X1) = 2*X0; [ a__U62 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0; [ Marked_a__U61 ] (X0,X1,X2) = 2*X2 + 2*X1; [ a__U21 ] (X0,X1) = 2*X0; [ U61 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0; [ U11 ] (X0,X1,X2) = 2*X0; [ a__U15 ] (X0,X1) = 1*X0; [ U32 ] (X0) = 1*X0; [ s ] (X0) = 1*X0; [ a__U41 ] (X0) = 1*X0; [ Marked_a__plus ] (X0,X1) = 2*X1 + 2*X0; [ U14 ] (X0,X1,X2) = 2*X0; [ a__isNatKind ] (X0) = 0; [ U16 ] (X0) = 1*X0; [ mark ] (X0) = 1*X0; [ Marked_a__U62 ] (X0,X1,X2) = 2*X2 + 2*X1; [ a__U22 ] (X0,X1) = 2*X0; [ U52 ] (X0,X1) = 1*X1 + 2*X0; [ plus ] (X0,X1) = 1*X1 + 1*X0; [ a__U14 ] (X0,X1,X2) = 2*X0; [ U31 ] (X0,X1) = 1*X0; [ a__U64 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1*X0; [ a__U31 ] (X0,X1) = 1*X0; [ U64 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1*X0; [ U13 ] (X0,X1,X2) = 2*X0; [ tt ] () = 0; [ Marked_mark ] (X0) = 2*X0; [ U22 ] (X0,X1) = 2*X0; [ a__U61 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0; [ Marked_a__U52 ] (X0,X1) = 2*X1; [ a__U23 ] (X0) = 2*X0; [ U62 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0; [ U12 ] (X0,X1,X2) = 1*X0; [ a__isNat ] (X0) = 0; [ U41 ] (X0) = 1*X0; [ a__plus ] (X0,X1) = 1*X1 + 1*X0; [ a__U52 ] (X0,X1) = 1*X1 + 2*X0; [ Marked_a__U64 ] (X0,X1,X2) = 2*X2 + 2*X1; [ U15 ] (X0,X1) = 1*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ a__U12 ] (X0,X1,X2) = 1*X0; [ isNat ] (X0) = 2; [ a__U51 ] (X0,X1) = 2*X1 + 1*X0 + 2; [ Marked_a__U63 ] (X0,X1,X2) = 1*X2 + 1*X1; [ a__U16 ] (X0) = 1*X0; [ U51 ] (X0,X1) = 2*X1 + 1*X0 + 2; [ 0 ] () = 2; [ a__U13 ] (X0,X1,X2) = 1*X0; [ U23 ] (X0) = 1*X0; [ a__U63 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; [ a__U32 ] (X0) = 1*X0; [ U63 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; [ isNatKind ] (X0) = 2; [ a__U11 ] (X0,X1,X2) = 1*X0; [ U21 ] (X0,X1) = 1*X0; [ a__U62 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; [ Marked_a__U61 ] (X0,X1,X2) = 1*X2 + 1*X1; [ a__U21 ] (X0,X1) = 1*X0; [ U61 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; [ U11 ] (X0,X1,X2) = 1*X0; [ a__U15 ] (X0,X1) = 1*X0; [ U32 ] (X0) = 1*X0; [ s ] (X0) = 1*X0 + 1; [ a__U41 ] (X0) = 1*X0; [ Marked_a__plus ] (X0,X1) = 1*X1 + 1*X0; [ U14 ] (X0,X1,X2) = 1*X0; [ a__isNatKind ] (X0) = 2; [ U16 ] (X0) = 1*X0; [ mark ] (X0) = 1*X0; [ Marked_a__U62 ] (X0,X1,X2) = 1*X2 + 1*X1; [ a__U22 ] (X0,X1) = 1*X0; [ U52 ] (X0,X1) = 2*X1 + 2*X0; [ plus ] (X0,X1) = 2*X1 + 2*X0; [ a__U14 ] (X0,X1,X2) = 1*X0; [ U31 ] (X0,X1) = 1*X0; [ a__U64 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; [ a__U31 ] (X0,X1) = 1*X0; [ U64 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; [ U13 ] (X0,X1,X2) = 1*X0; [ tt ] () = 2; [ Marked_mark ] (X0) = 1*X0; [ U22 ] (X0,X1) = 1*X0; [ a__U61 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; [ Marked_a__U52 ] (X0,X1) = 1*X1; [ a__U23 ] (X0) = 1*X0; [ U62 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; [ U12 ] (X0,X1,X2) = 1*X0; [ a__isNat ] (X0) = 2; [ U41 ] (X0) = 1*X0; [ a__plus ] (X0,X1) = 2*X1 + 2*X0; [ a__U52 ] (X0,X1) = 2*X1 + 2*X0; [ Marked_a__U64 ] (X0,X1,X2) = 1*X2 + 1*X1; [ U15 ] (X0,X1) = 1*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ a__U12 ] (X0,X1,X2) = 1*X0; [ isNat ] (X0) = 1; [ a__U51 ] (X0,X1) = 2*X1 + 2*X0; [ Marked_a__U63 ] (X0,X1,X2) = 1*X2 + 1*X1; [ a__U16 ] (X0) = 1*X0; [ U51 ] (X0,X1) = 2*X1 + 2*X0; [ 0 ] () = 1; [ a__U13 ] (X0,X1,X2) = 1*X0; [ U23 ] (X0) = 1*X0; [ a__U63 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0; [ a__U32 ] (X0) = 1*X0; [ U63 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0; [ isNatKind ] (X0) = 1; [ a__U11 ] (X0,X1,X2) = 1*X0; [ U21 ] (X0,X1) = 1*X0; [ a__U62 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0; [ Marked_a__U61 ] (X0,X1,X2) = 2*X2 + 1*X1 + 2*X0; [ a__U21 ] (X0,X1) = 1*X0; [ U61 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0; [ U11 ] (X0,X1,X2) = 1*X0; [ a__U15 ] (X0,X1) = 1*X0; [ U32 ] (X0) = 1*X0; [ s ] (X0) = 1*X0 + 1; [ a__U41 ] (X0) = 1*X0; [ U14 ] (X0,X1,X2) = 1*X0; [ a__isNatKind ] (X0) = 1; [ U16 ] (X0) = 1*X0; [ mark ] (X0) = 1*X0; [ Marked_a__U62 ] (X0,X1,X2) = 2*X2 + 1*X1; [ a__U22 ] (X0,X1) = 1*X0; [ U52 ] (X0,X1) = 2*X1 + 1*X0; [ plus ] (X0,X1) = 2*X1 + 2*X0; [ a__U14 ] (X0,X1,X2) = 1*X0; [ U31 ] (X0,X1) = 1*X0; [ a__U64 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; [ a__U31 ] (X0,X1) = 1*X0; [ U64 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; [ U13 ] (X0,X1,X2) = 1*X0; [ tt ] () = 1; [ Marked_mark ] (X0) = 1*X0; [ U22 ] (X0,X1) = 1*X0; [ a__U61 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0; [ Marked_a__U52 ] (X0,X1) = 1*X1; [ a__U23 ] (X0) = 1*X0; [ U62 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0; [ U12 ] (X0,X1,X2) = 1*X0; [ a__isNat ] (X0) = 1; [ U41 ] (X0) = 1*X0; [ a__plus ] (X0,X1) = 2*X1 + 2*X0; [ a__U52 ] (X0,X1) = 2*X1 + 1*X0; [ Marked_a__U64 ] (X0,X1,X2) = 1*X2 + 1*X1; [ U15 ] (X0,X1) = 1*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ a__U12 ] (X0,X1,X2) = 1*X0; [ isNat ] (X0) = 2; [ a__U51 ] (X0,X1) = 1*X1 + 2*X0; [ Marked_a__U63 ] (X0,X1,X2) = 2*X2 + 3*X1 + 1; [ a__U16 ] (X0) = 1*X0; [ U51 ] (X0,X1) = 1*X1 + 2*X0; [ 0 ] () = 2; [ a__U13 ] (X0,X1,X2) = 1*X0; [ U23 ] (X0) = 1*X0; [ a__U63 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ a__U32 ] (X0) = 1*X0; [ U63 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ isNatKind ] (X0) = 2; [ a__U11 ] (X0,X1,X2) = 1*X0; [ U21 ] (X0,X1) = 1*X0; [ a__U62 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ a__U21 ] (X0,X1) = 1*X0; [ U61 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ U11 ] (X0,X1,X2) = 1*X0; [ a__U15 ] (X0,X1) = 1*X0; [ U32 ] (X0) = 1*X0; [ s ] (X0) = 1*X0 + 2; [ a__U41 ] (X0) = 1*X0; [ U14 ] (X0,X1,X2) = 1*X0; [ a__isNatKind ] (X0) = 2; [ U16 ] (X0) = 1*X0; [ mark ] (X0) = 1*X0; [ Marked_a__U62 ] (X0,X1,X2) = 2*X2 + 3*X1 + 1*X0; [ a__U22 ] (X0,X1) = 1*X0; [ U52 ] (X0,X1) = 1*X1 + 2*X0; [ plus ] (X0,X1) = 2*X1 + 1*X0; [ a__U14 ] (X0,X1,X2) = 1*X0; [ U31 ] (X0,X1) = 1*X0; [ a__U64 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ a__U31 ] (X0,X1) = 1*X0; [ U64 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ U13 ] (X0,X1,X2) = 1*X0; [ tt ] () = 2; [ Marked_mark ] (X0) = 2*X0 + 1; [ U22 ] (X0,X1) = 1*X0; [ a__U61 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ Marked_a__U52 ] (X0,X1) = 2*X1 + 1; [ a__U23 ] (X0) = 1*X0; [ U62 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ U12 ] (X0,X1,X2) = 1*X0; [ a__isNat ] (X0) = 2; [ U41 ] (X0) = 1*X0; [ a__plus ] (X0,X1) = 2*X1 + 1*X0; [ a__U52 ] (X0,X1) = 1*X1 + 2*X0; [ Marked_a__U64 ] (X0,X1,X2) = 2*X2 + 3*X1 + 1; [ U15 ] (X0,X1) = 1*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ a__U12 ] (X0,X1,X2) = 2*X0; [ isNat ] (X0) = 0; [ a__U51 ] (X0,X1) = 1*X1; [ Marked_a__U63 ] (X0,X1,X2) = 2*X2 + 3*X1; [ a__U16 ] (X0) = 1*X0; [ U51 ] (X0,X1) = 1*X1; [ 0 ] () = 1; [ a__U13 ] (X0,X1,X2) = 1*X0; [ U23 ] (X0) = 1*X0; [ a__U63 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1*X0 + 2; [ a__U32 ] (X0) = 1*X0; [ U63 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1*X0 + 2; [ isNatKind ] (X0) = 0; [ a__U11 ] (X0,X1,X2) = 1*X0; [ U21 ] (X0,X1) = 1*X0; [ a__U62 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1*X0 + 2; [ a__U21 ] (X0,X1) = 1*X0; [ U61 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0 + 2; [ U11 ] (X0,X1,X2) = 1*X0; [ a__U15 ] (X0,X1) = 1*X0; [ U32 ] (X0) = 1*X0; [ s ] (X0) = 1*X0 + 1; [ a__U41 ] (X0) = 1*X0; [ U14 ] (X0,X1,X2) = 1*X0; [ a__isNatKind ] (X0) = 0; [ U16 ] (X0) = 1*X0; [ mark ] (X0) = 1*X0; [ a__U22 ] (X0,X1) = 2*X0; [ U52 ] (X0,X1) = 1*X1 + 2*X0; [ plus ] (X0,X1) = 2*X1 + 1*X0; [ a__U14 ] (X0,X1,X2) = 1*X0; [ U31 ] (X0,X1) = 1*X0; [ a__U64 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0 + 1; [ a__U31 ] (X0,X1) = 1*X0; [ U64 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0 + 1; [ U13 ] (X0,X1,X2) = 1*X0; [ tt ] () = 0; [ Marked_mark ] (X0) = 2*X0; [ U22 ] (X0,X1) = 2*X0; [ a__U61 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0 + 2; [ Marked_a__U52 ] (X0,X1) = 2*X1; [ a__U23 ] (X0) = 1*X0; [ U62 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1*X0 + 2; [ U12 ] (X0,X1,X2) = 2*X0; [ a__isNat ] (X0) = 0; [ U41 ] (X0) = 1*X0; [ a__plus ] (X0,X1) = 2*X1 + 1*X0; [ a__U52 ] (X0,X1) = 1*X1 + 2*X0; [ Marked_a__U64 ] (X0,X1,X2) = 2*X2 + 3*X1; [ U15 ] (X0,X1) = 1*X0; removing < Marked_mark(U63(X1,X2,X3)),Marked_mark(X1)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ a__U12 ] (X0,X1,X2) = 0; [ isNat ] (X0) = 0; [ a__U51 ] (X0,X1) = 1*X1 + 2; [ a__U16 ] (X0) = 0; [ U51 ] (X0,X1) = 1*X1 + 2; [ 0 ] () = 2; [ a__U13 ] (X0,X1,X2) = 0; [ U23 ] (X0) = 0; [ a__U63 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1; [ a__U32 ] (X0) = 0; [ U63 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1; [ isNatKind ] (X0) = 0; [ Marked_a__isNat ] (X0) = 2*X0; [ a__U11 ] (X0,X1,X2) = 0; [ Marked_a__U11 ] (X0,X1,X2) = 2*X2 + 2*X1; [ U21 ] (X0,X1) = 0; [ a__U62 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2; [ a__U21 ] (X0,X1) = 0; [ U61 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2; [ U11 ] (X0,X1,X2) = 0; [ Marked_a__U21 ] (X0,X1) = 2*X1 + 1; [ a__U15 ] (X0,X1) = 0; [ U32 ] (X0) = 0; [ s ] (X0) = 1*X0 + 1; [ a__U41 ] (X0) = 0; [ U14 ] (X0,X1,X2) = 0; [ Marked_a__U14 ] (X0,X1,X2) = 2*X2 + 2*X1; [ a__isNatKind ] (X0) = 0; [ Marked_a__U12 ] (X0,X1,X2) = 2*X2 + 2*X1; [ U16 ] (X0) = 0; [ mark ] (X0) = 1*X0; [ a__U22 ] (X0,X1) = 0; [ U52 ] (X0,X1) = 1*X1; [ plus ] (X0,X1) = 2*X1 + 1*X0; [ Marked_a__U22 ] (X0,X1) = 2*X1; [ a__U14 ] (X0,X1,X2) = 0; [ U31 ] (X0,X1) = 0; [ a__U64 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1; [ a__U31 ] (X0,X1) = 0; [ U64 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1; [ U13 ] (X0,X1,X2) = 0; [ Marked_a__U15 ] (X0,X1) = 2*X1; [ tt ] () = 0; [ U22 ] (X0,X1) = 0; [ a__U61 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2; [ a__U23 ] (X0) = 0; [ U62 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2; [ U12 ] (X0,X1,X2) = 0; [ a__isNat ] (X0) = 0; [ U41 ] (X0) = 0; [ a__plus ] (X0,X1) = 2*X1 + 1*X0; [ a__U52 ] (X0,X1) = 1*X1; [ U15 ] (X0,X1) = 0; [ Marked_a__U13 ] (X0,X1,X2) = 2*X2 + 2*X1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ a__U12 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2; [ isNat ] (X0) = 2*X0; [ a__U51 ] (X0,X1) = 2*X1 + 2; [ a__U16 ] (X0) = 1*X0; [ U51 ] (X0,X1) = 2*X1 + 2; [ 0 ] () = 1; [ a__U13 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2; [ U23 ] (X0) = 2; [ a__U63 ] (X0,X1,X2) = 1*X0; [ a__U32 ] (X0) = 2; [ U63 ] (X0,X1,X2) = 1*X0; [ isNatKind ] (X0) = 2*X0; [ Marked_a__isNat ] (X0) = 2*X0; [ a__U11 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0; [ Marked_a__U11 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; [ U21 ] (X0,X1) = 2; [ a__U62 ] (X0,X1,X2) = 2*X2 + 2; [ a__U21 ] (X0,X1) = 2; [ U61 ] (X0,X1,X2) = 1*X2 + 2; [ U11 ] (X0,X1,X2) = 2*X2 + 1*X1 + 2*X0; [ a__U15 ] (X0,X1) = 2*X1 + 1*X0; [ U32 ] (X0) = 2; [ s ] (X0) = 1; [ a__U41 ] (X0) = 2; [ U14 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ Marked_a__U14 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1; [ a__isNatKind ] (X0) = 2*X0; [ Marked_a__U12 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2; [ U16 ] (X0) = 1*X0; [ mark ] (X0) = 2*X0; [ a__U22 ] (X0,X1) = 2; [ U52 ] (X0,X1) = 1*X1 + 2; [ plus ] (X0,X1) = 2*X1 + 3*X0; [ a__U14 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2; [ U31 ] (X0,X1) = 2*X0; [ a__U64 ] (X0,X1,X2) = 1; [ a__U31 ] (X0,X1) = 2*X0; [ U64 ] (X0,X1,X2) = 1; [ U13 ] (X0,X1,X2) = 2*X2 + 1*X1 + 2; [ Marked_a__U15 ] (X0,X1) = 2*X1; [ tt ] () = 2; [ U22 ] (X0,X1) = 2; [ a__U61 ] (X0,X1,X2) = 2*X2 + 2; [ a__U23 ] (X0) = 2; [ U62 ] (X0,X1,X2) = 2*X2 + 2; [ U12 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2; [ a__isNat ] (X0) = 2*X0; [ U41 ] (X0) = 2; [ a__plus ] (X0,X1) = 2*X1 + 3*X0; [ a__U52 ] (X0,X1) = 2*X1 + 2; [ U15 ] (X0,X1) = 1*X1 + 1*X0; [ Marked_a__U13 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1; removing < Marked_a__U14(tt,V1,V2),Marked_a__U15(a__isNat(V1),V2)> [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 2.921933 seconds (real time) Cime Exit Status: 0