- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(U11(tt,V1,V2)) -> mark(U12(isNat(V1),V2)) [2] active(U12(tt,V2)) -> mark(U13(isNat(V2))) [3] active(U13(tt)) -> mark(tt) [4] active(U21(tt,V1)) -> mark(U22(isNat(V1))) [5] active(U22(tt)) -> mark(tt) [6] active(U31(tt,V1,V2)) -> mark(U32(isNat(V1),V2)) [7] active(U32(tt,V2)) -> mark(U33(isNat(V2))) [8] active(U33(tt)) -> mark(tt) [9] active(U41(tt,N)) -> mark(N) [10] active(U51(tt,M,N)) -> mark(s(plus(N,M))) [11] active(U61(tt)) -> mark(0) [12] active(U71(tt,M,N)) -> mark(plus(x(N,M),N)) [13] active(and(tt,X)) -> mark(X) [14] active(isNat(0)) -> mark(tt) [15] active(isNat(plus(V1,V2))) -> mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2)) [16] active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) [17] active(isNat(x(V1,V2))) -> mark(U31(and(isNatKind(V1),isNatKind(V2)),V1,V2)) [18] active(isNatKind(0)) -> mark(tt) [19] active(isNatKind(plus(V1,V2))) -> mark(and(isNatKind(V1),isNatKind(V2))) [20] active(isNatKind(s(V1))) -> mark(isNatKind(V1)) [21] active(isNatKind(x(V1,V2))) -> mark(and(isNatKind(V1),isNatKind(V2))) [22] active(plus(N,0)) -> mark(U41(and(isNat(N),isNatKind(N)),N)) [23] active(plus(N,s(M))) -> mark(U51(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)) [24] active(x(N,0)) -> mark(U61(and(isNat(N),isNatKind(N)))) [25] active(x(N,s(M))) -> mark(U71(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)) [26] active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) [27] active(U12(X1,X2)) -> U12(active(X1),X2) [28] active(U13(X)) -> U13(active(X)) [29] active(U21(X1,X2)) -> U21(active(X1),X2) [30] active(U22(X)) -> U22(active(X)) [31] active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3) [32] active(U32(X1,X2)) -> U32(active(X1),X2) [33] active(U33(X)) -> U33(active(X)) [34] active(U41(X1,X2)) -> U41(active(X1),X2) [35] active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) [36] active(s(X)) -> s(active(X)) [37] active(plus(X1,X2)) -> plus(active(X1),X2) [38] active(plus(X1,X2)) -> plus(X1,active(X2)) [39] active(U61(X)) -> U61(active(X)) [40] active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) [41] active(x(X1,X2)) -> x(active(X1),X2) [42] active(x(X1,X2)) -> x(X1,active(X2)) [43] active(and(X1,X2)) -> and(active(X1),X2) [44] U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) [45] U12(mark(X1),X2) -> mark(U12(X1,X2)) [46] U13(mark(X)) -> mark(U13(X)) [47] U21(mark(X1),X2) -> mark(U21(X1,X2)) [48] U22(mark(X)) -> mark(U22(X)) [49] U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3)) [50] U32(mark(X1),X2) -> mark(U32(X1,X2)) [51] U33(mark(X)) -> mark(U33(X)) [52] U41(mark(X1),X2) -> mark(U41(X1,X2)) [53] U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) [54] s(mark(X)) -> mark(s(X)) [55] plus(mark(X1),X2) -> mark(plus(X1,X2)) [56] plus(X1,mark(X2)) -> mark(plus(X1,X2)) [57] U61(mark(X)) -> mark(U61(X)) [58] U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) [59] x(mark(X1),X2) -> mark(x(X1,X2)) [60] x(X1,mark(X2)) -> mark(x(X1,X2)) [61] and(mark(X1),X2) -> mark(and(X1,X2)) [62] proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) [63] proper(tt) -> ok(tt) [64] proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) [65] proper(isNat(X)) -> isNat(proper(X)) [66] proper(U13(X)) -> U13(proper(X)) [67] proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) [68] proper(U22(X)) -> U22(proper(X)) [69] proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3)) [70] proper(U32(X1,X2)) -> U32(proper(X1),proper(X2)) [71] proper(U33(X)) -> U33(proper(X)) [72] proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) [73] proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) [74] proper(s(X)) -> s(proper(X)) [75] proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) [76] proper(U61(X)) -> U61(proper(X)) [77] proper(0) -> ok(0) [78] proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) [79] proper(x(X1,X2)) -> x(proper(X1),proper(X2)) [80] proper(and(X1,X2)) -> and(proper(X1),proper(X2)) [81] proper(isNatKind(X)) -> isNatKind(proper(X)) [82] U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) [83] U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) [84] isNat(ok(X)) -> ok(isNat(X)) [85] U13(ok(X)) -> ok(U13(X)) [86] U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) [87] U22(ok(X)) -> ok(U22(X)) [88] U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3)) [89] U32(ok(X1),ok(X2)) -> ok(U32(X1,X2)) [90] U33(ok(X)) -> ok(U33(X)) [91] U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) [92] U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) [93] s(ok(X)) -> ok(s(X)) [94] plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) [95] U61(ok(X)) -> ok(U61(X)) [96] U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) [97] x(ok(X1),ok(X2)) -> ok(x(X1,X2)) [98] and(ok(X1),ok(X2)) -> ok(and(X1,X2)) [99] isNatKind(ok(X)) -> ok(isNatKind(X)) [100] top(mark(X)) -> top(proper(X)) [101] top(ok(X)) -> top(active(X)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 21 components: { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> } { --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { U12(mark(X1),X2) >= mark(U12(X1,X2)) ; U12(ok(X1),ok(X2)) >= ok(U12(X1,X2)) ; isNat(ok(X)) >= ok(isNat(X)) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; active(U12(X1,X2)) >= U12(active(X1),X2) ; active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) ; active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1),isNatKind(V2)), V1,V2)) ; active(isNat(0)) >= mark(tt) ; active(isNat(x(V1,V2))) >= mark(U31(and(isNatKind(V1),isNatKind(V2)),V1,V2)) ; active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U11(X1,X2,X3)) >= U11(active(X1),X2,X3) ; active(U13(tt)) >= mark(tt) ; active(U13(X)) >= U13(active(X)) ; active(U22(tt)) >= mark(tt) ; active(U22(X)) >= U22(active(X)) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U21(X1,X2)) >= U21(active(X1),X2) ; active(U32(tt,V2)) >= mark(U33(isNat(V2))) ; active(U32(X1,X2)) >= U32(active(X1),X2) ; active(U31(tt,V1,V2)) >= mark(U32(isNat(V1),V2)) ; active(U31(X1,X2,X3)) >= U31(active(X1),X2,X3) ; active(U33(tt)) >= mark(tt) ; active(U33(X)) >= U33(active(X)) ; active(U41(tt,N)) >= mark(N) ; active(U41(X1,X2)) >= U41(active(X1),X2) ; active(s(X)) >= s(active(X)) ; active(plus(N,s(M))) >= mark(U51(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U41(and(isNat(N),isNatKind(N)),N)) ; active(plus(X1,X2)) >= plus(active(X1),X2) ; active(plus(X1,X2)) >= plus(X1,active(X2)) ; active(U51(tt,M,N)) >= mark(s(plus(N,M))) ; active(U51(X1,X2,X3)) >= U51(active(X1),X2,X3) ; active(U61(tt)) >= mark(0) ; active(U61(X)) >= U61(active(X)) ; active(x(N,s(M))) >= mark(U71(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(x(N,0)) >= mark(U61(and(isNat(N),isNatKind(N)))) ; active(x(X1,X2)) >= x(active(X1),X2) ; active(x(X1,X2)) >= x(X1,active(X2)) ; active(U71(tt,M,N)) >= mark(plus(x(N,M),N)) ; active(U71(X1,X2,X3)) >= U71(active(X1),X2,X3) ; active(and(tt,X)) >= mark(X) ; active(and(X1,X2)) >= and(active(X1),X2) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; active(isNatKind(x(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; U11(mark(X1),X2,X3) >= mark(U11(X1,X2,X3)) ; U11(ok(X1),ok(X2),ok(X3)) >= ok(U11(X1,X2,X3)) ; U13(mark(X)) >= mark(U13(X)) ; U13(ok(X)) >= ok(U13(X)) ; U22(mark(X)) >= mark(U22(X)) ; U22(ok(X)) >= ok(U22(X)) ; U21(mark(X1),X2) >= mark(U21(X1,X2)) ; U21(ok(X1),ok(X2)) >= ok(U21(X1,X2)) ; U32(mark(X1),X2) >= mark(U32(X1,X2)) ; U32(ok(X1),ok(X2)) >= ok(U32(X1,X2)) ; U31(mark(X1),X2,X3) >= mark(U31(X1,X2,X3)) ; U31(ok(X1),ok(X2),ok(X3)) >= ok(U31(X1,X2,X3)) ; U33(mark(X)) >= mark(U33(X)) ; U33(ok(X)) >= ok(U33(X)) ; U41(mark(X1),X2) >= mark(U41(X1,X2)) ; U41(ok(X1),ok(X2)) >= ok(U41(X1,X2)) ; s(mark(X)) >= mark(s(X)) ; s(ok(X)) >= ok(s(X)) ; plus(mark(X1),X2) >= mark(plus(X1,X2)) ; plus(ok(X1),ok(X2)) >= ok(plus(X1,X2)) ; plus(X1,mark(X2)) >= mark(plus(X1,X2)) ; U51(mark(X1),X2,X3) >= mark(U51(X1,X2,X3)) ; U51(ok(X1),ok(X2),ok(X3)) >= ok(U51(X1,X2,X3)) ; U61(mark(X)) >= mark(U61(X)) ; U61(ok(X)) >= ok(U61(X)) ; x(mark(X1),X2) >= mark(x(X1,X2)) ; x(ok(X1),ok(X2)) >= ok(x(X1,X2)) ; x(X1,mark(X2)) >= mark(x(X1,X2)) ; U71(mark(X1),X2,X3) >= mark(U71(X1,X2,X3)) ; U71(ok(X1),ok(X2),ok(X3)) >= ok(U71(X1,X2,X3)) ; and(mark(X1),X2) >= mark(and(X1,X2)) ; and(ok(X1),ok(X2)) >= ok(and(X1,X2)) ; isNatKind(ok(X)) >= ok(isNatKind(X)) ; proper(U12(X1,X2)) >= U12(proper(X1),proper(X2)) ; proper(isNat(X)) >= isNat(proper(X)) ; proper(U11(X1,X2,X3)) >= U11(proper(X1),proper(X2),proper(X3)) ; proper(tt) >= ok(tt) ; proper(U13(X)) >= U13(proper(X)) ; proper(U22(X)) >= U22(proper(X)) ; proper(U21(X1,X2)) >= U21(proper(X1),proper(X2)) ; proper(U32(X1,X2)) >= U32(proper(X1),proper(X2)) ; proper(U31(X1,X2,X3)) >= U31(proper(X1),proper(X2),proper(X3)) ; proper(U33(X)) >= U33(proper(X)) ; proper(U41(X1,X2)) >= U41(proper(X1),proper(X2)) ; proper(s(X)) >= s(proper(X)) ; proper(plus(X1,X2)) >= plus(proper(X1),proper(X2)) ; proper(U51(X1,X2,X3)) >= U51(proper(X1),proper(X2),proper(X3)) ; proper(0) >= ok(0) ; proper(U61(X)) >= U61(proper(X)) ; proper(x(X1,X2)) >= x(proper(X1),proper(X2)) ; proper(U71(X1,X2,X3)) >= U71(proper(X1),proper(X2),proper(X3)) ; proper(and(X1,X2)) >= and(proper(X1),proper(X2)) ; proper(isNatKind(X)) >= isNatKind(proper(X)) ; top(mark(X)) >= top(proper(X)) ; top(ok(X)) >= top(active(X)) ; Marked_top(mark(X)) >= Marked_top(proper(X)) ; Marked_top(ok(X)) >= Marked_top(active(X)) ; } + Disjunctions:{ { Marked_top(mark(X)) > Marked_top(proper(X)) ; } { Marked_top(ok(X)) > Marked_top(active(X)) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. === TIMER virtual : 50.000000 === trying sub matrices of size: 1 Matrix interpretation constraints generated. Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. Termination constraints generated. Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 50.000000 === === STOPING TIMER real === Sat timeout reached === STOPING TIMER virtual === No solution found for these parameters. No solution found for these constraints. APPLY CRITERIA (ID_CRIT) NOT SOLVED No proof found Cime worked for 99.201629 seconds (real time) Cime Exit Status: 0