- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(U11(tt,V2)) -> mark(U12(isNat(V2))) [2] active(U12(tt)) -> mark(tt) [3] active(U21(tt)) -> mark(tt) [4] active(U31(tt,V2)) -> mark(U32(isNat(V2))) [5] active(U32(tt)) -> mark(tt) [6] active(U41(tt,N)) -> mark(N) [7] active(U51(tt,M,N)) -> mark(U52(isNat(N),M,N)) [8] active(U52(tt,M,N)) -> mark(s(plus(N,M))) [9] active(U61(tt)) -> mark(0) [10] active(U71(tt,M,N)) -> mark(U72(isNat(N),M,N)) [11] active(U72(tt,M,N)) -> mark(plus(x(N,M),N)) [12] active(isNat(0)) -> mark(tt) [13] active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) [14] active(isNat(s(V1))) -> mark(U21(isNat(V1))) [15] active(isNat(x(V1,V2))) -> mark(U31(isNat(V1),V2)) [16] active(plus(N,0)) -> mark(U41(isNat(N),N)) [17] active(plus(N,s(M))) -> mark(U51(isNat(M),M,N)) [18] active(x(N,0)) -> mark(U61(isNat(N))) [19] active(x(N,s(M))) -> mark(U71(isNat(M),M,N)) [20] active(U11(X1,X2)) -> U11(active(X1),X2) [21] active(U12(X)) -> U12(active(X)) [22] active(U21(X)) -> U21(active(X)) [23] active(U31(X1,X2)) -> U31(active(X1),X2) [24] active(U32(X)) -> U32(active(X)) [25] active(U41(X1,X2)) -> U41(active(X1),X2) [26] active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3) [27] active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3) [28] active(s(X)) -> s(active(X)) [29] active(plus(X1,X2)) -> plus(active(X1),X2) [30] active(plus(X1,X2)) -> plus(X1,active(X2)) [31] active(U61(X)) -> U61(active(X)) [32] active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) [33] active(U72(X1,X2,X3)) -> U72(active(X1),X2,X3) [34] active(x(X1,X2)) -> x(active(X1),X2) [35] active(x(X1,X2)) -> x(X1,active(X2)) [36] U11(mark(X1),X2) -> mark(U11(X1,X2)) [37] U12(mark(X)) -> mark(U12(X)) [38] U21(mark(X)) -> mark(U21(X)) [39] U31(mark(X1),X2) -> mark(U31(X1,X2)) [40] U32(mark(X)) -> mark(U32(X)) [41] U41(mark(X1),X2) -> mark(U41(X1,X2)) [42] U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3)) [43] U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3)) [44] s(mark(X)) -> mark(s(X)) [45] plus(mark(X1),X2) -> mark(plus(X1,X2)) [46] plus(X1,mark(X2)) -> mark(plus(X1,X2)) [47] U61(mark(X)) -> mark(U61(X)) [48] U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) [49] U72(mark(X1),X2,X3) -> mark(U72(X1,X2,X3)) [50] x(mark(X1),X2) -> mark(x(X1,X2)) [51] x(X1,mark(X2)) -> mark(x(X1,X2)) [52] proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) [53] proper(tt) -> ok(tt) [54] proper(U12(X)) -> U12(proper(X)) [55] proper(isNat(X)) -> isNat(proper(X)) [56] proper(U21(X)) -> U21(proper(X)) [57] proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) [58] proper(U32(X)) -> U32(proper(X)) [59] proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) [60] proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3)) [61] proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3)) [62] proper(s(X)) -> s(proper(X)) [63] proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) [64] proper(U61(X)) -> U61(proper(X)) [65] proper(0) -> ok(0) [66] proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) [67] proper(U72(X1,X2,X3)) -> U72(proper(X1),proper(X2),proper(X3)) [68] proper(x(X1,X2)) -> x(proper(X1),proper(X2)) [69] U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) [70] U12(ok(X)) -> ok(U12(X)) [71] isNat(ok(X)) -> ok(isNat(X)) [72] U21(ok(X)) -> ok(U21(X)) [73] U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) [74] U32(ok(X)) -> ok(U32(X)) [75] U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) [76] U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3)) [77] U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3)) [78] s(ok(X)) -> ok(s(X)) [79] plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) [80] U61(ok(X)) -> ok(U61(X)) [81] U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) [82] U72(ok(X1),ok(X2),ok(X3)) -> ok(U72(X1,X2,X3)) [83] x(ok(X1),ok(X2)) -> ok(x(X1,X2)) [84] top(mark(X)) -> top(proper(X)) [85] top(ok(X)) -> top(active(X)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 18 components: { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { U12(mark(X)) >= mark(U12(X)) ; U12(ok(X)) >= ok(U12(X)) ; isNat(ok(X)) >= ok(isNat(X)) ; active(U12(tt)) >= mark(tt) ; active(U12(X)) >= U12(active(X)) ; active(isNat(s(V1))) >= mark(U21(isNat(V1))) ; active(isNat(plus(V1,V2))) >= mark(U11(isNat(V1),V2)) ; active(isNat(0)) >= mark(tt) ; active(isNat(x(V1,V2))) >= mark(U31(isNat(V1),V2)) ; active(U11(tt,V2)) >= mark(U12(isNat(V2))) ; active(U11(X1,X2)) >= U11(active(X1),X2) ; active(U21(tt)) >= mark(tt) ; active(U21(X)) >= U21(active(X)) ; active(U32(tt)) >= mark(tt) ; active(U32(X)) >= U32(active(X)) ; active(U31(tt,V2)) >= mark(U32(isNat(V2))) ; active(U31(X1,X2)) >= U31(active(X1),X2) ; active(U41(tt,N)) >= mark(N) ; active(U41(X1,X2)) >= U41(active(X1),X2) ; active(U52(tt,M,N)) >= mark(s(plus(N,M))) ; active(U52(X1,X2,X3)) >= U52(active(X1),X2,X3) ; active(U51(tt,M,N)) >= mark(U52(isNat(N),M,N)) ; active(U51(X1,X2,X3)) >= U51(active(X1),X2,X3) ; active(s(X)) >= s(active(X)) ; active(plus(N,s(M))) >= mark(U51(isNat(M),M,N)) ; active(plus(N,0)) >= mark(U41(isNat(N),N)) ; active(plus(X1,X2)) >= plus(active(X1),X2) ; active(plus(X1,X2)) >= plus(X1,active(X2)) ; active(U61(tt)) >= mark(0) ; active(U61(X)) >= U61(active(X)) ; active(U72(tt,M,N)) >= mark(plus(x(N,M),N)) ; active(U72(X1,X2,X3)) >= U72(active(X1),X2,X3) ; active(U71(tt,M,N)) >= mark(U72(isNat(N),M,N)) ; active(U71(X1,X2,X3)) >= U71(active(X1),X2,X3) ; active(x(N,s(M))) >= mark(U71(isNat(M),M,N)) ; active(x(N,0)) >= mark(U61(isNat(N))) ; active(x(X1,X2)) >= x(active(X1),X2) ; active(x(X1,X2)) >= x(X1,active(X2)) ; U11(mark(X1),X2) >= mark(U11(X1,X2)) ; U11(ok(X1),ok(X2)) >= ok(U11(X1,X2)) ; U21(mark(X)) >= mark(U21(X)) ; U21(ok(X)) >= ok(U21(X)) ; U32(mark(X)) >= mark(U32(X)) ; U32(ok(X)) >= ok(U32(X)) ; U31(mark(X1),X2) >= mark(U31(X1,X2)) ; U31(ok(X1),ok(X2)) >= ok(U31(X1,X2)) ; U41(mark(X1),X2) >= mark(U41(X1,X2)) ; U41(ok(X1),ok(X2)) >= ok(U41(X1,X2)) ; U52(mark(X1),X2,X3) >= mark(U52(X1,X2,X3)) ; U52(ok(X1),ok(X2),ok(X3)) >= ok(U52(X1,X2,X3)) ; U51(mark(X1),X2,X3) >= mark(U51(X1,X2,X3)) ; U51(ok(X1),ok(X2),ok(X3)) >= ok(U51(X1,X2,X3)) ; 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)) ; U61(mark(X)) >= mark(U61(X)) ; U61(ok(X)) >= ok(U61(X)) ; U72(mark(X1),X2,X3) >= mark(U72(X1,X2,X3)) ; U72(ok(X1),ok(X2),ok(X3)) >= ok(U72(X1,X2,X3)) ; U71(mark(X1),X2,X3) >= mark(U71(X1,X2,X3)) ; U71(ok(X1),ok(X2),ok(X3)) >= ok(U71(X1,X2,X3)) ; 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)) ; proper(U12(X)) >= U12(proper(X)) ; proper(isNat(X)) >= isNat(proper(X)) ; proper(U11(X1,X2)) >= U11(proper(X1),proper(X2)) ; proper(tt) >= ok(tt) ; proper(U21(X)) >= U21(proper(X)) ; proper(U32(X)) >= U32(proper(X)) ; proper(U31(X1,X2)) >= U31(proper(X1),proper(X2)) ; proper(U41(X1,X2)) >= U41(proper(X1),proper(X2)) ; proper(U52(X1,X2,X3)) >= U52(proper(X1),proper(X2),proper(X3)) ; proper(U51(X1,X2,X3)) >= U51(proper(X1),proper(X2),proper(X3)) ; proper(s(X)) >= s(proper(X)) ; proper(plus(X1,X2)) >= plus(proper(X1),proper(X2)) ; proper(0) >= ok(0) ; proper(U61(X)) >= U61(proper(X)) ; proper(U72(X1,X2,X3)) >= U72(proper(X1),proper(X2),proper(X3)) ; proper(U71(X1,X2,X3)) >= U71(proper(X1),proper(X2),proper(X3)) ; proper(x(X1,X2)) >= x(proper(X1),proper(X2)) ; 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 78.911409 seconds (real time) Cime Exit Status: 0