- : unit = () - : 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] mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) [21] mark(tt) -> active(tt) [22] mark(U12(X)) -> active(U12(mark(X))) [23] mark(isNat(X)) -> active(isNat(X)) [24] mark(U21(X)) -> active(U21(mark(X))) [25] mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) [26] mark(U32(X)) -> active(U32(mark(X))) [27] mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) [28] mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3)) [29] mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3)) [30] mark(s(X)) -> active(s(mark(X))) [31] mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) [32] mark(U61(X)) -> active(U61(mark(X))) [33] mark(0) -> active(0) [34] mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) [35] mark(U72(X1,X2,X3)) -> active(U72(mark(X1),X2,X3)) [36] mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) [37] U11(mark(X1),X2) -> U11(X1,X2) [38] U11(X1,mark(X2)) -> U11(X1,X2) [39] U11(active(X1),X2) -> U11(X1,X2) [40] U11(X1,active(X2)) -> U11(X1,X2) [41] U12(mark(X)) -> U12(X) [42] U12(active(X)) -> U12(X) [43] isNat(mark(X)) -> isNat(X) [44] isNat(active(X)) -> isNat(X) [45] U21(mark(X)) -> U21(X) [46] U21(active(X)) -> U21(X) [47] U31(mark(X1),X2) -> U31(X1,X2) [48] U31(X1,mark(X2)) -> U31(X1,X2) [49] U31(active(X1),X2) -> U31(X1,X2) [50] U31(X1,active(X2)) -> U31(X1,X2) [51] U32(mark(X)) -> U32(X) [52] U32(active(X)) -> U32(X) [53] U41(mark(X1),X2) -> U41(X1,X2) [54] U41(X1,mark(X2)) -> U41(X1,X2) [55] U41(active(X1),X2) -> U41(X1,X2) [56] U41(X1,active(X2)) -> U41(X1,X2) [57] U51(mark(X1),X2,X3) -> U51(X1,X2,X3) [58] U51(X1,mark(X2),X3) -> U51(X1,X2,X3) [59] U51(X1,X2,mark(X3)) -> U51(X1,X2,X3) [60] U51(active(X1),X2,X3) -> U51(X1,X2,X3) [61] U51(X1,active(X2),X3) -> U51(X1,X2,X3) [62] U51(X1,X2,active(X3)) -> U51(X1,X2,X3) [63] U52(mark(X1),X2,X3) -> U52(X1,X2,X3) [64] U52(X1,mark(X2),X3) -> U52(X1,X2,X3) [65] U52(X1,X2,mark(X3)) -> U52(X1,X2,X3) [66] U52(active(X1),X2,X3) -> U52(X1,X2,X3) [67] U52(X1,active(X2),X3) -> U52(X1,X2,X3) [68] U52(X1,X2,active(X3)) -> U52(X1,X2,X3) [69] s(mark(X)) -> s(X) [70] s(active(X)) -> s(X) [71] plus(mark(X1),X2) -> plus(X1,X2) [72] plus(X1,mark(X2)) -> plus(X1,X2) [73] plus(active(X1),X2) -> plus(X1,X2) [74] plus(X1,active(X2)) -> plus(X1,X2) [75] U61(mark(X)) -> U61(X) [76] U61(active(X)) -> U61(X) [77] U71(mark(X1),X2,X3) -> U71(X1,X2,X3) [78] U71(X1,mark(X2),X3) -> U71(X1,X2,X3) [79] U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) [80] U71(active(X1),X2,X3) -> U71(X1,X2,X3) [81] U71(X1,active(X2),X3) -> U71(X1,X2,X3) [82] U71(X1,X2,active(X3)) -> U71(X1,X2,X3) [83] U72(mark(X1),X2,X3) -> U72(X1,X2,X3) [84] U72(X1,mark(X2),X3) -> U72(X1,X2,X3) [85] U72(X1,X2,mark(X3)) -> U72(X1,X2,X3) [86] U72(active(X1),X2,X3) -> U72(X1,X2,X3) [87] U72(X1,active(X2),X3) -> U72(X1,X2,X3) [88] U72(X1,X2,active(X3)) -> U72(X1,X2,X3) [89] x(mark(X1),X2) -> x(X1,X2) [90] x(X1,mark(X2)) -> x(X1,X2) [91] x(active(X1),X2) -> x(X1,X2) [92] x(X1,active(X2)) -> x(X1,X2) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 16 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X)) >= active(U12(mark(X))) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ; mark(tt) >= active(tt) ; mark(U21(X)) >= active(U21(mark(X))) ; mark(U32(X)) >= active(U32(mark(X))) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(U41(X1,X2)) >= active(U41(mark(X1),X2)) ; mark(U52(X1,X2,X3)) >= active(U52(mark(X1),X2,X3)) ; mark(U51(X1,X2,X3)) >= active(U51(mark(X1),X2,X3)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(0) >= active(0) ; mark(U61(X)) >= active(U61(mark(X))) ; mark(U72(X1,X2,X3)) >= active(U72(mark(X1),X2,X3)) ; mark(U71(X1,X2,X3)) >= active(U71(mark(X1),X2,X3)) ; mark(x(X1,X2)) >= active(x(mark(X1),mark(X2))) ; U12(mark(X)) >= U12(X) ; U12(active(X)) >= U12(X) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt)) >= mark(tt) ; 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(U21(tt)) >= mark(tt) ; active(U32(tt)) >= mark(tt) ; active(U31(tt,V2)) >= mark(U32(isNat(V2))) ; active(U41(tt,N)) >= mark(N) ; active(U52(tt,M,N)) >= mark(s(plus(N,M))) ; active(U51(tt,M,N)) >= mark(U52(isNat(N),M,N)) ; active(plus(N,s(M))) >= mark(U51(isNat(M),M,N)) ; active(plus(N,0)) >= mark(U41(isNat(N),N)) ; active(U61(tt)) >= mark(0) ; active(U72(tt,M,N)) >= mark(plus(x(N,M),N)) ; active(U71(tt,M,N)) >= mark(U72(isNat(N),M,N)) ; active(x(N,s(M))) >= mark(U71(isNat(M),M,N)) ; active(x(N,0)) >= mark(U61(isNat(N))) ; U11(mark(X1),X2) >= U11(X1,X2) ; U11(active(X1),X2) >= U11(X1,X2) ; U11(X1,mark(X2)) >= U11(X1,X2) ; U11(X1,active(X2)) >= U11(X1,X2) ; U21(mark(X)) >= U21(X) ; U21(active(X)) >= U21(X) ; U32(mark(X)) >= U32(X) ; U32(active(X)) >= U32(X) ; U31(mark(X1),X2) >= U31(X1,X2) ; U31(active(X1),X2) >= U31(X1,X2) ; U31(X1,mark(X2)) >= U31(X1,X2) ; U31(X1,active(X2)) >= U31(X1,X2) ; U41(mark(X1),X2) >= U41(X1,X2) ; U41(active(X1),X2) >= U41(X1,X2) ; U41(X1,mark(X2)) >= U41(X1,X2) ; U41(X1,active(X2)) >= U41(X1,X2) ; U52(mark(X1),X2,X3) >= U52(X1,X2,X3) ; U52(active(X1),X2,X3) >= U52(X1,X2,X3) ; U52(X1,mark(X2),X3) >= U52(X1,X2,X3) ; U52(X1,active(X2),X3) >= U52(X1,X2,X3) ; U52(X1,X2,mark(X3)) >= U52(X1,X2,X3) ; U52(X1,X2,active(X3)) >= U52(X1,X2,X3) ; U51(mark(X1),X2,X3) >= U51(X1,X2,X3) ; U51(active(X1),X2,X3) >= U51(X1,X2,X3) ; U51(X1,mark(X2),X3) >= U51(X1,X2,X3) ; U51(X1,active(X2),X3) >= U51(X1,X2,X3) ; U51(X1,X2,mark(X3)) >= U51(X1,X2,X3) ; U51(X1,X2,active(X3)) >= U51(X1,X2,X3) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; plus(mark(X1),X2) >= plus(X1,X2) ; plus(active(X1),X2) >= plus(X1,X2) ; plus(X1,mark(X2)) >= plus(X1,X2) ; plus(X1,active(X2)) >= plus(X1,X2) ; U61(mark(X)) >= U61(X) ; U61(active(X)) >= U61(X) ; U72(mark(X1),X2,X3) >= U72(X1,X2,X3) ; U72(active(X1),X2,X3) >= U72(X1,X2,X3) ; U72(X1,mark(X2),X3) >= U72(X1,X2,X3) ; U72(X1,active(X2),X3) >= U72(X1,X2,X3) ; U72(X1,X2,mark(X3)) >= U72(X1,X2,X3) ; U72(X1,X2,active(X3)) >= U72(X1,X2,X3) ; U71(mark(X1),X2,X3) >= U71(X1,X2,X3) ; U71(active(X1),X2,X3) >= U71(X1,X2,X3) ; U71(X1,mark(X2),X3) >= U71(X1,X2,X3) ; U71(X1,active(X2),X3) >= U71(X1,X2,X3) ; U71(X1,X2,mark(X3)) >= U71(X1,X2,X3) ; U71(X1,X2,active(X3)) >= U71(X1,X2,X3) ; x(mark(X1),X2) >= x(X1,X2) ; x(active(X1),X2) >= x(X1,X2) ; x(X1,mark(X2)) >= x(X1,X2) ; x(X1,active(X2)) >= x(X1,X2) ; Marked_mark(U12(X)) >= Marked_mark(X) ; Marked_mark(U12(X)) >= Marked_active(U12(mark(X))) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2)) ; Marked_mark(U21(X)) >= Marked_mark(X) ; Marked_mark(U21(X)) >= Marked_active(U21(mark(X))) ; Marked_mark(U32(X)) >= Marked_mark(X) ; Marked_mark(U32(X)) >= Marked_active(U32(mark(X))) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(U41(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U41(X1,X2)) >= Marked_active(U41(mark(X1),X2)) ; Marked_mark(U52(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U52(X1,X2,X3)) >= Marked_active(U52(mark(X1),X2,X3)) ; Marked_mark(U51(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U51(X1,X2,X3)) >= Marked_active(U51(mark(X1),X2,X3)) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_active(s(mark(X))) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) ; Marked_mark(U61(X)) >= Marked_mark(X) ; Marked_mark(U61(X)) >= Marked_active(U61(mark(X))) ; Marked_mark(U72(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U72(X1,X2,X3)) >= Marked_active(U72(mark(X1),X2,X3)) ; Marked_mark(U71(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U71(X1,X2,X3)) >= Marked_active(U71(mark(X1),X2,X3)) ; Marked_mark(x(X1,X2)) >= Marked_mark(X1) ; Marked_mark(x(X1,X2)) >= Marked_mark(X2) ; Marked_mark(x(X1,X2)) >= Marked_active(x(mark(X1),mark(X2))) ; Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNat(V1))) ; Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(isNat(V1),V2)) ; Marked_active(isNat(x(V1,V2))) >= Marked_mark(U31(isNat(V1),V2)) ; Marked_active(U11(tt,V2)) >= Marked_mark(U12(isNat(V2))) ; Marked_active(U31(tt,V2)) >= Marked_mark(U32(isNat(V2))) ; Marked_active(U41(tt,N)) >= Marked_mark(N) ; Marked_active(U52(tt,M,N)) >= Marked_mark(s(plus(N,M))) ; Marked_active(U51(tt,M,N)) >= Marked_mark(U52(isNat(N),M,N)) ; Marked_active(plus(N,s(M))) >= Marked_mark(U51(isNat(M),M,N)) ; Marked_active(plus(N,0)) >= Marked_mark(U41(isNat(N),N)) ; Marked_active(U72(tt,M,N)) >= Marked_mark(plus(x(N,M),N)) ; Marked_active(U71(tt,M,N)) >= Marked_mark(U72(isNat(N),M,N)) ; Marked_active(x(N,s(M))) >= Marked_mark(U71(isNat(M),M,N)) ; Marked_active(x(N,0)) >= Marked_mark(U61(isNat(N))) ; } + Disjunctions:{ { Marked_mark(U12(X)) > Marked_mark(X) ; } { Marked_mark(U12(X)) > Marked_active(U12(mark(X))) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U11(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2)) > Marked_active(U11(mark(X1),X2)) ; } { Marked_mark(U21(X)) > Marked_mark(X) ; } { Marked_mark(U21(X)) > Marked_active(U21(mark(X))) ; } { Marked_mark(U32(X)) > Marked_mark(X) ; } { Marked_mark(U32(X)) > Marked_active(U32(mark(X))) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(U41(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U41(X1,X2)) > Marked_active(U41(mark(X1),X2)) ; } { Marked_mark(U52(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U52(X1,X2,X3)) > Marked_active(U52(mark(X1),X2,X3)) ; } { Marked_mark(U51(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U51(X1,X2,X3)) > Marked_active(U51(mark(X1),X2,X3)) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_active(s(mark(X))) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(plus(X1,X2)) > Marked_active(plus(mark(X1),mark(X2))) ; } { Marked_mark(U61(X)) > Marked_mark(X) ; } { Marked_mark(U61(X)) > Marked_active(U61(mark(X))) ; } { Marked_mark(U72(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U72(X1,X2,X3)) > Marked_active(U72(mark(X1),X2,X3)) ; } { Marked_mark(U71(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U71(X1,X2,X3)) > Marked_active(U71(mark(X1),X2,X3)) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(x(X1,X2)) > Marked_active(x(mark(X1),mark(X2))) ; } { Marked_active(isNat(s(V1))) > Marked_mark(U21(isNat(V1))) ; } { Marked_active(isNat(plus(V1,V2))) > Marked_mark(U11(isNat(V1),V2)) ; } { Marked_active(isNat(x(V1,V2))) > Marked_mark(U31(isNat(V1),V2)) ; } { Marked_active(U11(tt,V2)) > Marked_mark(U12(isNat(V2))) ; } { Marked_active(U31(tt,V2)) > Marked_mark(U32(isNat(V2))) ; } { Marked_active(U41(tt,N)) > Marked_mark(N) ; } { Marked_active(U52(tt,M,N)) > Marked_mark(s(plus(N,M))) ; } { Marked_active(U51(tt,M,N)) > Marked_mark(U52(isNat(N),M,N)) ; } { Marked_active(plus(N,s(M))) > Marked_mark(U51(isNat(M),M,N)) ; } { Marked_active(plus(N,0)) > Marked_mark(U41(isNat(N),N)) ; } { Marked_active(U72(tt,M,N)) > Marked_mark(plus(x(N,M),N)) ; } { Marked_active(U71(tt,M,N)) > Marked_mark(U72(isNat(N),M,N)) ; } { Marked_active(x(N,s(M))) > Marked_mark(U71(isNat(M),M,N)) ; } { Marked_active(x(N,0)) > Marked_mark(U61(isNat(N))) ; } } === 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: mark(U12(X)) >= active(U12(mark(X))) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) constraint: mark(tt) >= active(tt) constraint: mark(U21(X)) >= active(U21(mark(X))) constraint: mark(U32(X)) >= active(U32(mark(X))) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(U41(X1,X2)) >= active(U41(mark(X1),X2)) constraint: mark(U52(X1,X2,X3)) >= active(U52(mark(X1),X2,X3)) constraint: mark(U51(X1,X2,X3)) >= active(U51(mark(X1),X2,X3)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(0) >= active(0) constraint: mark(U61(X)) >= active(U61(mark(X))) constraint: mark(U72(X1,X2,X3)) >= active(U72(mark(X1),X2,X3)) constraint: mark(U71(X1,X2,X3)) >= active(U71(mark(X1),X2,X3)) constraint: mark(x(X1,X2)) >= active(x(mark(X1),mark(X2))) constraint: U12(mark(X)) >= U12(X) constraint: U12(active(X)) >= U12(X) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt)) >= mark(tt) constraint: active(isNat(s(V1))) >= mark(U21(isNat(V1))) constraint: active(isNat(plus(V1,V2))) >= mark(U11(isNat(V1),V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(isNat(x(V1,V2))) >= mark(U31(isNat(V1),V2)) constraint: active(U11(tt,V2)) >= mark(U12(isNat(V2))) constraint: active(U21(tt)) >= mark(tt) constraint: active(U32(tt)) >= mark(tt) constraint: active(U31(tt,V2)) >= mark(U32(isNat(V2))) constraint: active(U41(tt,N)) >= mark(N) constraint: active(U52(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(U51(tt,M,N)) >= mark(U52(isNat(N),M,N)) constraint: active(plus(N,s(M))) >= mark(U51(isNat(M),M,N)) constraint: active(plus(N,0)) >= mark(U41(isNat(N),N)) constraint: active(U61(tt)) >= mark(0) constraint: active(U72(tt,M,N)) >= mark(plus(x(N,M),N)) constraint: active(U71(tt,M,N)) >= mark(U72(isNat(N),M,N)) constraint: active(x(N,s(M))) >= mark(U71(isNat(M),M,N)) constraint: active(x(N,0)) >= mark(U61(isNat(N))) constraint: U11(mark(X1),X2) >= U11(X1,X2) constraint: U11(active(X1),X2) >= U11(X1,X2) constraint: U11(X1,mark(X2)) >= U11(X1,X2) constraint: U11(X1,active(X2)) >= U11(X1,X2) constraint: U21(mark(X)) >= U21(X) constraint: U21(active(X)) >= U21(X) constraint: U32(mark(X)) >= U32(X) constraint: U32(active(X)) >= U32(X) constraint: U31(mark(X1),X2) >= U31(X1,X2) constraint: U31(active(X1),X2) >= U31(X1,X2) constraint: U31(X1,mark(X2)) >= U31(X1,X2) constraint: U31(X1,active(X2)) >= U31(X1,X2) constraint: U41(mark(X1),X2) >= U41(X1,X2) constraint: U41(active(X1),X2) >= U41(X1,X2) constraint: U41(X1,mark(X2)) >= U41(X1,X2) constraint: U41(X1,active(X2)) >= U41(X1,X2) constraint: U52(mark(X1),X2,X3) >= U52(X1,X2,X3) constraint: U52(active(X1),X2,X3) >= U52(X1,X2,X3) constraint: U52(X1,mark(X2),X3) >= U52(X1,X2,X3) constraint: U52(X1,active(X2),X3) >= U52(X1,X2,X3) constraint: U52(X1,X2,mark(X3)) >= U52(X1,X2,X3) constraint: U52(X1,X2,active(X3)) >= U52(X1,X2,X3) constraint: U51(mark(X1),X2,X3) >= U51(X1,X2,X3) constraint: U51(active(X1),X2,X3) >= U51(X1,X2,X3) constraint: U51(X1,mark(X2),X3) >= U51(X1,X2,X3) constraint: U51(X1,active(X2),X3) >= U51(X1,X2,X3) constraint: U51(X1,X2,mark(X3)) >= U51(X1,X2,X3) constraint: U51(X1,X2,active(X3)) >= U51(X1,X2,X3) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: plus(mark(X1),X2) >= plus(X1,X2) constraint: plus(active(X1),X2) >= plus(X1,X2) constraint: plus(X1,mark(X2)) >= plus(X1,X2) constraint: plus(X1,active(X2)) >= plus(X1,X2) constraint: U61(mark(X)) >= U61(X) constraint: U61(active(X)) >= U61(X) constraint: U72(mark(X1),X2,X3) >= U72(X1,X2,X3) constraint: U72(active(X1),X2,X3) >= U72(X1,X2,X3) constraint: U72(X1,mark(X2),X3) >= U72(X1,X2,X3) constraint: U72(X1,active(X2),X3) >= U72(X1,X2,X3) constraint: U72(X1,X2,mark(X3)) >= U72(X1,X2,X3) constraint: U72(X1,X2,active(X3)) >= U72(X1,X2,X3) constraint: U71(mark(X1),X2,X3) >= U71(X1,X2,X3) constraint: U71(active(X1),X2,X3) >= U71(X1,X2,X3) constraint: U71(X1,mark(X2),X3) >= U71(X1,X2,X3) constraint: U71(X1,active(X2),X3) >= U71(X1,X2,X3) constraint: U71(X1,X2,mark(X3)) >= U71(X1,X2,X3) constraint: U71(X1,X2,active(X3)) >= U71(X1,X2,X3) constraint: x(mark(X1),X2) >= x(X1,X2) constraint: x(active(X1),X2) >= x(X1,X2) constraint: x(X1,mark(X2)) >= x(X1,X2) constraint: x(X1,active(X2)) >= x(X1,X2) constraint: Marked_mark(U12(X)) >= Marked_mark(X) constraint: Marked_mark(U12(X)) >= Marked_active(U12(mark(X))) constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X)) constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2)) constraint: Marked_mark(U21(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X)) >= Marked_active(U21(mark(X))) constraint: Marked_mark(U32(X)) >= Marked_mark(X) constraint: Marked_mark(U32(X)) >= Marked_active(U32(mark(X))) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) constraint: Marked_mark(U41(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U41(X1,X2)) >= Marked_active(U41(mark(X1),X2)) constraint: Marked_mark(U52(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U52(X1,X2,X3)) >= Marked_active(U52(mark(X1),X2,X3)) constraint: Marked_mark(U51(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U51(X1,X2,X3)) >= Marked_active(U51(mark(X1),X2,X3)) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(s(X)) >= Marked_active(s(mark(X))) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) constraint: Marked_mark(U61(X)) >= Marked_mark(X) constraint: Marked_mark(U61(X)) >= Marked_active(U61(mark(X))) constraint: Marked_mark(U72(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U72(X1,X2,X3)) >= Marked_active(U72(mark(X1),X2,X3)) constraint: Marked_mark(U71(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U71(X1,X2,X3)) >= Marked_active(U71(mark(X1),X2,X3)) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(x(X1,X2)) >= Marked_active(x(mark(X1),mark(X2))) constraint: Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNat(V1))) constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(isNat(V1),V2)) constraint: Marked_active(isNat(x(V1,V2))) >= Marked_mark(U31(isNat(V1),V2)) constraint: Marked_active(U11(tt,V2)) >= Marked_mark(U12(isNat(V2))) constraint: Marked_active(U31(tt,V2)) >= Marked_mark(U32(isNat(V2))) constraint: Marked_active(U41(tt,N)) >= Marked_mark(N) constraint: Marked_active(U52(tt,M,N)) >= Marked_mark(s(plus(N,M))) constraint: Marked_active(U51(tt,M,N)) >= Marked_mark(U52(isNat(N),M,N)) constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U51(isNat(M),M,N)) constraint: Marked_active(plus(N,0)) >= Marked_mark(U41(isNat(N),N)) constraint: Marked_active(U72(tt,M,N)) >= Marked_mark(plus(x(N,M),N)) constraint: Marked_active(U71(tt,M,N)) >= Marked_mark(U72(isNat(N),M,N)) constraint: Marked_active(x(N,s(M))) >= Marked_mark(U71(isNat(M),M,N)) constraint: Marked_active(x(N,0)) >= Marked_mark(U61(isNat(N))) APPLY CRITERIA (Subterm criterion) ST: Marked_U11 -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_U12 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_isNat -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U21 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U31 -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_U32 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U41 -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_U51 -> 3 APPLY CRITERIA (Subterm criterion) ST: Marked_U52 -> 3 APPLY CRITERIA (Subterm criterion) ST: Marked_s -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_plus -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_U61 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U71 -> 3 APPLY CRITERIA (Subterm criterion) ST: Marked_U72 -> 3 APPLY CRITERIA (Subterm criterion) ST: Marked_x -> 2 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X)) >= active(U12(mark(X))) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ; mark(tt) >= active(tt) ; mark(U21(X)) >= active(U21(mark(X))) ; mark(U32(X)) >= active(U32(mark(X))) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(U41(X1,X2)) >= active(U41(mark(X1),X2)) ; mark(U52(X1,X2,X3)) >= active(U52(mark(X1),X2,X3)) ; mark(U51(X1,X2,X3)) >= active(U51(mark(X1),X2,X3)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(0) >= active(0) ; mark(U61(X)) >= active(U61(mark(X))) ; mark(U72(X1,X2,X3)) >= active(U72(mark(X1),X2,X3)) ; mark(U71(X1,X2,X3)) >= active(U71(mark(X1),X2,X3)) ; mark(x(X1,X2)) >= active(x(mark(X1),mark(X2))) ; U12(mark(X)) >= U12(X) ; U12(active(X)) >= U12(X) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt)) >= mark(tt) ; 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(U21(tt)) >= mark(tt) ; active(U32(tt)) >= mark(tt) ; active(U31(tt,V2)) >= mark(U32(isNat(V2))) ; active(U41(tt,N)) >= mark(N) ; active(U52(tt,M,N)) >= mark(s(plus(N,M))) ; active(U51(tt,M,N)) >= mark(U52(isNat(N),M,N)) ; active(plus(N,s(M))) >= mark(U51(isNat(M),M,N)) ; active(plus(N,0)) >= mark(U41(isNat(N),N)) ; active(U61(tt)) >= mark(0) ; active(U72(tt,M,N)) >= mark(plus(x(N,M),N)) ; active(U71(tt,M,N)) >= mark(U72(isNat(N),M,N)) ; active(x(N,s(M))) >= mark(U71(isNat(M),M,N)) ; active(x(N,0)) >= mark(U61(isNat(N))) ; U11(mark(X1),X2) >= U11(X1,X2) ; U11(active(X1),X2) >= U11(X1,X2) ; U11(X1,mark(X2)) >= U11(X1,X2) ; U11(X1,active(X2)) >= U11(X1,X2) ; U21(mark(X)) >= U21(X) ; U21(active(X)) >= U21(X) ; U32(mark(X)) >= U32(X) ; U32(active(X)) >= U32(X) ; U31(mark(X1),X2) >= U31(X1,X2) ; U31(active(X1),X2) >= U31(X1,X2) ; U31(X1,mark(X2)) >= U31(X1,X2) ; U31(X1,active(X2)) >= U31(X1,X2) ; U41(mark(X1),X2) >= U41(X1,X2) ; U41(active(X1),X2) >= U41(X1,X2) ; U41(X1,mark(X2)) >= U41(X1,X2) ; U41(X1,active(X2)) >= U41(X1,X2) ; U52(mark(X1),X2,X3) >= U52(X1,X2,X3) ; U52(active(X1),X2,X3) >= U52(X1,X2,X3) ; U52(X1,mark(X2),X3) >= U52(X1,X2,X3) ; U52(X1,active(X2),X3) >= U52(X1,X2,X3) ; U52(X1,X2,mark(X3)) >= U52(X1,X2,X3) ; U52(X1,X2,active(X3)) >= U52(X1,X2,X3) ; U51(mark(X1),X2,X3) >= U51(X1,X2,X3) ; U51(active(X1),X2,X3) >= U51(X1,X2,X3) ; U51(X1,mark(X2),X3) >= U51(X1,X2,X3) ; U51(X1,active(X2),X3) >= U51(X1,X2,X3) ; U51(X1,X2,mark(X3)) >= U51(X1,X2,X3) ; U51(X1,X2,active(X3)) >= U51(X1,X2,X3) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; plus(mark(X1),X2) >= plus(X1,X2) ; plus(active(X1),X2) >= plus(X1,X2) ; plus(X1,mark(X2)) >= plus(X1,X2) ; plus(X1,active(X2)) >= plus(X1,X2) ; U61(mark(X)) >= U61(X) ; U61(active(X)) >= U61(X) ; U72(mark(X1),X2,X3) >= U72(X1,X2,X3) ; U72(active(X1),X2,X3) >= U72(X1,X2,X3) ; U72(X1,mark(X2),X3) >= U72(X1,X2,X3) ; U72(X1,active(X2),X3) >= U72(X1,X2,X3) ; U72(X1,X2,mark(X3)) >= U72(X1,X2,X3) ; U72(X1,X2,active(X3)) >= U72(X1,X2,X3) ; U71(mark(X1),X2,X3) >= U71(X1,X2,X3) ; U71(active(X1),X2,X3) >= U71(X1,X2,X3) ; U71(X1,mark(X2),X3) >= U71(X1,X2,X3) ; U71(X1,active(X2),X3) >= U71(X1,X2,X3) ; U71(X1,X2,mark(X3)) >= U71(X1,X2,X3) ; U71(X1,X2,active(X3)) >= U71(X1,X2,X3) ; x(mark(X1),X2) >= x(X1,X2) ; x(active(X1),X2) >= x(X1,X2) ; x(X1,mark(X2)) >= x(X1,X2) ; x(X1,active(X2)) >= x(X1,X2) ; Marked_mark(U12(X)) >= Marked_mark(X) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2)) ; Marked_mark(U21(X)) >= Marked_mark(X) ; Marked_mark(U32(X)) >= Marked_mark(X) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(U41(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U41(X1,X2)) >= Marked_active(U41(mark(X1),X2)) ; Marked_mark(U52(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U52(X1,X2,X3)) >= Marked_active(U52(mark(X1),X2,X3)) ; Marked_mark(U51(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U51(X1,X2,X3)) >= Marked_active(U51(mark(X1),X2,X3)) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) ; Marked_mark(U61(X)) >= Marked_mark(X) ; Marked_mark(U72(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U72(X1,X2,X3)) >= Marked_active(U72(mark(X1),X2,X3)) ; Marked_mark(U71(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U71(X1,X2,X3)) >= Marked_active(U71(mark(X1),X2,X3)) ; Marked_mark(x(X1,X2)) >= Marked_mark(X1) ; Marked_mark(x(X1,X2)) >= Marked_mark(X2) ; Marked_mark(x(X1,X2)) >= Marked_active(x(mark(X1),mark(X2))) ; Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNat(V1))) ; Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(isNat(V1),V2)) ; Marked_active(isNat(x(V1,V2))) >= Marked_mark(U31(isNat(V1),V2)) ; Marked_active(U11(tt,V2)) >= Marked_mark(U12(isNat(V2))) ; Marked_active(U31(tt,V2)) >= Marked_mark(U32(isNat(V2))) ; Marked_active(U41(tt,N)) >= Marked_mark(N) ; Marked_active(U52(tt,M,N)) >= Marked_mark(s(plus(N,M))) ; Marked_active(U51(tt,M,N)) >= Marked_mark(U52(isNat(N),M,N)) ; Marked_active(plus(N,s(M))) >= Marked_mark(U51(isNat(M),M,N)) ; Marked_active(plus(N,0)) >= Marked_mark(U41(isNat(N),N)) ; Marked_active(U72(tt,M,N)) >= Marked_mark(plus(x(N,M),N)) ; Marked_active(U71(tt,M,N)) >= Marked_mark(U72(isNat(N),M,N)) ; Marked_active(x(N,s(M))) >= Marked_mark(U71(isNat(M),M,N)) ; Marked_active(x(N,0)) >= Marked_mark(U61(isNat(N))) ; } + Disjunctions:{ { Marked_mark(U12(X)) > Marked_mark(X) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U11(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2)) > Marked_active(U11(mark(X1),X2)) ; } { Marked_mark(U21(X)) > Marked_mark(X) ; } { Marked_mark(U32(X)) > Marked_mark(X) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(U41(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U41(X1,X2)) > Marked_active(U41(mark(X1),X2)) ; } { Marked_mark(U52(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U52(X1,X2,X3)) > Marked_active(U52(mark(X1),X2,X3)) ; } { Marked_mark(U51(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U51(X1,X2,X3)) > Marked_active(U51(mark(X1),X2,X3)) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(plus(X1,X2)) > Marked_active(plus(mark(X1),mark(X2))) ; } { Marked_mark(U61(X)) > Marked_mark(X) ; } { Marked_mark(U72(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U72(X1,X2,X3)) > Marked_active(U72(mark(X1),X2,X3)) ; } { Marked_mark(U71(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U71(X1,X2,X3)) > Marked_active(U71(mark(X1),X2,X3)) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(x(X1,X2)) > Marked_active(x(mark(X1),mark(X2))) ; } { Marked_active(isNat(s(V1))) > Marked_mark(U21(isNat(V1))) ; } { Marked_active(isNat(plus(V1,V2))) > Marked_mark(U11(isNat(V1),V2)) ; } { Marked_active(isNat(x(V1,V2))) > Marked_mark(U31(isNat(V1),V2)) ; } { Marked_active(U11(tt,V2)) > Marked_mark(U12(isNat(V2))) ; } { Marked_active(U31(tt,V2)) > Marked_mark(U32(isNat(V2))) ; } { Marked_active(U41(tt,N)) > Marked_mark(N) ; } { Marked_active(U52(tt,M,N)) > Marked_mark(s(plus(N,M))) ; } { Marked_active(U51(tt,M,N)) > Marked_mark(U52(isNat(N),M,N)) ; } { Marked_active(plus(N,s(M))) > Marked_mark(U51(isNat(M),M,N)) ; } { Marked_active(plus(N,0)) > Marked_mark(U41(isNat(N),N)) ; } { Marked_active(U72(tt,M,N)) > Marked_mark(plus(x(N,M),N)) ; } { Marked_active(U71(tt,M,N)) > Marked_mark(U72(isNat(N),M,N)) ; } { Marked_active(x(N,s(M))) > Marked_mark(U71(isNat(M),M,N)) ; } { Marked_active(x(N,0)) > Marked_mark(U61(isNat(N))) ; } } === 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 === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(U12(X)) >= active(U12(mark(X))) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) constraint: mark(tt) >= active(tt) constraint: mark(U21(X)) >= active(U21(mark(X))) constraint: mark(U32(X)) >= active(U32(mark(X))) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(U41(X1,X2)) >= active(U41(mark(X1),X2)) constraint: mark(U52(X1,X2,X3)) >= active(U52(mark(X1),X2,X3)) constraint: mark(U51(X1,X2,X3)) >= active(U51(mark(X1),X2,X3)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(0) >= active(0) constraint: mark(U61(X)) >= active(U61(mark(X))) constraint: mark(U72(X1,X2,X3)) >= active(U72(mark(X1),X2,X3)) constraint: mark(U71(X1,X2,X3)) >= active(U71(mark(X1),X2,X3)) constraint: mark(x(X1,X2)) >= active(x(mark(X1),mark(X2))) constraint: U12(mark(X)) >= U12(X) constraint: U12(active(X)) >= U12(X) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt)) >= mark(tt) constraint: active(isNat(s(V1))) >= mark(U21(isNat(V1))) constraint: active(isNat(plus(V1,V2))) >= mark(U11(isNat(V1),V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(isNat(x(V1,V2))) >= mark(U31(isNat(V1),V2)) constraint: active(U11(tt,V2)) >= mark(U12(isNat(V2))) constraint: active(U21(tt)) >= mark(tt) constraint: active(U32(tt)) >= mark(tt) constraint: active(U31(tt,V2)) >= mark(U32(isNat(V2))) constraint: active(U41(tt,N)) >= mark(N) constraint: active(U52(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(U51(tt,M,N)) >= mark(U52(isNat(N),M,N)) constraint: active(plus(N,s(M))) >= mark(U51(isNat(M),M,N)) constraint: active(plus(N,0)) >= mark(U41(isNat(N),N)) constraint: active(U61(tt)) >= mark(0) constraint: active(U72(tt,M,N)) >= mark(plus(x(N,M),N)) constraint: active(U71(tt,M,N)) >= mark(U72(isNat(N),M,N)) constraint: active(x(N,s(M))) >= mark(U71(isNat(M),M,N)) constraint: active(x(N,0)) >= mark(U61(isNat(N))) constraint: U11(mark(X1),X2) >= U11(X1,X2) constraint: U11(active(X1),X2) >= U11(X1,X2) constraint: U11(X1,mark(X2)) >= U11(X1,X2) constraint: U11(X1,active(X2)) >= U11(X1,X2) constraint: U21(mark(X)) >= U21(X) constraint: U21(active(X)) >= U21(X) constraint: U32(mark(X)) >= U32(X) constraint: U32(active(X)) >= U32(X) constraint: U31(mark(X1),X2) >= U31(X1,X2) constraint: U31(active(X1),X2) >= U31(X1,X2) constraint: U31(X1,mark(X2)) >= U31(X1,X2) constraint: U31(X1,active(X2)) >= U31(X1,X2) constraint: U41(mark(X1),X2) >= U41(X1,X2) constraint: U41(active(X1),X2) >= U41(X1,X2) constraint: U41(X1,mark(X2)) >= U41(X1,X2) constraint: U41(X1,active(X2)) >= U41(X1,X2) constraint: U52(mark(X1),X2,X3) >= U52(X1,X2,X3) constraint: U52(active(X1),X2,X3) >= U52(X1,X2,X3) constraint: U52(X1,mark(X2),X3) >= U52(X1,X2,X3) constraint: U52(X1,active(X2),X3) >= U52(X1,X2,X3) constraint: U52(X1,X2,mark(X3)) >= U52(X1,X2,X3) constraint: U52(X1,X2,active(X3)) >= U52(X1,X2,X3) constraint: U51(mark(X1),X2,X3) >= U51(X1,X2,X3) constraint: U51(active(X1),X2,X3) >= U51(X1,X2,X3) constraint: U51(X1,mark(X2),X3) >= U51(X1,X2,X3) constraint: U51(X1,active(X2),X3) >= U51(X1,X2,X3) constraint: U51(X1,X2,mark(X3)) >= U51(X1,X2,X3) constraint: U51(X1,X2,active(X3)) >= U51(X1,X2,X3) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: plus(mark(X1),X2) >= plus(X1,X2) constraint: plus(active(X1),X2) >= plus(X1,X2) constraint: plus(X1,mark(X2)) >= plus(X1,X2) constraint: plus(X1,active(X2)) >= plus(X1,X2) constraint: U61(mark(X)) >= U61(X) constraint: U61(active(X)) >= U61(X) constraint: U72(mark(X1),X2,X3) >= U72(X1,X2,X3) constraint: U72(active(X1),X2,X3) >= U72(X1,X2,X3) constraint: U72(X1,mark(X2),X3) >= U72(X1,X2,X3) constraint: U72(X1,active(X2),X3) >= U72(X1,X2,X3) constraint: U72(X1,X2,mark(X3)) >= U72(X1,X2,X3) constraint: U72(X1,X2,active(X3)) >= U72(X1,X2,X3) constraint: U71(mark(X1),X2,X3) >= U71(X1,X2,X3) constraint: U71(active(X1),X2,X3) >= U71(X1,X2,X3) constraint: U71(X1,mark(X2),X3) >= U71(X1,X2,X3) constraint: U71(X1,active(X2),X3) >= U71(X1,X2,X3) constraint: U71(X1,X2,mark(X3)) >= U71(X1,X2,X3) constraint: U71(X1,X2,active(X3)) >= U71(X1,X2,X3) constraint: x(mark(X1),X2) >= x(X1,X2) constraint: x(active(X1),X2) >= x(X1,X2) constraint: x(X1,mark(X2)) >= x(X1,X2) constraint: x(X1,active(X2)) >= x(X1,X2) constraint: Marked_mark(U12(X)) >= Marked_mark(X) constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X)) constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2)) constraint: Marked_mark(U21(X)) >= Marked_mark(X) constraint: Marked_mark(U32(X)) >= Marked_mark(X) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) constraint: Marked_mark(U41(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U41(X1,X2)) >= Marked_active(U41(mark(X1),X2)) constraint: Marked_mark(U52(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U52(X1,X2,X3)) >= Marked_active(U52(mark(X1),X2,X3)) constraint: Marked_mark(U51(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U51(X1,X2,X3)) >= Marked_active(U51(mark(X1),X2,X3)) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) constraint: Marked_mark(U61(X)) >= Marked_mark(X) constraint: Marked_mark(U72(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U72(X1,X2,X3)) >= Marked_active(U72(mark(X1),X2,X3)) constraint: Marked_mark(U71(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U71(X1,X2,X3)) >= Marked_active(U71(mark(X1),X2,X3)) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(x(X1,X2)) >= Marked_active(x(mark(X1),mark(X2))) constraint: Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNat(V1))) constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(isNat(V1),V2)) constraint: Marked_active(isNat(x(V1,V2))) >= Marked_mark(U31(isNat(V1),V2)) constraint: Marked_active(U11(tt,V2)) >= Marked_mark(U12(isNat(V2))) constraint: Marked_active(U31(tt,V2)) >= Marked_mark(U32(isNat(V2))) constraint: Marked_active(U41(tt,N)) >= Marked_mark(N) constraint: Marked_active(U52(tt,M,N)) >= Marked_mark(s(plus(N,M))) constraint: Marked_active(U51(tt,M,N)) >= Marked_mark(U52(isNat(N),M,N)) constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U51(isNat(M),M,N)) constraint: Marked_active(plus(N,0)) >= Marked_mark(U41(isNat(N),N)) constraint: Marked_active(U72(tt,M,N)) >= Marked_mark(plus(x(N,M),N)) constraint: Marked_active(U71(tt,M,N)) >= Marked_mark(U72(isNat(N),M,N)) constraint: Marked_active(x(N,s(M))) >= Marked_mark(U71(isNat(M),M,N)) constraint: Marked_active(x(N,0)) >= Marked_mark(U61(isNat(N))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X)) >= active(U12(mark(X))) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2)) >= active(U11(mark(X1),X2)) ; mark(tt) >= active(tt) ; mark(U21(X)) >= active(U21(mark(X))) ; mark(U32(X)) >= active(U32(mark(X))) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(U41(X1,X2)) >= active(U41(mark(X1),X2)) ; mark(U52(X1,X2,X3)) >= active(U52(mark(X1),X2,X3)) ; mark(U51(X1,X2,X3)) >= active(U51(mark(X1),X2,X3)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(0) >= active(0) ; mark(U61(X)) >= active(U61(mark(X))) ; mark(U72(X1,X2,X3)) >= active(U72(mark(X1),X2,X3)) ; mark(U71(X1,X2,X3)) >= active(U71(mark(X1),X2,X3)) ; mark(x(X1,X2)) >= active(x(mark(X1),mark(X2))) ; U12(mark(X)) >= U12(X) ; U12(active(X)) >= U12(X) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt)) >= mark(tt) ; 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(U21(tt)) >= mark(tt) ; active(U32(tt)) >= mark(tt) ; active(U31(tt,V2)) >= mark(U32(isNat(V2))) ; active(U41(tt,N)) >= mark(N) ; active(U52(tt,M,N)) >= mark(s(plus(N,M))) ; active(U51(tt,M,N)) >= mark(U52(isNat(N),M,N)) ; active(plus(N,s(M))) >= mark(U51(isNat(M),M,N)) ; active(plus(N,0)) >= mark(U41(isNat(N),N)) ; active(U61(tt)) >= mark(0) ; active(U72(tt,M,N)) >= mark(plus(x(N,M),N)) ; active(U71(tt,M,N)) >= mark(U72(isNat(N),M,N)) ; active(x(N,s(M))) >= mark(U71(isNat(M),M,N)) ; active(x(N,0)) >= mark(U61(isNat(N))) ; U11(mark(X1),X2) >= U11(X1,X2) ; U11(active(X1),X2) >= U11(X1,X2) ; U11(X1,mark(X2)) >= U11(X1,X2) ; U11(X1,active(X2)) >= U11(X1,X2) ; U21(mark(X)) >= U21(X) ; U21(active(X)) >= U21(X) ; U32(mark(X)) >= U32(X) ; U32(active(X)) >= U32(X) ; U31(mark(X1),X2) >= U31(X1,X2) ; U31(active(X1),X2) >= U31(X1,X2) ; U31(X1,mark(X2)) >= U31(X1,X2) ; U31(X1,active(X2)) >= U31(X1,X2) ; U41(mark(X1),X2) >= U41(X1,X2) ; U41(active(X1),X2) >= U41(X1,X2) ; U41(X1,mark(X2)) >= U41(X1,X2) ; U41(X1,active(X2)) >= U41(X1,X2) ; U52(mark(X1),X2,X3) >= U52(X1,X2,X3) ; U52(active(X1),X2,X3) >= U52(X1,X2,X3) ; U52(X1,mark(X2),X3) >= U52(X1,X2,X3) ; U52(X1,active(X2),X3) >= U52(X1,X2,X3) ; U52(X1,X2,mark(X3)) >= U52(X1,X2,X3) ; U52(X1,X2,active(X3)) >= U52(X1,X2,X3) ; U51(mark(X1),X2,X3) >= U51(X1,X2,X3) ; U51(active(X1),X2,X3) >= U51(X1,X2,X3) ; U51(X1,mark(X2),X3) >= U51(X1,X2,X3) ; U51(X1,active(X2),X3) >= U51(X1,X2,X3) ; U51(X1,X2,mark(X3)) >= U51(X1,X2,X3) ; U51(X1,X2,active(X3)) >= U51(X1,X2,X3) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; plus(mark(X1),X2) >= plus(X1,X2) ; plus(active(X1),X2) >= plus(X1,X2) ; plus(X1,mark(X2)) >= plus(X1,X2) ; plus(X1,active(X2)) >= plus(X1,X2) ; U61(mark(X)) >= U61(X) ; U61(active(X)) >= U61(X) ; U72(mark(X1),X2,X3) >= U72(X1,X2,X3) ; U72(active(X1),X2,X3) >= U72(X1,X2,X3) ; U72(X1,mark(X2),X3) >= U72(X1,X2,X3) ; U72(X1,active(X2),X3) >= U72(X1,X2,X3) ; U72(X1,X2,mark(X3)) >= U72(X1,X2,X3) ; U72(X1,X2,active(X3)) >= U72(X1,X2,X3) ; U71(mark(X1),X2,X3) >= U71(X1,X2,X3) ; U71(active(X1),X2,X3) >= U71(X1,X2,X3) ; U71(X1,mark(X2),X3) >= U71(X1,X2,X3) ; U71(X1,active(X2),X3) >= U71(X1,X2,X3) ; U71(X1,X2,mark(X3)) >= U71(X1,X2,X3) ; U71(X1,X2,active(X3)) >= U71(X1,X2,X3) ; x(mark(X1),X2) >= x(X1,X2) ; x(active(X1),X2) >= x(X1,X2) ; x(X1,mark(X2)) >= x(X1,X2) ; x(X1,active(X2)) >= x(X1,X2) ; Marked_mark(U12(X)) >= Marked_mark(X) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2)) >= Marked_active(U11(mark(X1),X2)) ; Marked_mark(U21(X)) >= Marked_mark(X) ; Marked_mark(U32(X)) >= Marked_mark(X) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(U41(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U41(X1,X2)) >= Marked_active(U41(mark(X1),X2)) ; Marked_mark(U52(X1,X2,X3)) >= Marked_active(U52(mark(X1),X2,X3)) ; Marked_mark(U51(X1,X2,X3)) >= Marked_active(U51(mark(X1),X2,X3)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) ; Marked_mark(U61(X)) >= Marked_mark(X) ; Marked_mark(U72(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U72(X1,X2,X3)) >= Marked_active(U72(mark(X1),X2,X3)) ; Marked_mark(U71(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U71(X1,X2,X3)) >= Marked_active(U71(mark(X1),X2,X3)) ; Marked_mark(x(X1,X2)) >= Marked_mark(X1) ; Marked_mark(x(X1,X2)) >= Marked_mark(X2) ; Marked_mark(x(X1,X2)) >= Marked_active(x(mark(X1),mark(X2))) ; Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNat(V1))) ; Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(isNat(V1),V2)) ; Marked_active(isNat(x(V1,V2))) >= Marked_mark(U31(isNat(V1),V2)) ; Marked_active(U11(tt,V2)) >= Marked_mark(U12(isNat(V2))) ; Marked_active(U31(tt,V2)) >= Marked_mark(U32(isNat(V2))) ; Marked_active(U41(tt,N)) >= Marked_mark(N) ; Marked_active(U52(tt,M,N)) >= Marked_mark(s(plus(N,M))) ; Marked_active(U51(tt,M,N)) >= Marked_mark(U52(isNat(N),M,N)) ; Marked_active(plus(N,s(M))) >= Marked_mark(U51(isNat(M),M,N)) ; Marked_active(plus(N,0)) >= Marked_mark(U41(isNat(N),N)) ; Marked_active(U72(tt,M,N)) >= Marked_mark(plus(x(N,M),N)) ; Marked_active(U71(tt,M,N)) >= Marked_mark(U72(isNat(N),M,N)) ; Marked_active(x(N,0)) >= Marked_mark(U61(isNat(N))) ; } + Disjunctions:{ { Marked_mark(U12(X)) > Marked_mark(X) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U11(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2)) > Marked_active(U11(mark(X1),X2)) ; } { Marked_mark(U21(X)) > Marked_mark(X) ; } { Marked_mark(U32(X)) > Marked_mark(X) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(U41(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U41(X1,X2)) > Marked_active(U41(mark(X1),X2)) ; } { Marked_mark(U52(X1,X2,X3)) > Marked_active(U52(mark(X1),X2,X3)) ; } { Marked_mark(U51(X1,X2,X3)) > Marked_active(U51(mark(X1),X2,X3)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(plus(X1,X2)) > Marked_active(plus(mark(X1),mark(X2))) ; } { Marked_mark(U61(X)) > Marked_mark(X) ; } { Marked_mark(U72(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U72(X1,X2,X3)) > Marked_active(U72(mark(X1),X2,X3)) ; } { Marked_mark(U71(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U71(X1,X2,X3)) > Marked_active(U71(mark(X1),X2,X3)) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(x(X1,X2)) > Marked_active(x(mark(X1),mark(X2))) ; } { Marked_active(isNat(s(V1))) > Marked_mark(U21(isNat(V1))) ; } { Marked_active(isNat(plus(V1,V2))) > Marked_mark(U11(isNat(V1),V2)) ; } { Marked_active(isNat(x(V1,V2))) > Marked_mark(U31(isNat(V1),V2)) ; } { Marked_active(U11(tt,V2)) > Marked_mark(U12(isNat(V2))) ; } { Marked_active(U31(tt,V2)) > Marked_mark(U32(isNat(V2))) ; } { Marked_active(U41(tt,N)) > Marked_mark(N) ; } { Marked_active(U52(tt,M,N)) > Marked_mark(s(plus(N,M))) ; } { Marked_active(U51(tt,M,N)) > Marked_mark(U52(isNat(N),M,N)) ; } { Marked_active(plus(N,s(M))) > Marked_mark(U51(isNat(M),M,N)) ; } { Marked_active(plus(N,0)) > Marked_mark(U41(isNat(N),N)) ; } { Marked_active(U72(tt,M,N)) > Marked_mark(plus(x(N,M),N)) ; } { Marked_active(U71(tt,M,N)) > Marked_mark(U72(isNat(N),M,N)) ; } { Marked_active(x(N,0)) > Marked_mark(U61(isNat(N))) ; } } === 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 === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. Global timeout: 300.000000