- : unit = () - : 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,N)) -> mark(N) [7] active(U41(tt,M,N)) -> mark(s(plus(N,M))) [8] active(and(tt,X)) -> mark(X) [9] active(isNat(0)) -> mark(tt) [10] active(isNat(plus(V1,V2))) -> mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2)) [11] active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) [12] active(isNatKind(0)) -> mark(tt) [13] active(isNatKind(plus(V1,V2))) -> mark(and(isNatKind(V1),isNatKind(V2))) [14] active(isNatKind(s(V1))) -> mark(isNatKind(V1)) [15] active(plus(N,0)) -> mark(U31(and(isNat(N),isNatKind(N)),N)) [16] active(plus(N,s(M))) -> mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)) [17] mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) [18] mark(tt) -> active(tt) [19] mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) [20] mark(isNat(X)) -> active(isNat(X)) [21] mark(U13(X)) -> active(U13(mark(X))) [22] mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) [23] mark(U22(X)) -> active(U22(mark(X))) [24] mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) [25] mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) [26] mark(s(X)) -> active(s(mark(X))) [27] mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) [28] mark(and(X1,X2)) -> active(and(mark(X1),X2)) [29] mark(0) -> active(0) [30] mark(isNatKind(X)) -> active(isNatKind(X)) [31] U11(mark(X1),X2,X3) -> U11(X1,X2,X3) [32] U11(X1,mark(X2),X3) -> U11(X1,X2,X3) [33] U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) [34] U11(active(X1),X2,X3) -> U11(X1,X2,X3) [35] U11(X1,active(X2),X3) -> U11(X1,X2,X3) [36] U11(X1,X2,active(X3)) -> U11(X1,X2,X3) [37] U12(mark(X1),X2) -> U12(X1,X2) [38] U12(X1,mark(X2)) -> U12(X1,X2) [39] U12(active(X1),X2) -> U12(X1,X2) [40] U12(X1,active(X2)) -> U12(X1,X2) [41] isNat(mark(X)) -> isNat(X) [42] isNat(active(X)) -> isNat(X) [43] U13(mark(X)) -> U13(X) [44] U13(active(X)) -> U13(X) [45] U21(mark(X1),X2) -> U21(X1,X2) [46] U21(X1,mark(X2)) -> U21(X1,X2) [47] U21(active(X1),X2) -> U21(X1,X2) [48] U21(X1,active(X2)) -> U21(X1,X2) [49] U22(mark(X)) -> U22(X) [50] U22(active(X)) -> U22(X) [51] U31(mark(X1),X2) -> U31(X1,X2) [52] U31(X1,mark(X2)) -> U31(X1,X2) [53] U31(active(X1),X2) -> U31(X1,X2) [54] U31(X1,active(X2)) -> U31(X1,X2) [55] U41(mark(X1),X2,X3) -> U41(X1,X2,X3) [56] U41(X1,mark(X2),X3) -> U41(X1,X2,X3) [57] U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) [58] U41(active(X1),X2,X3) -> U41(X1,X2,X3) [59] U41(X1,active(X2),X3) -> U41(X1,X2,X3) [60] U41(X1,X2,active(X3)) -> U41(X1,X2,X3) [61] s(mark(X)) -> s(X) [62] s(active(X)) -> s(X) [63] plus(mark(X1),X2) -> plus(X1,X2) [64] plus(X1,mark(X2)) -> plus(X1,X2) [65] plus(active(X1),X2) -> plus(X1,X2) [66] plus(X1,active(X2)) -> plus(X1,X2) [67] and(mark(X1),X2) -> and(X1,X2) [68] and(X1,mark(X2)) -> and(X1,X2) [69] and(active(X1),X2) -> and(X1,X2) [70] and(X1,active(X2)) -> and(X1,X2) [71] isNatKind(mark(X)) -> isNatKind(X) [72] isNatKind(active(X)) -> isNatKind(X) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 13 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U13(X)) >= Marked_active(U13(mark(X))) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U22(X)) >= Marked_active(U22(mark(X))) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; 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(U41(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNatKind(V1),V1)) ; Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(plus(N,s(M))) >= Marked_mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) ; Marked_active(plus(N,0)) >= Marked_mark(U31(and(isNat(N),isNatKind(N)),N)) ; Marked_active(U41(tt,M,N)) >= Marked_mark(s(plus(N,M))) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U13(X)) > Marked_active(U13(mark(X))) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U22(X)) > Marked_active(U22(mark(X))) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { 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(U41(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U41(X1,X2,X3)) > Marked_active(U41(mark(X1),X2,X3)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(isNat(s(V1))) > Marked_mark(U21(isNatKind(V1),V1)) ; } { Marked_active(isNat(plus(V1,V2))) > Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U21(tt,V1)) > Marked_mark(U22(isNat(V1))) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(plus(N,s(M))) > Marked_mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) ; } { Marked_active(plus(N,0)) > Marked_mark(U31(and(isNat(N),isNatKind(N)),N)) ; } { Marked_active(U41(tt,M,N)) > Marked_mark(s(plus(N,M))) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U13(X)) >= Marked_active(U13(mark(X))) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U22(X)) >= Marked_active(U22(mark(X))) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) 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(U41(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNatKind(V1),V1)) constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and( isNatKind( V1), isNatKind(V2)), V1,V2)) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U41(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M,N)) constraint: Marked_active(plus(N,0)) >= Marked_mark(U31(and(isNat(N), isNatKind(N)), N)) constraint: Marked_active(U41(tt,M,N)) >= Marked_mark(s(plus(N,M))) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Subterm criterion) ST: Marked_U11 -> 3 APPLY CRITERIA (Subterm criterion) ST: Marked_U12 -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_isNat -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U13 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U21 -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_U22 -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_U31 -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_U41 -> 3 APPLY CRITERIA (Subterm criterion) ST: Marked_s -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_plus -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_and -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_isNatKind -> 1 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U13(X)) >= Marked_active(U13(mark(X))) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U22(X)) >= Marked_active(U22(mark(X))) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; 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(U41(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNatKind(V1),V1)) ; Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(plus(N,s(M))) >= Marked_mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) ; Marked_active(U41(tt,M,N)) >= Marked_mark(s(plus(N,M))) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U13(X)) > Marked_active(U13(mark(X))) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U22(X)) > Marked_active(U22(mark(X))) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { 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(U41(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U41(X1,X2,X3)) > Marked_active(U41(mark(X1),X2,X3)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(isNat(s(V1))) > Marked_mark(U21(isNatKind(V1),V1)) ; } { Marked_active(isNat(plus(V1,V2))) > Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U21(tt,V1)) > Marked_mark(U22(isNat(V1))) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(plus(N,s(M))) > Marked_mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) ; } { Marked_active(U41(tt,M,N)) > Marked_mark(s(plus(N,M))) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U13(X)) >= Marked_active(U13(mark(X))) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U22(X)) >= Marked_active(U22(mark(X))) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) 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(U41(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNatKind(V1),V1)) constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and( isNatKind( V1), isNatKind(V2)), V1,V2)) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U41(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M,N)) constraint: Marked_active(U41(tt,M,N)) >= Marked_mark(s(plus(N,M))) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; 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(U41(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNatKind(V1),V1)) ; Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(plus(N,s(M))) >= Marked_mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) ; Marked_active(U41(tt,M,N)) >= Marked_mark(s(plus(N,M))) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { 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(U41(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U41(X1,X2,X3)) > Marked_active(U41(mark(X1),X2,X3)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(isNat(s(V1))) > Marked_mark(U21(isNatKind(V1),V1)) ; } { Marked_active(isNat(plus(V1,V2))) > Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U21(tt,V1)) > Marked_mark(U22(isNat(V1))) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(plus(N,s(M))) > Marked_mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) ; } { Marked_active(U41(tt,M,N)) > Marked_mark(s(plus(N,M))) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) 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(U41(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNatKind(V1),V1)) constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and( isNatKind( V1), isNatKind(V2)), V1,V2)) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U41(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M,N)) constraint: Marked_active(U41(tt,M,N)) >= Marked_mark(s(plus(N,M))) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; 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(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNatKind(V1),V1)) ; Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(U41(tt,M,N)) >= Marked_mark(s(plus(N,M))) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { 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(U41(X1,X2,X3)) > Marked_active(U41(mark(X1),X2,X3)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(isNat(s(V1))) > Marked_mark(U21(isNatKind(V1),V1)) ; } { Marked_active(isNat(plus(V1,V2))) > Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U21(tt,V1)) > Marked_mark(U22(isNat(V1))) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(U41(tt,M,N)) > Marked_mark(s(plus(N,M))) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) 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(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNatKind(V1),V1)) constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and( isNatKind( V1), isNatKind(V2)), V1,V2)) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(U41(tt,M,N)) >= Marked_mark(s(plus(N,M))) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNatKind(V1),V1)) ; Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(U41(tt,M,N)) >= Marked_mark(s(plus(N,M))) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(U41(X1,X2,X3)) > Marked_active(U41(mark(X1),X2,X3)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(isNat(s(V1))) > Marked_mark(U21(isNatKind(V1),V1)) ; } { Marked_active(isNat(plus(V1,V2))) > Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U21(tt,V1)) > Marked_mark(U22(isNat(V1))) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(U41(tt,M,N)) > Marked_mark(s(plus(N,M))) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(isNat(s(V1))) >= Marked_mark(U21(isNatKind(V1),V1)) constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and( isNatKind( V1), isNatKind(V2)), V1,V2)) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(U41(tt,M,N)) >= Marked_mark(s(plus(N,M))) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(U41(tt,M,N)) >= Marked_mark(s(plus(N,M))) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(U41(X1,X2,X3)) > Marked_active(U41(mark(X1),X2,X3)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(isNat(plus(V1,V2))) > Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U21(tt,V1)) > Marked_mark(U22(isNat(V1))) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(U41(tt,M,N)) > Marked_mark(s(plus(N,M))) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and( isNatKind( V1), isNatKind(V2)), V1,V2)) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(U41(tt,M,N)) >= Marked_mark(s(plus(N,M))) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(U41(X1,X2,X3)) > Marked_active(U41(mark(X1),X2,X3)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(isNat(plus(V1,V2))) > Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U21(tt,V1)) > Marked_mark(U22(isNat(V1))) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(U41(X1,X2,X3)) >= Marked_active(U41(mark(X1),X2,X3)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and( isNatKind( V1), isNatKind(V2)), V1,V2)) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(isNat(plus(V1,V2))) > Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U21(tt,V1)) > Marked_mark(U22(isNat(V1))) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and( isNatKind( V1), isNatKind(V2)), V1,V2)) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(isNat(plus(V1,V2))) > Marked_mark(U11(and(isNatKind(V1), isNatKind(V2)), V1,V2)) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U21(tt,V1)) > Marked_mark(U22(isNat(V1))) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(isNat(plus(V1,V2))) >= Marked_mark(U11(and( isNatKind( V1), isNatKind(V2)), V1,V2)) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(isNat(X)) >= Marked_active(isNat(X)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(isNat(X)) > Marked_active(isNat(X)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U21(tt,V1)) > Marked_mark(U22(isNat(V1))) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(isNat(X)) >= Marked_active(isNat(X)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U22(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U22(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U21(tt,V1)) > Marked_mark(U22(isNat(V1))) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U22(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U21(tt,V1)) > Marked_mark(U22(isNat(V1))) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U21(tt,V1)) >= Marked_mark(U22(isNat(V1))) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) ; Marked_mark(U31(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U21(X1,X2)) > Marked_active(U21(mark(X1),X2)) ; } { Marked_mark(U31(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U21(X1,X2)) >= Marked_active(U21(mark(X1),X2)) constraint: Marked_mark(U31(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(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(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(U31(tt,N)) >= Marked_mark(N) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(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(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(U31(tt,N)) > Marked_mark(N) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(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(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(U31(tt,N)) >= Marked_mark(N) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(U31(X1,X2)) > Marked_active(U31(mark(X1),X2)) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(U31(X1,X2)) >= Marked_active(U31(mark(X1),X2)) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(s(V1))) > Marked_mark(isNatKind(V1)) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(s(V1))) >= Marked_mark(isNatKind(V1)) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and(isNatKind(V1), isNatKind(V2))) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(isNatKind(plus(V1,V2))) > Marked_mark(and(isNatKind(V1), isNatKind(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(isNatKind(plus(V1,V2))) >= Marked_mark(and( isNatKind( V1), isNatKind(V2))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(isNatKind(X)) > Marked_active(isNatKind(X)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(isNatKind(X)) >= Marked_active(isNatKind(X)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(V1),V2)) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_active(U12(tt,V2)) > Marked_mark(U13(isNat(V2))) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_active(U12(tt,V2)) >= Marked_mark(U13(isNat(V2))) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2)) > Marked_active(U12(mark(X1),X2)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2)) >= Marked_active(U12(mark(X1),X2)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) ; mark(isNat(X)) >= active(isNat(X)) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U13(X)) >= active(U13(mark(X))) ; mark(U22(X)) >= active(U22(mark(X))) ; mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) ; mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) ; mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(0) >= active(0) ; mark(isNatKind(X)) >= active(isNatKind(X)) ; U12(mark(X1),X2) >= U12(X1,X2) ; U12(active(X1),X2) >= U12(X1,X2) ; U12(X1,mark(X2)) >= U12(X1,X2) ; U12(X1,active(X2)) >= U12(X1,X2) ; isNat(mark(X)) >= isNat(X) ; isNat(active(X)) >= isNat(X) ; active(U12(tt,V2)) >= mark(U13(isNat(V2))) ; 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(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) ; active(U13(tt)) >= mark(tt) ; active(U22(tt)) >= mark(tt) ; active(U21(tt,V1)) >= mark(U22(isNat(V1))) ; active(U31(tt,N)) >= mark(N) ; active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))),M,N)) ; active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) ; active(U41(tt,M,N)) >= mark(s(plus(N,M))) ; active(and(tt,X)) >= mark(X) ; active(isNatKind(s(V1))) >= mark(isNatKind(V1)) ; active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1),isNatKind(V2))) ; active(isNatKind(0)) >= mark(tt) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; U13(mark(X)) >= U13(X) ; U13(active(X)) >= U13(X) ; U22(mark(X)) >= U22(X) ; U22(active(X)) >= U22(X) ; U21(mark(X1),X2) >= U21(X1,X2) ; U21(active(X1),X2) >= U21(X1,X2) ; U21(X1,mark(X2)) >= U21(X1,X2) ; U21(X1,active(X2)) >= U21(X1,X2) ; 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) ; 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) ; U41(mark(X1),X2,X3) >= U41(X1,X2,X3) ; U41(active(X1),X2,X3) >= U41(X1,X2,X3) ; U41(X1,mark(X2),X3) >= U41(X1,X2,X3) ; U41(X1,active(X2),X3) >= U41(X1,X2,X3) ; U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) ; U41(X1,X2,active(X3)) >= U41(X1,X2,X3) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; isNatKind(mark(X)) >= isNatKind(X) ; isNatKind(active(X)) >= isNatKind(X) ; Marked_mark(U12(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(U13(X)) >= Marked_mark(X) ; Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(U13(X)) > Marked_mark(X) ; } { Marked_active(U11(tt,V1,V2)) > Marked_mark(U12(isNat(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: mark(U12(X1,X2)) >= active(U12(mark(X1),X2)) constraint: mark(isNat(X)) >= active(isNat(X)) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U13(X)) >= active(U13(mark(X))) constraint: mark(U22(X)) >= active(U22(mark(X))) constraint: mark(U21(X1,X2)) >= active(U21(mark(X1),X2)) constraint: mark(U31(X1,X2)) >= active(U31(mark(X1),X2)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(U41(X1,X2,X3)) >= active(U41(mark(X1),X2,X3)) constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(isNatKind(X)) >= active(isNatKind(X)) constraint: U12(mark(X1),X2) >= U12(X1,X2) constraint: U12(active(X1),X2) >= U12(X1,X2) constraint: U12(X1,mark(X2)) >= U12(X1,X2) constraint: U12(X1,active(X2)) >= U12(X1,X2) constraint: isNat(mark(X)) >= isNat(X) constraint: isNat(active(X)) >= isNat(X) constraint: active(U12(tt,V2)) >= mark(U13(isNat(V2))) constraint: active(isNat(s(V1))) >= mark(U21(isNatKind(V1),V1)) constraint: active(isNat(plus(V1,V2))) >= mark(U11(and(isNatKind(V1), isNatKind(V2)),V1, V2)) constraint: active(isNat(0)) >= mark(tt) constraint: active(U11(tt,V1,V2)) >= mark(U12(isNat(V1),V2)) constraint: active(U13(tt)) >= mark(tt) constraint: active(U22(tt)) >= mark(tt) constraint: active(U21(tt,V1)) >= mark(U22(isNat(V1))) constraint: active(U31(tt,N)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(U41(and(and(isNat(M),isNatKind(M)), and(isNat(N),isNatKind(N))), M,N)) constraint: active(plus(N,0)) >= mark(U31(and(isNat(N),isNatKind(N)),N)) constraint: active(U41(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(and(tt,X)) >= mark(X) constraint: active(isNatKind(s(V1))) >= mark(isNatKind(V1)) constraint: active(isNatKind(plus(V1,V2))) >= mark(and(isNatKind(V1), isNatKind(V2))) constraint: active(isNatKind(0)) >= mark(tt) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: U13(mark(X)) >= U13(X) constraint: U13(active(X)) >= U13(X) constraint: U22(mark(X)) >= U22(X) constraint: U22(active(X)) >= U22(X) constraint: U21(mark(X1),X2) >= U21(X1,X2) constraint: U21(active(X1),X2) >= U21(X1,X2) constraint: U21(X1,mark(X2)) >= U21(X1,X2) constraint: U21(X1,active(X2)) >= U21(X1,X2) 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: 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: U41(mark(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(active(X1),X2,X3) >= U41(X1,X2,X3) constraint: U41(X1,mark(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,active(X2),X3) >= U41(X1,X2,X3) constraint: U41(X1,X2,mark(X3)) >= U41(X1,X2,X3) constraint: U41(X1,X2,active(X3)) >= U41(X1,X2,X3) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: isNatKind(mark(X)) >= isNatKind(X) constraint: isNatKind(active(X)) >= isNatKind(X) constraint: Marked_mark(U12(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(U13(X)) >= Marked_mark(X) constraint: Marked_active(U11(tt,V1,V2)) >= Marked_mark(U12(isNat(V1),V2)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_mark -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_U11 -> 2 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_U11 -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_U12 -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_U21 -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_U31 -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_U41 -> 2 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_U41 -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_plus -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_and -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { 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,N)) -> mark(N) [7] active(U41(tt,M,N)) -> mark(s(plus(N,M))) [8] active(and(tt,X)) -> mark(X) [9] active(isNat(0)) -> mark(tt) [10] active(isNat(plus(V1,V2))) -> mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2)) [11] active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) [12] active(isNatKind(0)) -> mark(tt) [13] active(isNatKind(plus(V1,V2))) -> mark(and(isNatKind(V1),isNatKind(V2))) [14] active(isNatKind(s(V1))) -> mark(isNatKind(V1)) [15] active(plus(N,0)) -> mark(U31(and(isNat(N),isNatKind(N)),N)) [16] active(plus(N,s(M))) -> mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)) [17] mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) [18] mark(tt) -> active(tt) [19] mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) [20] mark(isNat(X)) -> active(isNat(X)) [21] mark(U13(X)) -> active(U13(mark(X))) [22] mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) [23] mark(U22(X)) -> active(U22(mark(X))) [24] mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) [25] mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) [26] mark(s(X)) -> active(s(mark(X))) [27] mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) [28] mark(and(X1,X2)) -> active(and(mark(X1),X2)) [29] mark(0) -> active(0) [30] mark(isNatKind(X)) -> active(isNatKind(X)) [31] U11(mark(X1),X2,X3) -> U11(X1,X2,X3) [32] U11(X1,mark(X2),X3) -> U11(X1,X2,X3) [33] U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) [34] U11(active(X1),X2,X3) -> U11(X1,X2,X3) [35] U11(X1,active(X2),X3) -> U11(X1,X2,X3) [36] U11(X1,X2,active(X3)) -> U11(X1,X2,X3) [37] U12(mark(X1),X2) -> U12(X1,X2) [38] U12(X1,mark(X2)) -> U12(X1,X2) [39] U12(active(X1),X2) -> U12(X1,X2) [40] U12(X1,active(X2)) -> U12(X1,X2) [41] isNat(mark(X)) -> isNat(X) [42] isNat(active(X)) -> isNat(X) [43] U13(mark(X)) -> U13(X) [44] U13(active(X)) -> U13(X) [45] U21(mark(X1),X2) -> U21(X1,X2) [46] U21(X1,mark(X2)) -> U21(X1,X2) [47] U21(active(X1),X2) -> U21(X1,X2) [48] U21(X1,active(X2)) -> U21(X1,X2) [49] U22(mark(X)) -> U22(X) [50] U22(active(X)) -> U22(X) [51] U31(mark(X1),X2) -> U31(X1,X2) [52] U31(X1,mark(X2)) -> U31(X1,X2) [53] U31(active(X1),X2) -> U31(X1,X2) [54] U31(X1,active(X2)) -> U31(X1,X2) [55] U41(mark(X1),X2,X3) -> U41(X1,X2,X3) [56] U41(X1,mark(X2),X3) -> U41(X1,X2,X3) [57] U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) [58] U41(active(X1),X2,X3) -> U41(X1,X2,X3) [59] U41(X1,active(X2),X3) -> U41(X1,X2,X3) [60] U41(X1,X2,active(X3)) -> U41(X1,X2,X3) [61] s(mark(X)) -> s(X) [62] s(active(X)) -> s(X) [63] plus(mark(X1),X2) -> plus(X1,X2) [64] plus(X1,mark(X2)) -> plus(X1,X2) [65] plus(active(X1),X2) -> plus(X1,X2) [66] plus(X1,active(X2)) -> plus(X1,X2) [67] and(mark(X1),X2) -> and(X1,X2) [68] and(X1,mark(X2)) -> and(X1,X2) [69] and(active(X1),X2) -> and(X1,X2) [70] and(X1,active(X2)) -> and(X1,X2) [71] isNatKind(mark(X)) -> isNatKind(X) [72] isNatKind(active(X)) -> isNatKind(X) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 1*X0; [ U11 ] (X0,X1,X2) = 1*X0; [ U41 ] (X0,X1,X2) = 2*X2 + 1*X1 + 1*X0; [ Marked_mark ] (X0) = 2*X0; [ isNat ] (X0) = 0; [ s ] (X0) = 1*X0; [ U13 ] (X0) = 2*X0; [ 0 ] () = 1; [ U12 ] (X0,X1) = 1*X0; [ U31 ] (X0,X1) = 2*X1 + 2*X0; [ tt ] () = 0; [ and ] (X0,X1) = 2*X1 + 2*X0; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 1*X1 + 2*X0; [ U22 ] (X0) = 2*X0; [ isNatKind ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ U21 ] (X0,X1) = 1; [ U11 ] (X0,X1,X2) = 1; [ U41 ] (X0,X1,X2) = 1; [ Marked_mark ] (X0) = 2; [ isNat ] (X0) = 1; [ s ] (X0) = 0; [ U13 ] (X0) = 0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 1; [ U31 ] (X0,X1) = 1; [ tt ] () = 0; [ and ] (X0,X1) = 1; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 0; [ plus ] (X0,X1) = 1; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 2*X0; [ U11 ] (X0,X1,X2) = 2*X0; [ U41 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0 + 2; [ Marked_mark ] (X0) = 2*X0; [ isNat ] (X0) = 0; [ s ] (X0) = 1*X0 + 2; [ U13 ] (X0) = 2*X0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 1*X0; [ U31 ] (X0,X1) = 2*X1 + 2*X0; [ tt ] () = 0; [ and ] (X0,X1) = 2*X1 + 2*X0; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 2*X1 + 2*X0; [ U22 ] (X0) = 2*X0; [ isNatKind ] (X0) = 0; removing < Marked_mark(s(X)),Marked_mark(X)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ U21 ] (X0,X1) = 2; [ U11 ] (X0,X1,X2) = 2; [ U41 ] (X0,X1,X2) = 2; [ Marked_mark ] (X0) = 2; [ isNat ] (X0) = 2; [ s ] (X0) = 0; [ U13 ] (X0) = 0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 2; [ U31 ] (X0,X1) = 2; [ tt ] () = 0; [ and ] (X0,X1) = 2; [ Marked_active ] (X0) = 1*X0; [ active ] (X0) = 0; [ plus ] (X0,X1) = 0; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 1*X1 + 2*X0; [ U11 ] (X0,X1,X2) = 2*X2 + 3*X1 + 1*X0; [ U41 ] (X0,X1,X2) = 3*X2 + 2*X1 + 2; [ Marked_mark ] (X0) = 2*X0; [ isNat ] (X0) = 1*X0; [ s ] (X0) = 1*X0 + 2; [ U13 ] (X0) = 1*X0; [ 0 ] () = 2; [ U12 ] (X0,X1) = 2*X1 + 2*X0; [ U31 ] (X0,X1) = 1*X1 + 2*X0; [ tt ] () = 0; [ and ] (X0,X1) = 2*X1 + 1*X0; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 2*X1 + 3*X0; [ U22 ] (X0) = 1*X0; [ isNatKind ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 2*X0; [ U11 ] (X0,X1,X2) = 2*X0; [ U41 ] (X0,X1,X2) = 3; [ Marked_mark ] (X0) = 2*X0; [ isNat ] (X0) = 0; [ s ] (X0) = 2; [ U13 ] (X0) = 2*X0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 2*X0; [ U31 ] (X0,X1) = 1*X1 + 2*X0; [ tt ] () = 0; [ and ] (X0,X1) = 2*X1 + 2*X0; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 2*X1 + 1*X0; [ U22 ] (X0) = 2*X0; [ isNatKind ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ U21 ] (X0,X1) = 1; [ U11 ] (X0,X1,X2) = 1; [ U41 ] (X0,X1,X2) = 0; [ Marked_mark ] (X0) = 2; [ isNat ] (X0) = 1; [ s ] (X0) = 0; [ U13 ] (X0) = 0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 1; [ U31 ] (X0,X1) = 1; [ tt ] () = 0; [ and ] (X0,X1) = 1; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 0; [ plus ] (X0,X1) = 0; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 1*X0; [ U11 ] (X0,X1,X2) = 2*X0; [ U41 ] (X0,X1,X2) = 1; [ Marked_mark ] (X0) = 2*X0; [ isNat ] (X0) = 0; [ s ] (X0) = 0; [ U13 ] (X0) = 1*X0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 1*X0; [ U31 ] (X0,X1) = 1*X1 + 1*X0; [ tt ] () = 0; [ and ] (X0,X1) = 2*X1 + 1*X0; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 1*X1 + 1*X0 + 2; [ U22 ] (X0) = 2*X0; [ isNatKind ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 2*X1 + 2*X0; [ U11 ] (X0,X1,X2) = 2*X2 + 2*X1 + 1*X0; [ U41 ] (X0,X1,X2) = 3*X2 + 1*X1 + 2; [ Marked_mark ] (X0) = 2*X0; [ isNat ] (X0) = 2*X0; [ s ] (X0) = 1*X0; [ U13 ] (X0) = 1*X0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 2*X1 + 1*X0; [ U31 ] (X0,X1) = 1*X1 + 1*X0; [ tt ] () = 0; [ and ] (X0,X1) = 2*X1 + 1*X0; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 1*X1 + 3*X0 + 2; [ U22 ] (X0) = 1*X0; [ isNatKind ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ U21 ] (X0,X1) = 1; [ U11 ] (X0,X1,X2) = 1; [ U41 ] (X0,X1,X2) = 0; [ Marked_mark ] (X0) = 2; [ isNat ] (X0) = 0; [ s ] (X0) = 0; [ U13 ] (X0) = 0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 1; [ U31 ] (X0,X1) = 1; [ tt ] () = 0; [ and ] (X0,X1) = 1; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 0; [ plus ] (X0,X1) = 0; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 1*X1 + 2*X0 + 2; [ U11 ] (X0,X1,X2) = 2*X2 + 3*X1 + 2*X0; [ U41 ] (X0,X1,X2) = 3*X2 + 2*X1 + 3; [ Marked_mark ] (X0) = 2*X0; [ isNat ] (X0) = 1*X0; [ s ] (X0) = 1*X0 + 2; [ U13 ] (X0) = 1*X0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 2*X1 + 2*X0; [ U31 ] (X0,X1) = 1*X1 + 1*X0; [ tt ] () = 0; [ and ] (X0,X1) = 1*X1 + 2*X0; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 2*X1 + 3*X0; [ U22 ] (X0) = 1*X0 + 2; [ isNatKind ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 1; [ U11 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0; [ U41 ] (X0,X1,X2) = 3; [ Marked_mark ] (X0) = 2*X0; [ isNat ] (X0) = 1*X0; [ s ] (X0) = 2; [ U13 ] (X0) = 1*X0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 1*X1 + 2*X0; [ U31 ] (X0,X1) = 1*X1 + 2*X0; [ tt ] () = 0; [ and ] (X0,X1) = 2*X1 + 1*X0; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 2*X1 + 3*X0; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ U21 ] (X0,X1) = 0; [ U11 ] (X0,X1,X2) = 2; [ U41 ] (X0,X1,X2) = 0; [ Marked_mark ] (X0) = 2; [ isNat ] (X0) = 0; [ s ] (X0) = 0; [ U13 ] (X0) = 0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 2; [ U31 ] (X0,X1) = 2; [ tt ] () = 0; [ and ] (X0,X1) = 2; [ Marked_active ] (X0) = 1*X0; [ active ] (X0) = 0; [ plus ] (X0,X1) = 0; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 0; [ U11 ] (X0,X1,X2) = 2*X0; [ U41 ] (X0,X1,X2) = 2*X2; [ Marked_mark ] (X0) = 2*X0; [ isNat ] (X0) = 0; [ s ] (X0) = 0; [ U13 ] (X0) = 2*X0; [ 0 ] () = 1; [ U12 ] (X0,X1) = 2*X0; [ U31 ] (X0,X1) = 2*X1 + 2*X0 + 1; [ tt ] () = 0; [ and ] (X0,X1) = 2*X1 + 2*X0; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 1*X1 + 2*X0; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ U21 ] (X0,X1) = 0; [ U11 ] (X0,X1,X2) = 2; [ U41 ] (X0,X1,X2) = 0; [ Marked_mark ] (X0) = 2; [ isNat ] (X0) = 0; [ s ] (X0) = 0; [ U13 ] (X0) = 0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 2; [ U31 ] (X0,X1) = 0; [ tt ] () = 0; [ and ] (X0,X1) = 2; [ Marked_active ] (X0) = 1*X0; [ active ] (X0) = 0; [ plus ] (X0,X1) = 0; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 0; [ U11 ] (X0,X1,X2) = 3*X2 + 3*X1 + 2*X0; [ U41 ] (X0,X1,X2) = 3*X2 + 3*X1 + 2; [ Marked_mark ] (X0) = 2*X0; [ isNat ] (X0) = 3*X0; [ s ] (X0) = 1*X0 + 1; [ U13 ] (X0) = 1*X0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 3*X1 + 1*X0; [ U31 ] (X0,X1) = 2*X1; [ tt ] () = 0; [ and ] (X0,X1) = 2*X1 + 2*X0; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 3*X1 + 3*X0; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 1*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 2*X1; [ U11 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0; [ U41 ] (X0,X1,X2) = 3*X2 + 2*X1 + 2; [ Marked_mark ] (X0) = 1*X0; [ isNat ] (X0) = 2*X0; [ s ] (X0) = 1*X0; [ U13 ] (X0) = 1*X0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 2*X1 + 1*X0; [ U31 ] (X0,X1) = 1*X1; [ tt ] () = 0; [ and ] (X0,X1) = 1*X1 + 2*X0; [ Marked_active ] (X0) = 1*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 2*X1 + 3*X0 + 2; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 1*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ U21 ] (X0,X1) = 0; [ U11 ] (X0,X1,X2) = 1; [ U41 ] (X0,X1,X2) = 0; [ Marked_mark ] (X0) = 1; [ isNat ] (X0) = 0; [ s ] (X0) = 0; [ U13 ] (X0) = 0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 1; [ U31 ] (X0,X1) = 0; [ tt ] () = 0; [ and ] (X0,X1) = 1; [ Marked_active ] (X0) = 1*X0; [ active ] (X0) = 0; [ plus ] (X0,X1) = 0; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 0; [ U11 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0; [ U41 ] (X0,X1,X2) = 3*X2 + 3*X1 + 2; [ Marked_mark ] (X0) = 2*X0; [ isNat ] (X0) = 2*X0; [ s ] (X0) = 1*X0; [ U13 ] (X0) = 1*X0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 2*X1 + 1*X0; [ U31 ] (X0,X1) = 2*X1; [ tt ] () = 0; [ and ] (X0,X1) = 1*X1 + 1*X0 + 2; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 3*X1 + 3*X0 + 2; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 2*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ U21 ] (X0,X1) = 0; [ U11 ] (X0,X1,X2) = 1; [ U41 ] (X0,X1,X2) = 0; [ Marked_mark ] (X0) = 1; [ isNat ] (X0) = 0; [ s ] (X0) = 0; [ U13 ] (X0) = 0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 1; [ U31 ] (X0,X1) = 0; [ tt ] () = 0; [ and ] (X0,X1) = 0; [ Marked_active ] (X0) = 1*X0; [ active ] (X0) = 0; [ plus ] (X0,X1) = 0; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 2*X0; [ U11 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ U41 ] (X0,X1,X2) = 2; [ Marked_mark ] (X0) = 2*X0; [ isNat ] (X0) = 1*X0 + 2; [ s ] (X0) = 2; [ U13 ] (X0) = 1*X0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 1*X1 + 2*X0; [ U31 ] (X0,X1) = 1*X1; [ tt ] () = 2; [ and ] (X0,X1) = 1*X1; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 2*X1 + 2*X0 + 2; [ U22 ] (X0) = 3; [ isNatKind ] (X0) = 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ U21 ] (X0,X1) = 0; [ U11 ] (X0,X1,X2) = 1; [ U41 ] (X0,X1,X2) = 0; [ Marked_mark ] (X0) = 3; [ isNat ] (X0) = 0; [ s ] (X0) = 0; [ U13 ] (X0) = 0; [ 0 ] () = 0; [ U12 ] (X0,X1) = 0; [ U31 ] (X0,X1) = 0; [ tt ] () = 0; [ and ] (X0,X1) = 0; [ Marked_active ] (X0) = 2*X0 + 1; [ active ] (X0) = 0; [ plus ] (X0,X1) = 0; [ U22 ] (X0) = 0; [ isNatKind ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U21 ] (X0,X1) = 2; [ U11 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ U41 ] (X0,X1,X2) = 2*X2 + 3*X1 + 3; [ Marked_mark ] (X0) = 2*X0 + 3; [ isNat ] (X0) = 1*X0 + 2; [ s ] (X0) = 1*X0 + 1; [ U13 ] (X0) = 1*X0; [ 0 ] () = 2; [ U12 ] (X0,X1) = 1*X1 + 1*X0; [ U31 ] (X0,X1) = 1*X1; [ tt ] () = 2; [ and ] (X0,X1) = 1*X1; [ Marked_active ] (X0) = 2*X0; [ active ] (X0) = 1*X0; [ plus ] (X0,X1) = 3*X1 + 2*X0; [ U22 ] (X0) = 2; [ isNatKind ] (X0) = 1*X0; removing < Marked_mark(U11(X1,X2,X3)),Marked_active(U11(mark(X1),X2,X3))> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 11.809891 seconds (real time) Cime Exit Status: 0