- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] U101(tt,M,N) -> U102(isNatKind(activate(M)),activate(M),activate(N)) [2] U102(tt,M,N) -> U103(isNat(activate(N)),activate(M),activate(N)) [3] U103(tt,M,N) -> U104(isNatKind(activate(N)),activate(M),activate(N)) [4] U104(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) [5] U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) [6] U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) [7] U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) [8] U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) [9] U15(tt,V2) -> U16(isNat(activate(V2))) [10] U16(tt) -> tt [11] U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) [12] U22(tt,V1) -> U23(isNat(activate(V1))) [13] U23(tt) -> tt [14] U31(tt,V1,V2) -> U32(isNatKind(activate(V1)),activate(V1),activate(V2)) [15] U32(tt,V1,V2) -> U33(isNatKind(activate(V2)),activate(V1),activate(V2)) [16] U33(tt,V1,V2) -> U34(isNatKind(activate(V2)),activate(V1),activate(V2)) [17] U34(tt,V1,V2) -> U35(isNat(activate(V1)),activate(V2)) [18] U35(tt,V2) -> U36(isNat(activate(V2))) [19] U36(tt) -> tt [20] U41(tt,V2) -> U42(isNatKind(activate(V2))) [21] U42(tt) -> tt [22] U51(tt) -> tt [23] U61(tt,V2) -> U62(isNatKind(activate(V2))) [24] U62(tt) -> tt [25] U71(tt,N) -> U72(isNatKind(activate(N)),activate(N)) [26] U72(tt,N) -> activate(N) [27] U81(tt,M,N) -> U82(isNatKind(activate(M)),activate(M),activate(N)) [28] U82(tt,M,N) -> U83(isNat(activate(N)),activate(M),activate(N)) [29] U83(tt,M,N) -> U84(isNatKind(activate(N)),activate(M),activate(N)) [30] U84(tt,M,N) -> s(plus(activate(N),activate(M))) [31] U91(tt,N) -> U92(isNatKind(activate(N))) [32] U92(tt) -> 0 [33] isNat(n__0) -> tt [34] isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) [35] isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) [36] isNat(n__x(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V1),activate(V2)) [37] isNatKind(n__0) -> tt [38] isNatKind(n__plus(V1,V2)) -> U41(isNatKind(activate(V1)),activate(V2)) [39] isNatKind(n__s(V1)) -> U51(isNatKind(activate(V1))) [40] isNatKind(n__x(V1,V2)) -> U61(isNatKind(activate(V1)),activate(V2)) [41] plus(N,0) -> U71(isNat(N),N) [42] plus(N,s(M)) -> U81(isNat(M),M,N) [43] x(N,0) -> U91(isNat(N),N) [44] x(N,s(M)) -> U101(isNat(M),M,N) [45] 0 -> n__0 [46] plus(X1,X2) -> n__plus(X1,X2) [47] s(X) -> n__s(X) [48] x(X1,X2) -> n__x(X1,X2) [49] activate(n__0) -> 0 [50] activate(n__plus(X1,X2)) -> plus(X1,X2) [51] activate(n__s(X)) -> s(X) [52] activate(n__x(X1,X2)) -> x(X1,X2) [53] activate(X) -> X Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { U102(tt,M,N) >= U103(isNat(activate(N)),activate(M),activate(N)) ; isNatKind(n__0) >= tt ; isNatKind(n__plus(V1,V2)) >= U41(isNatKind(activate(V1)),activate(V2)) ; isNatKind(n__s(V1)) >= U51(isNatKind(activate(V1))) ; isNatKind(n__x(V1,V2)) >= U61(isNatKind(activate(V1)),activate(V2)) ; activate(n__0) >= 0 ; activate(n__plus(X1,X2)) >= plus(X1,X2) ; activate(n__s(X)) >= s(X) ; activate(n__x(X1,X2)) >= x(X1,X2) ; activate(X) >= X ; U101(tt,M,N) >= U102(isNatKind(activate(M)),activate(M),activate(N)) ; U103(tt,M,N) >= U104(isNatKind(activate(N)),activate(M),activate(N)) ; isNat(n__0) >= tt ; isNat(n__plus(V1,V2)) >= U11(isNatKind(activate(V1)),activate(V1), activate(V2)) ; isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) ; isNat(n__x(V1,V2)) >= U31(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U104(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ; plus(N,s(M)) >= U81(isNat(M),M,N) ; plus(N,0) >= U71(isNat(N),N) ; plus(X1,X2) >= n__plus(X1,X2) ; x(N,s(M)) >= U101(isNat(M),M,N) ; x(N,0) >= U91(isNat(N),N) ; x(X1,X2) >= n__x(X1,X2) ; U12(tt,V1,V2) >= U13(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U11(tt,V1,V2) >= U12(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U13(tt,V1,V2) >= U14(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U14(tt,V1,V2) >= U15(isNat(activate(V1)),activate(V2)) ; U15(tt,V2) >= U16(isNat(activate(V2))) ; U16(tt) >= tt ; U22(tt,V1) >= U23(isNat(activate(V1))) ; U21(tt,V1) >= U22(isNatKind(activate(V1)),activate(V1)) ; U23(tt) >= tt ; U32(tt,V1,V2) >= U33(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U31(tt,V1,V2) >= U32(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U33(tt,V1,V2) >= U34(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U34(tt,V1,V2) >= U35(isNat(activate(V1)),activate(V2)) ; U35(tt,V2) >= U36(isNat(activate(V2))) ; U36(tt) >= tt ; U42(tt) >= tt ; U41(tt,V2) >= U42(isNatKind(activate(V2))) ; U51(tt) >= tt ; U62(tt) >= tt ; U61(tt,V2) >= U62(isNatKind(activate(V2))) ; U72(tt,N) >= activate(N) ; U71(tt,N) >= U72(isNatKind(activate(N)),activate(N)) ; U82(tt,M,N) >= U83(isNat(activate(N)),activate(M),activate(N)) ; U81(tt,M,N) >= U82(isNatKind(activate(M)),activate(M),activate(N)) ; U83(tt,M,N) >= U84(isNatKind(activate(N)),activate(M),activate(N)) ; U84(tt,M,N) >= s(plus(activate(N),activate(M))) ; s(X) >= n__s(X) ; U92(tt) >= 0 ; U91(tt,N) >= U92(isNatKind(activate(N))) ; 0 >= n__0 ; Marked_activate(n__plus(X1,X2)) >= Marked_plus(X1,X2) ; Marked_activate(n__x(X1,X2)) >= Marked_x(X1,X2) ; Marked_x(N,s(M)) >= Marked_U101(isNat(M),M,N) ; Marked_x(N,s(M)) >= Marked_isNat(M) ; Marked_x(N,0) >= Marked_isNat(N) ; Marked_x(N,0) >= Marked_U91(isNat(N),N) ; Marked_plus(N,s(M)) >= Marked_isNat(M) ; Marked_plus(N,s(M)) >= Marked_U81(isNat(M),M,N) ; Marked_plus(N,0) >= Marked_isNat(N) ; Marked_plus(N,0) >= Marked_U71(isNat(N),N) ; Marked_U101(tt,M,N) >= Marked_activate(M) ; Marked_U101(tt,M,N) >= Marked_activate(N) ; Marked_U101(tt,M,N) >= Marked_isNatKind(activate(M)) ; Marked_U101(tt,M,N) >= Marked_U102(isNatKind(activate(M)),activate(M), activate(N)) ; Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V1) ; Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V2) ; Marked_isNat(n__plus(V1,V2)) >= Marked_isNatKind(activate(V1)) ; Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNatKind(activate(V1)), activate(V1),activate(V2)) ; Marked_isNat(n__s(V1)) >= Marked_activate(V1) ; Marked_isNat(n__s(V1)) >= Marked_isNatKind(activate(V1)) ; Marked_isNat(n__s(V1)) >= Marked_U21(isNatKind(activate(V1)),activate(V1)) ; Marked_isNat(n__x(V1,V2)) >= Marked_activate(V1) ; Marked_isNat(n__x(V1,V2)) >= Marked_activate(V2) ; Marked_isNat(n__x(V1,V2)) >= Marked_isNatKind(activate(V1)) ; Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNatKind(activate(V1)),activate(V1), activate(V2)) ; Marked_U91(tt,N) >= Marked_activate(N) ; Marked_U91(tt,N) >= Marked_isNatKind(activate(N)) ; Marked_U81(tt,M,N) >= Marked_activate(M) ; Marked_U81(tt,M,N) >= Marked_activate(N) ; Marked_U81(tt,M,N) >= Marked_isNatKind(activate(M)) ; Marked_U81(tt,M,N) >= Marked_U82(isNatKind(activate(M)),activate(M), activate(N)) ; Marked_U71(tt,N) >= Marked_activate(N) ; Marked_U71(tt,N) >= Marked_isNatKind(activate(N)) ; Marked_U71(tt,N) >= Marked_U72(isNatKind(activate(N)),activate(N)) ; Marked_isNatKind(n__plus(V1,V2)) >= Marked_activate(V1) ; Marked_isNatKind(n__plus(V1,V2)) >= Marked_activate(V2) ; Marked_isNatKind(n__plus(V1,V2)) >= Marked_isNatKind(activate(V1)) ; Marked_isNatKind(n__plus(V1,V2)) >= Marked_U41(isNatKind(activate(V1)), activate(V2)) ; Marked_isNatKind(n__s(V1)) >= Marked_activate(V1) ; Marked_isNatKind(n__s(V1)) >= Marked_isNatKind(activate(V1)) ; Marked_isNatKind(n__x(V1,V2)) >= Marked_activate(V1) ; Marked_isNatKind(n__x(V1,V2)) >= Marked_activate(V2) ; Marked_isNatKind(n__x(V1,V2)) >= Marked_isNatKind(activate(V1)) ; Marked_isNatKind(n__x(V1,V2)) >= Marked_U61(isNatKind(activate(V1)), activate(V2)) ; Marked_U61(tt,V2) >= Marked_activate(V2) ; Marked_U61(tt,V2) >= Marked_isNatKind(activate(V2)) ; Marked_U41(tt,V2) >= Marked_activate(V2) ; Marked_U41(tt,V2) >= Marked_isNatKind(activate(V2)) ; Marked_U31(tt,V1,V2) >= Marked_activate(V1) ; Marked_U31(tt,V1,V2) >= Marked_activate(V2) ; Marked_U31(tt,V1,V2) >= Marked_isNatKind(activate(V1)) ; Marked_U31(tt,V1,V2) >= Marked_U32(isNatKind(activate(V1)),activate(V1), activate(V2)) ; Marked_U21(tt,V1) >= Marked_activate(V1) ; Marked_U21(tt,V1) >= Marked_isNatKind(activate(V1)) ; Marked_U21(tt,V1) >= Marked_U22(isNatKind(activate(V1)),activate(V1)) ; Marked_U11(tt,V1,V2) >= Marked_activate(V1) ; Marked_U11(tt,V1,V2) >= Marked_activate(V2) ; Marked_U11(tt,V1,V2) >= Marked_isNatKind(activate(V1)) ; Marked_U11(tt,V1,V2) >= Marked_U12(isNatKind(activate(V1)),activate(V1), activate(V2)) ; Marked_U84(tt,M,N) >= Marked_activate(M) ; Marked_U84(tt,M,N) >= Marked_activate(N) ; Marked_U84(tt,M,N) >= Marked_plus(activate(N),activate(M)) ; Marked_U83(tt,M,N) >= Marked_activate(M) ; Marked_U83(tt,M,N) >= Marked_activate(N) ; Marked_U83(tt,M,N) >= Marked_isNatKind(activate(N)) ; Marked_U83(tt,M,N) >= Marked_U84(isNatKind(activate(N)),activate(M), activate(N)) ; Marked_U82(tt,M,N) >= Marked_activate(M) ; Marked_U82(tt,M,N) >= Marked_activate(N) ; Marked_U82(tt,M,N) >= Marked_isNat(activate(N)) ; Marked_U82(tt,M,N) >= Marked_U83(isNat(activate(N)),activate(M),activate(N)) ; Marked_U72(tt,N) >= Marked_activate(N) ; Marked_U35(tt,V2) >= Marked_activate(V2) ; Marked_U35(tt,V2) >= Marked_isNat(activate(V2)) ; Marked_U34(tt,V1,V2) >= Marked_activate(V1) ; Marked_U34(tt,V1,V2) >= Marked_activate(V2) ; Marked_U34(tt,V1,V2) >= Marked_isNat(activate(V1)) ; Marked_U34(tt,V1,V2) >= Marked_U35(isNat(activate(V1)),activate(V2)) ; Marked_U33(tt,V1,V2) >= Marked_activate(V1) ; Marked_U33(tt,V1,V2) >= Marked_activate(V2) ; Marked_U33(tt,V1,V2) >= Marked_isNatKind(activate(V2)) ; Marked_U33(tt,V1,V2) >= Marked_U34(isNatKind(activate(V2)),activate(V1), activate(V2)) ; Marked_U32(tt,V1,V2) >= Marked_activate(V1) ; Marked_U32(tt,V1,V2) >= Marked_activate(V2) ; Marked_U32(tt,V1,V2) >= Marked_isNatKind(activate(V2)) ; Marked_U32(tt,V1,V2) >= Marked_U33(isNatKind(activate(V2)),activate(V1), activate(V2)) ; Marked_U22(tt,V1) >= Marked_activate(V1) ; Marked_U22(tt,V1) >= Marked_isNat(activate(V1)) ; Marked_U15(tt,V2) >= Marked_activate(V2) ; Marked_U15(tt,V2) >= Marked_isNat(activate(V2)) ; Marked_U14(tt,V1,V2) >= Marked_activate(V1) ; Marked_U14(tt,V1,V2) >= Marked_activate(V2) ; Marked_U14(tt,V1,V2) >= Marked_isNat(activate(V1)) ; Marked_U14(tt,V1,V2) >= Marked_U15(isNat(activate(V1)),activate(V2)) ; Marked_U13(tt,V1,V2) >= Marked_activate(V1) ; Marked_U13(tt,V1,V2) >= Marked_activate(V2) ; Marked_U13(tt,V1,V2) >= Marked_isNatKind(activate(V2)) ; Marked_U13(tt,V1,V2) >= Marked_U14(isNatKind(activate(V2)),activate(V1), activate(V2)) ; Marked_U12(tt,V1,V2) >= Marked_activate(V1) ; Marked_U12(tt,V1,V2) >= Marked_activate(V2) ; Marked_U12(tt,V1,V2) >= Marked_isNatKind(activate(V2)) ; Marked_U12(tt,V1,V2) >= Marked_U13(isNatKind(activate(V2)),activate(V1), activate(V2)) ; Marked_U104(tt,M,N) >= Marked_activate(M) ; Marked_U104(tt,M,N) >= Marked_activate(N) ; Marked_U104(tt,M,N) >= Marked_x(activate(N),activate(M)) ; Marked_U104(tt,M,N) >= Marked_plus(x(activate(N),activate(M)),activate(N)) ; Marked_U103(tt,M,N) >= Marked_activate(M) ; Marked_U103(tt,M,N) >= Marked_activate(N) ; Marked_U103(tt,M,N) >= Marked_isNatKind(activate(N)) ; Marked_U103(tt,M,N) >= Marked_U104(isNatKind(activate(N)),activate(M), activate(N)) ; Marked_U102(tt,M,N) >= Marked_activate(M) ; Marked_U102(tt,M,N) >= Marked_activate(N) ; Marked_U102(tt,M,N) >= Marked_isNat(activate(N)) ; Marked_U102(tt,M,N) >= Marked_U103(isNat(activate(N)),activate(M), activate(N)) ; } + Disjunctions:{ { Marked_activate(n__plus(X1,X2)) > Marked_plus(X1,X2) ; } { Marked_activate(n__x(X1,X2)) > Marked_x(X1,X2) ; } { Marked_x(N,s(M)) > Marked_U101(isNat(M),M,N) ; } { Marked_x(N,s(M)) > Marked_isNat(M) ; } { Marked_x(N,0) > Marked_isNat(N) ; } { Marked_x(N,0) > Marked_U91(isNat(N),N) ; } { Marked_plus(N,s(M)) > Marked_isNat(M) ; } { Marked_plus(N,s(M)) > Marked_U81(isNat(M),M,N) ; } { Marked_plus(N,0) > Marked_isNat(N) ; } { Marked_plus(N,0) > Marked_U71(isNat(N),N) ; } { Marked_U101(tt,M,N) > Marked_activate(M) ; } { Marked_U101(tt,M,N) > Marked_activate(N) ; } { Marked_U101(tt,M,N) > Marked_isNatKind(activate(M)) ; } { Marked_U101(tt,M,N) > Marked_U102(isNatKind(activate(M)),activate(M), activate(N)) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_activate(V1) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_activate(V2) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_isNatKind(activate(V1)) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_U11(isNatKind(activate(V1)), activate(V1),activate(V2)) ; } { Marked_isNat(n__s(V1)) > Marked_activate(V1) ; } { Marked_isNat(n__s(V1)) > Marked_isNatKind(activate(V1)) ; } { Marked_isNat(n__s(V1)) > Marked_U21(isNatKind(activate(V1)),activate(V1)) ; } { Marked_isNat(n__x(V1,V2)) > Marked_activate(V1) ; } { Marked_isNat(n__x(V1,V2)) > Marked_activate(V2) ; } { Marked_isNat(n__x(V1,V2)) > Marked_isNatKind(activate(V1)) ; } { Marked_isNat(n__x(V1,V2)) > Marked_U31(isNatKind(activate(V1)),activate(V1), activate(V2)) ; } { Marked_U91(tt,N) > Marked_activate(N) ; } { Marked_U91(tt,N) > Marked_isNatKind(activate(N)) ; } { Marked_U81(tt,M,N) > Marked_activate(M) ; } { Marked_U81(tt,M,N) > Marked_activate(N) ; } { Marked_U81(tt,M,N) > Marked_isNatKind(activate(M)) ; } { Marked_U81(tt,M,N) > Marked_U82(isNatKind(activate(M)),activate(M), activate(N)) ; } { Marked_U71(tt,N) > Marked_activate(N) ; } { Marked_U71(tt,N) > Marked_isNatKind(activate(N)) ; } { Marked_U71(tt,N) > Marked_U72(isNatKind(activate(N)),activate(N)) ; } { Marked_isNatKind(n__plus(V1,V2)) > Marked_activate(V1) ; } { Marked_isNatKind(n__plus(V1,V2)) > Marked_activate(V2) ; } { Marked_isNatKind(n__plus(V1,V2)) > Marked_isNatKind(activate(V1)) ; } { Marked_isNatKind(n__plus(V1,V2)) > Marked_U41(isNatKind(activate(V1)), activate(V2)) ; } { Marked_isNatKind(n__s(V1)) > Marked_activate(V1) ; } { Marked_isNatKind(n__s(V1)) > Marked_isNatKind(activate(V1)) ; } { Marked_isNatKind(n__x(V1,V2)) > Marked_activate(V1) ; } { Marked_isNatKind(n__x(V1,V2)) > Marked_activate(V2) ; } { Marked_isNatKind(n__x(V1,V2)) > Marked_isNatKind(activate(V1)) ; } { Marked_isNatKind(n__x(V1,V2)) > Marked_U61(isNatKind(activate(V1)), activate(V2)) ; } { Marked_U61(tt,V2) > Marked_activate(V2) ; } { Marked_U61(tt,V2) > Marked_isNatKind(activate(V2)) ; } { Marked_U41(tt,V2) > Marked_activate(V2) ; } { Marked_U41(tt,V2) > Marked_isNatKind(activate(V2)) ; } { Marked_U31(tt,V1,V2) > Marked_activate(V1) ; } { Marked_U31(tt,V1,V2) > Marked_activate(V2) ; } { Marked_U31(tt,V1,V2) > Marked_isNatKind(activate(V1)) ; } { Marked_U31(tt,V1,V2) > Marked_U32(isNatKind(activate(V1)),activate(V1), activate(V2)) ; } { Marked_U21(tt,V1) > Marked_activate(V1) ; } { Marked_U21(tt,V1) > Marked_isNatKind(activate(V1)) ; } { Marked_U21(tt,V1) > Marked_U22(isNatKind(activate(V1)),activate(V1)) ; } { Marked_U11(tt,V1,V2) > Marked_activate(V1) ; } { Marked_U11(tt,V1,V2) > Marked_activate(V2) ; } { Marked_U11(tt,V1,V2) > Marked_isNatKind(activate(V1)) ; } { Marked_U11(tt,V1,V2) > Marked_U12(isNatKind(activate(V1)),activate(V1), activate(V2)) ; } { Marked_U84(tt,M,N) > Marked_activate(M) ; } { Marked_U84(tt,M,N) > Marked_activate(N) ; } { Marked_U84(tt,M,N) > Marked_plus(activate(N),activate(M)) ; } { Marked_U83(tt,M,N) > Marked_activate(M) ; } { Marked_U83(tt,M,N) > Marked_activate(N) ; } { Marked_U83(tt,M,N) > Marked_isNatKind(activate(N)) ; } { Marked_U83(tt,M,N) > Marked_U84(isNatKind(activate(N)),activate(M), activate(N)) ; } { Marked_U82(tt,M,N) > Marked_activate(M) ; } { Marked_U82(tt,M,N) > Marked_activate(N) ; } { Marked_U82(tt,M,N) > Marked_isNat(activate(N)) ; } { Marked_U82(tt,M,N) > Marked_U83(isNat(activate(N)),activate(M),activate(N)) ; } { Marked_U72(tt,N) > Marked_activate(N) ; } { Marked_U35(tt,V2) > Marked_activate(V2) ; } { Marked_U35(tt,V2) > Marked_isNat(activate(V2)) ; } { Marked_U34(tt,V1,V2) > Marked_activate(V1) ; } { Marked_U34(tt,V1,V2) > Marked_activate(V2) ; } { Marked_U34(tt,V1,V2) > Marked_isNat(activate(V1)) ; } { Marked_U34(tt,V1,V2) > Marked_U35(isNat(activate(V1)),activate(V2)) ; } { Marked_U33(tt,V1,V2) > Marked_activate(V1) ; } { Marked_U33(tt,V1,V2) > Marked_activate(V2) ; } { Marked_U33(tt,V1,V2) > Marked_isNatKind(activate(V2)) ; } { Marked_U33(tt,V1,V2) > Marked_U34(isNatKind(activate(V2)),activate(V1), activate(V2)) ; } { Marked_U32(tt,V1,V2) > Marked_activate(V1) ; } { Marked_U32(tt,V1,V2) > Marked_activate(V2) ; } { Marked_U32(tt,V1,V2) > Marked_isNatKind(activate(V2)) ; } { Marked_U32(tt,V1,V2) > Marked_U33(isNatKind(activate(V2)),activate(V1), activate(V2)) ; } { Marked_U22(tt,V1) > Marked_activate(V1) ; } { Marked_U22(tt,V1) > Marked_isNat(activate(V1)) ; } { Marked_U15(tt,V2) > Marked_activate(V2) ; } { Marked_U15(tt,V2) > Marked_isNat(activate(V2)) ; } { Marked_U14(tt,V1,V2) > Marked_activate(V1) ; } { Marked_U14(tt,V1,V2) > Marked_activate(V2) ; } { Marked_U14(tt,V1,V2) > Marked_isNat(activate(V1)) ; } { Marked_U14(tt,V1,V2) > Marked_U15(isNat(activate(V1)),activate(V2)) ; } { Marked_U13(tt,V1,V2) > Marked_activate(V1) ; } { Marked_U13(tt,V1,V2) > Marked_activate(V2) ; } { Marked_U13(tt,V1,V2) > Marked_isNatKind(activate(V2)) ; } { Marked_U13(tt,V1,V2) > Marked_U14(isNatKind(activate(V2)),activate(V1), activate(V2)) ; } { Marked_U12(tt,V1,V2) > Marked_activate(V1) ; } { Marked_U12(tt,V1,V2) > Marked_activate(V2) ; } { Marked_U12(tt,V1,V2) > Marked_isNatKind(activate(V2)) ; } { Marked_U12(tt,V1,V2) > Marked_U13(isNatKind(activate(V2)),activate(V1), activate(V2)) ; } { Marked_U104(tt,M,N) > Marked_activate(M) ; } { Marked_U104(tt,M,N) > Marked_activate(N) ; } { Marked_U104(tt,M,N) > Marked_x(activate(N),activate(M)) ; } { Marked_U104(tt,M,N) > Marked_plus(x(activate(N),activate(M)),activate(N)) ; } { Marked_U103(tt,M,N) > Marked_activate(M) ; } { Marked_U103(tt,M,N) > Marked_activate(N) ; } { Marked_U103(tt,M,N) > Marked_isNatKind(activate(N)) ; } { Marked_U103(tt,M,N) > Marked_U104(isNatKind(activate(N)),activate(M), activate(N)) ; } { Marked_U102(tt,M,N) > Marked_activate(M) ; } { Marked_U102(tt,M,N) > Marked_activate(N) ; } { Marked_U102(tt,M,N) > Marked_isNat(activate(N)) ; } { Marked_U102(tt,M,N) > Marked_U103(isNat(activate(N)),activate(M),activate(N)) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: U102(tt,M,N) >= U103(isNat(activate(N)),activate(M),activate(N)) constraint: isNatKind(n__0) >= tt constraint: isNatKind(n__plus(V1,V2)) >= U41(isNatKind(activate(V1)), activate(V2)) constraint: isNatKind(n__s(V1)) >= U51(isNatKind(activate(V1))) constraint: isNatKind(n__x(V1,V2)) >= U61(isNatKind(activate(V1)),activate(V2)) constraint: activate(n__0) >= 0 constraint: activate(n__plus(X1,X2)) >= plus(X1,X2) constraint: activate(n__s(X)) >= s(X) constraint: activate(n__x(X1,X2)) >= x(X1,X2) constraint: activate(X) >= X constraint: U101(tt,M,N) >= U102(isNatKind(activate(M)),activate(M), activate(N)) constraint: U103(tt,M,N) >= U104(isNatKind(activate(N)),activate(M), activate(N)) constraint: isNat(n__0) >= tt constraint: isNat(n__plus(V1,V2)) >= U11(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) constraint: isNat(n__x(V1,V2)) >= U31(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U104(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) constraint: plus(N,s(M)) >= U81(isNat(M),M,N) constraint: plus(N,0) >= U71(isNat(N),N) constraint: plus(X1,X2) >= n__plus(X1,X2) constraint: x(N,s(M)) >= U101(isNat(M),M,N) constraint: x(N,0) >= U91(isNat(N),N) constraint: x(X1,X2) >= n__x(X1,X2) constraint: U12(tt,V1,V2) >= U13(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U11(tt,V1,V2) >= U12(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U13(tt,V1,V2) >= U14(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U14(tt,V1,V2) >= U15(isNat(activate(V1)),activate(V2)) constraint: U15(tt,V2) >= U16(isNat(activate(V2))) constraint: U16(tt) >= tt constraint: U22(tt,V1) >= U23(isNat(activate(V1))) constraint: U21(tt,V1) >= U22(isNatKind(activate(V1)),activate(V1)) constraint: U23(tt) >= tt constraint: U32(tt,V1,V2) >= U33(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U31(tt,V1,V2) >= U32(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U33(tt,V1,V2) >= U34(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U34(tt,V1,V2) >= U35(isNat(activate(V1)),activate(V2)) constraint: U35(tt,V2) >= U36(isNat(activate(V2))) constraint: U36(tt) >= tt constraint: U42(tt) >= tt constraint: U41(tt,V2) >= U42(isNatKind(activate(V2))) constraint: U51(tt) >= tt constraint: U62(tt) >= tt constraint: U61(tt,V2) >= U62(isNatKind(activate(V2))) constraint: U72(tt,N) >= activate(N) constraint: U71(tt,N) >= U72(isNatKind(activate(N)),activate(N)) constraint: U82(tt,M,N) >= U83(isNat(activate(N)),activate(M),activate(N)) constraint: U81(tt,M,N) >= U82(isNatKind(activate(M)),activate(M),activate(N)) constraint: U83(tt,M,N) >= U84(isNatKind(activate(N)),activate(M),activate(N)) constraint: U84(tt,M,N) >= s(plus(activate(N),activate(M))) constraint: s(X) >= n__s(X) constraint: U92(tt) >= 0 constraint: U91(tt,N) >= U92(isNatKind(activate(N))) constraint: 0 >= n__0 constraint: Marked_activate(n__plus(X1,X2)) >= Marked_plus(X1,X2) constraint: Marked_activate(n__x(X1,X2)) >= Marked_x(X1,X2) constraint: Marked_x(N,s(M)) >= Marked_U101(isNat(M),M,N) constraint: Marked_x(N,s(M)) >= Marked_isNat(M) constraint: Marked_x(N,0) >= Marked_isNat(N) constraint: Marked_x(N,0) >= Marked_U91(isNat(N),N) constraint: Marked_plus(N,s(M)) >= Marked_isNat(M) constraint: Marked_plus(N,s(M)) >= Marked_U81(isNat(M),M,N) constraint: Marked_plus(N,0) >= Marked_isNat(N) constraint: Marked_plus(N,0) >= Marked_U71(isNat(N),N) constraint: Marked_U101(tt,M,N) >= Marked_activate(M) constraint: Marked_U101(tt,M,N) >= Marked_activate(N) constraint: Marked_U101(tt,M,N) >= Marked_isNatKind(activate(M)) constraint: Marked_U101(tt,M,N) >= Marked_U102(isNatKind(activate(M)), activate(M),activate(N)) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V1) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V2) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_isNatKind(activate(V1)) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNatKind(activate(V1)), activate(V1),activate(V2)) constraint: Marked_isNat(n__s(V1)) >= Marked_activate(V1) constraint: Marked_isNat(n__s(V1)) >= Marked_isNatKind(activate(V1)) constraint: Marked_isNat(n__s(V1)) >= Marked_U21(isNatKind(activate(V1)), activate(V1)) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_activate(V1) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_activate(V2) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_isNatKind(activate(V1)) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNatKind(activate(V1)), activate(V1),activate(V2)) constraint: Marked_U91(tt,N) >= Marked_activate(N) constraint: Marked_U91(tt,N) >= Marked_isNatKind(activate(N)) constraint: Marked_U81(tt,M,N) >= Marked_activate(M) constraint: Marked_U81(tt,M,N) >= Marked_activate(N) constraint: Marked_U81(tt,M,N) >= Marked_isNatKind(activate(M)) constraint: Marked_U81(tt,M,N) >= Marked_U82(isNatKind(activate(M)), activate(M),activate(N)) constraint: Marked_U71(tt,N) >= Marked_activate(N) constraint: Marked_U71(tt,N) >= Marked_isNatKind(activate(N)) constraint: Marked_U71(tt,N) >= Marked_U72(isNatKind(activate(N)),activate(N)) constraint: Marked_isNatKind(n__plus(V1,V2)) >= Marked_activate(V1) constraint: Marked_isNatKind(n__plus(V1,V2)) >= Marked_activate(V2) constraint: Marked_isNatKind(n__plus(V1,V2)) >= Marked_isNatKind(activate(V1)) constraint: Marked_isNatKind(n__plus(V1,V2)) >= Marked_U41(isNatKind( activate( V1)),activate(V2)) constraint: Marked_isNatKind(n__s(V1)) >= Marked_activate(V1) constraint: Marked_isNatKind(n__s(V1)) >= Marked_isNatKind(activate(V1)) constraint: Marked_isNatKind(n__x(V1,V2)) >= Marked_activate(V1) constraint: Marked_isNatKind(n__x(V1,V2)) >= Marked_activate(V2) constraint: Marked_isNatKind(n__x(V1,V2)) >= Marked_isNatKind(activate(V1)) constraint: Marked_isNatKind(n__x(V1,V2)) >= Marked_U61(isNatKind(activate(V1)), activate(V2)) constraint: Marked_U61(tt,V2) >= Marked_activate(V2) constraint: Marked_U61(tt,V2) >= Marked_isNatKind(activate(V2)) constraint: Marked_U41(tt,V2) >= Marked_activate(V2) constraint: Marked_U41(tt,V2) >= Marked_isNatKind(activate(V2)) constraint: Marked_U31(tt,V1,V2) >= Marked_activate(V1) constraint: Marked_U31(tt,V1,V2) >= Marked_activate(V2) constraint: Marked_U31(tt,V1,V2) >= Marked_isNatKind(activate(V1)) constraint: Marked_U31(tt,V1,V2) >= Marked_U32(isNatKind(activate(V1)), activate(V1),activate(V2)) constraint: Marked_U21(tt,V1) >= Marked_activate(V1) constraint: Marked_U21(tt,V1) >= Marked_isNatKind(activate(V1)) constraint: Marked_U21(tt,V1) >= Marked_U22(isNatKind(activate(V1)), activate(V1)) constraint: Marked_U11(tt,V1,V2) >= Marked_activate(V1) constraint: Marked_U11(tt,V1,V2) >= Marked_activate(V2) constraint: Marked_U11(tt,V1,V2) >= Marked_isNatKind(activate(V1)) constraint: Marked_U11(tt,V1,V2) >= Marked_U12(isNatKind(activate(V1)), activate(V1),activate(V2)) constraint: Marked_U84(tt,M,N) >= Marked_activate(M) constraint: Marked_U84(tt,M,N) >= Marked_activate(N) constraint: Marked_U84(tt,M,N) >= Marked_plus(activate(N),activate(M)) constraint: Marked_U83(tt,M,N) >= Marked_activate(M) constraint: Marked_U83(tt,M,N) >= Marked_activate(N) constraint: Marked_U83(tt,M,N) >= Marked_isNatKind(activate(N)) constraint: Marked_U83(tt,M,N) >= Marked_U84(isNatKind(activate(N)), activate(M),activate(N)) constraint: Marked_U82(tt,M,N) >= Marked_activate(M) constraint: Marked_U82(tt,M,N) >= Marked_activate(N) constraint: Marked_U82(tt,M,N) >= Marked_isNat(activate(N)) constraint: Marked_U82(tt,M,N) >= Marked_U83(isNat(activate(N)),activate(M), activate(N)) constraint: Marked_U72(tt,N) >= Marked_activate(N) constraint: Marked_U35(tt,V2) >= Marked_activate(V2) constraint: Marked_U35(tt,V2) >= Marked_isNat(activate(V2)) constraint: Marked_U34(tt,V1,V2) >= Marked_activate(V1) constraint: Marked_U34(tt,V1,V2) >= Marked_activate(V2) constraint: Marked_U34(tt,V1,V2) >= Marked_isNat(activate(V1)) constraint: Marked_U34(tt,V1,V2) >= Marked_U35(isNat(activate(V1)), activate(V2)) constraint: Marked_U33(tt,V1,V2) >= Marked_activate(V1) constraint: Marked_U33(tt,V1,V2) >= Marked_activate(V2) constraint: Marked_U33(tt,V1,V2) >= Marked_isNatKind(activate(V2)) constraint: Marked_U33(tt,V1,V2) >= Marked_U34(isNatKind(activate(V2)), activate(V1),activate(V2)) constraint: Marked_U32(tt,V1,V2) >= Marked_activate(V1) constraint: Marked_U32(tt,V1,V2) >= Marked_activate(V2) constraint: Marked_U32(tt,V1,V2) >= Marked_isNatKind(activate(V2)) constraint: Marked_U32(tt,V1,V2) >= Marked_U33(isNatKind(activate(V2)), activate(V1),activate(V2)) constraint: Marked_U22(tt,V1) >= Marked_activate(V1) constraint: Marked_U22(tt,V1) >= Marked_isNat(activate(V1)) constraint: Marked_U15(tt,V2) >= Marked_activate(V2) constraint: Marked_U15(tt,V2) >= Marked_isNat(activate(V2)) constraint: Marked_U14(tt,V1,V2) >= Marked_activate(V1) constraint: Marked_U14(tt,V1,V2) >= Marked_activate(V2) constraint: Marked_U14(tt,V1,V2) >= Marked_isNat(activate(V1)) constraint: Marked_U14(tt,V1,V2) >= Marked_U15(isNat(activate(V1)), activate(V2)) constraint: Marked_U13(tt,V1,V2) >= Marked_activate(V1) constraint: Marked_U13(tt,V1,V2) >= Marked_activate(V2) constraint: Marked_U13(tt,V1,V2) >= Marked_isNatKind(activate(V2)) constraint: Marked_U13(tt,V1,V2) >= Marked_U14(isNatKind(activate(V2)), activate(V1),activate(V2)) constraint: Marked_U12(tt,V1,V2) >= Marked_activate(V1) constraint: Marked_U12(tt,V1,V2) >= Marked_activate(V2) constraint: Marked_U12(tt,V1,V2) >= Marked_isNatKind(activate(V2)) constraint: Marked_U12(tt,V1,V2) >= Marked_U13(isNatKind(activate(V2)), activate(V1),activate(V2)) constraint: Marked_U104(tt,M,N) >= Marked_activate(M) constraint: Marked_U104(tt,M,N) >= Marked_activate(N) constraint: Marked_U104(tt,M,N) >= Marked_x(activate(N),activate(M)) constraint: Marked_U104(tt,M,N) >= Marked_plus(x(activate(N),activate(M)), activate(N)) constraint: Marked_U103(tt,M,N) >= Marked_activate(M) constraint: Marked_U103(tt,M,N) >= Marked_activate(N) constraint: Marked_U103(tt,M,N) >= Marked_isNatKind(activate(N)) constraint: Marked_U103(tt,M,N) >= Marked_U104(isNatKind(activate(N)), activate(M),activate(N)) constraint: Marked_U102(tt,M,N) >= Marked_activate(M) constraint: Marked_U102(tt,M,N) >= Marked_activate(N) constraint: Marked_U102(tt,M,N) >= Marked_isNat(activate(N)) constraint: Marked_U102(tt,M,N) >= Marked_U103(isNat(activate(N)),activate(M), activate(N)) APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { U102(tt,M,N) >= U103(isNat(activate(N)),activate(M),activate(N)) ; isNatKind(n__0) >= tt ; isNatKind(n__plus(V1,V2)) >= U41(isNatKind(activate(V1)),activate(V2)) ; isNatKind(n__s(V1)) >= U51(isNatKind(activate(V1))) ; isNatKind(n__x(V1,V2)) >= U61(isNatKind(activate(V1)),activate(V2)) ; activate(n__0) >= 0 ; activate(n__plus(X1,X2)) >= plus(X1,X2) ; activate(n__s(X)) >= s(X) ; activate(n__x(X1,X2)) >= x(X1,X2) ; activate(X) >= X ; U101(tt,M,N) >= U102(isNatKind(activate(M)),activate(M),activate(N)) ; U103(tt,M,N) >= U104(isNatKind(activate(N)),activate(M),activate(N)) ; isNat(n__0) >= tt ; isNat(n__plus(V1,V2)) >= U11(isNatKind(activate(V1)),activate(V1), activate(V2)) ; isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) ; isNat(n__x(V1,V2)) >= U31(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U104(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ; plus(N,s(M)) >= U81(isNat(M),M,N) ; plus(N,0) >= U71(isNat(N),N) ; plus(X1,X2) >= n__plus(X1,X2) ; x(N,s(M)) >= U101(isNat(M),M,N) ; x(N,0) >= U91(isNat(N),N) ; x(X1,X2) >= n__x(X1,X2) ; U12(tt,V1,V2) >= U13(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U11(tt,V1,V2) >= U12(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U13(tt,V1,V2) >= U14(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U14(tt,V1,V2) >= U15(isNat(activate(V1)),activate(V2)) ; U15(tt,V2) >= U16(isNat(activate(V2))) ; U16(tt) >= tt ; U22(tt,V1) >= U23(isNat(activate(V1))) ; U21(tt,V1) >= U22(isNatKind(activate(V1)),activate(V1)) ; U23(tt) >= tt ; U32(tt,V1,V2) >= U33(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U31(tt,V1,V2) >= U32(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U33(tt,V1,V2) >= U34(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U34(tt,V1,V2) >= U35(isNat(activate(V1)),activate(V2)) ; U35(tt,V2) >= U36(isNat(activate(V2))) ; U36(tt) >= tt ; U42(tt) >= tt ; U41(tt,V2) >= U42(isNatKind(activate(V2))) ; U51(tt) >= tt ; U62(tt) >= tt ; U61(tt,V2) >= U62(isNatKind(activate(V2))) ; U72(tt,N) >= activate(N) ; U71(tt,N) >= U72(isNatKind(activate(N)),activate(N)) ; U82(tt,M,N) >= U83(isNat(activate(N)),activate(M),activate(N)) ; U81(tt,M,N) >= U82(isNatKind(activate(M)),activate(M),activate(N)) ; U83(tt,M,N) >= U84(isNatKind(activate(N)),activate(M),activate(N)) ; U84(tt,M,N) >= s(plus(activate(N),activate(M))) ; s(X) >= n__s(X) ; U92(tt) >= 0 ; U91(tt,N) >= U92(isNatKind(activate(N))) ; 0 >= n__0 ; Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNatKind(activate(V1)), activate(V1),activate(V2)) ; Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNatKind(activate(V1)),activate(V1), activate(V2)) ; Marked_U31(tt,V1,V2) >= Marked_U32(isNatKind(activate(V1)),activate(V1), activate(V2)) ; Marked_U11(tt,V1,V2) >= Marked_U12(isNatKind(activate(V1)),activate(V1), activate(V2)) ; Marked_U35(tt,V2) >= Marked_isNat(activate(V2)) ; Marked_U34(tt,V1,V2) >= Marked_isNat(activate(V1)) ; Marked_U34(tt,V1,V2) >= Marked_U35(isNat(activate(V1)),activate(V2)) ; Marked_U33(tt,V1,V2) >= Marked_U34(isNatKind(activate(V2)),activate(V1), activate(V2)) ; Marked_U32(tt,V1,V2) >= Marked_U33(isNatKind(activate(V2)),activate(V1), activate(V2)) ; Marked_U15(tt,V2) >= Marked_isNat(activate(V2)) ; Marked_U14(tt,V1,V2) >= Marked_isNat(activate(V1)) ; Marked_U14(tt,V1,V2) >= Marked_U15(isNat(activate(V1)),activate(V2)) ; Marked_U13(tt,V1,V2) >= Marked_U14(isNatKind(activate(V2)),activate(V1), activate(V2)) ; Marked_U12(tt,V1,V2) >= Marked_U13(isNatKind(activate(V2)),activate(V1), activate(V2)) ; } + Disjunctions:{ { Marked_isNat(n__plus(V1,V2)) > Marked_U11(isNatKind(activate(V1)), activate(V1),activate(V2)) ; } { Marked_isNat(n__x(V1,V2)) > Marked_U31(isNatKind(activate(V1)),activate(V1), activate(V2)) ; } { Marked_U31(tt,V1,V2) > Marked_U32(isNatKind(activate(V1)),activate(V1), activate(V2)) ; } { Marked_U11(tt,V1,V2) > Marked_U12(isNatKind(activate(V1)),activate(V1), activate(V2)) ; } { Marked_U35(tt,V2) > Marked_isNat(activate(V2)) ; } { Marked_U34(tt,V1,V2) > Marked_isNat(activate(V1)) ; } { Marked_U34(tt,V1,V2) > Marked_U35(isNat(activate(V1)),activate(V2)) ; } { Marked_U33(tt,V1,V2) > Marked_U34(isNatKind(activate(V2)),activate(V1), activate(V2)) ; } { Marked_U32(tt,V1,V2) > Marked_U33(isNatKind(activate(V2)),activate(V1), activate(V2)) ; } { Marked_U15(tt,V2) > Marked_isNat(activate(V2)) ; } { Marked_U14(tt,V1,V2) > Marked_isNat(activate(V1)) ; } { Marked_U14(tt,V1,V2) > Marked_U15(isNat(activate(V1)),activate(V2)) ; } { Marked_U13(tt,V1,V2) > Marked_U14(isNatKind(activate(V2)),activate(V1), activate(V2)) ; } { Marked_U12(tt,V1,V2) > Marked_U13(isNatKind(activate(V2)),activate(V1), activate(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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: U102(tt,M,N) >= U103(isNat(activate(N)),activate(M),activate(N)) constraint: isNatKind(n__0) >= tt constraint: isNatKind(n__plus(V1,V2)) >= U41(isNatKind(activate(V1)), activate(V2)) constraint: isNatKind(n__s(V1)) >= U51(isNatKind(activate(V1))) constraint: isNatKind(n__x(V1,V2)) >= U61(isNatKind(activate(V1)),activate(V2)) constraint: activate(n__0) >= 0 constraint: activate(n__plus(X1,X2)) >= plus(X1,X2) constraint: activate(n__s(X)) >= s(X) constraint: activate(n__x(X1,X2)) >= x(X1,X2) constraint: activate(X) >= X constraint: U101(tt,M,N) >= U102(isNatKind(activate(M)),activate(M), activate(N)) constraint: U103(tt,M,N) >= U104(isNatKind(activate(N)),activate(M), activate(N)) constraint: isNat(n__0) >= tt constraint: isNat(n__plus(V1,V2)) >= U11(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) constraint: isNat(n__x(V1,V2)) >= U31(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U104(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) constraint: plus(N,s(M)) >= U81(isNat(M),M,N) constraint: plus(N,0) >= U71(isNat(N),N) constraint: plus(X1,X2) >= n__plus(X1,X2) constraint: x(N,s(M)) >= U101(isNat(M),M,N) constraint: x(N,0) >= U91(isNat(N),N) constraint: x(X1,X2) >= n__x(X1,X2) constraint: U12(tt,V1,V2) >= U13(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U11(tt,V1,V2) >= U12(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U13(tt,V1,V2) >= U14(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U14(tt,V1,V2) >= U15(isNat(activate(V1)),activate(V2)) constraint: U15(tt,V2) >= U16(isNat(activate(V2))) constraint: U16(tt) >= tt constraint: U22(tt,V1) >= U23(isNat(activate(V1))) constraint: U21(tt,V1) >= U22(isNatKind(activate(V1)),activate(V1)) constraint: U23(tt) >= tt constraint: U32(tt,V1,V2) >= U33(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U31(tt,V1,V2) >= U32(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U33(tt,V1,V2) >= U34(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U34(tt,V1,V2) >= U35(isNat(activate(V1)),activate(V2)) constraint: U35(tt,V2) >= U36(isNat(activate(V2))) constraint: U36(tt) >= tt constraint: U42(tt) >= tt constraint: U41(tt,V2) >= U42(isNatKind(activate(V2))) constraint: U51(tt) >= tt constraint: U62(tt) >= tt constraint: U61(tt,V2) >= U62(isNatKind(activate(V2))) constraint: U72(tt,N) >= activate(N) constraint: U71(tt,N) >= U72(isNatKind(activate(N)),activate(N)) constraint: U82(tt,M,N) >= U83(isNat(activate(N)),activate(M),activate(N)) constraint: U81(tt,M,N) >= U82(isNatKind(activate(M)),activate(M),activate(N)) constraint: U83(tt,M,N) >= U84(isNatKind(activate(N)),activate(M),activate(N)) constraint: U84(tt,M,N) >= s(plus(activate(N),activate(M))) constraint: s(X) >= n__s(X) constraint: U92(tt) >= 0 constraint: U91(tt,N) >= U92(isNatKind(activate(N))) constraint: 0 >= n__0 constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNatKind(activate(V1)), activate(V1),activate(V2)) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNatKind(activate(V1)), activate(V1),activate(V2)) constraint: Marked_U31(tt,V1,V2) >= Marked_U32(isNatKind(activate(V1)), activate(V1),activate(V2)) constraint: Marked_U11(tt,V1,V2) >= Marked_U12(isNatKind(activate(V1)), activate(V1),activate(V2)) constraint: Marked_U35(tt,V2) >= Marked_isNat(activate(V2)) constraint: Marked_U34(tt,V1,V2) >= Marked_isNat(activate(V1)) constraint: Marked_U34(tt,V1,V2) >= Marked_U35(isNat(activate(V1)), activate(V2)) constraint: Marked_U33(tt,V1,V2) >= Marked_U34(isNatKind(activate(V2)), activate(V1),activate(V2)) constraint: Marked_U32(tt,V1,V2) >= Marked_U33(isNatKind(activate(V2)), activate(V1),activate(V2)) constraint: Marked_U15(tt,V2) >= Marked_isNat(activate(V2)) constraint: Marked_U14(tt,V1,V2) >= Marked_isNat(activate(V1)) constraint: Marked_U14(tt,V1,V2) >= Marked_U15(isNat(activate(V1)), activate(V2)) constraint: Marked_U13(tt,V1,V2) >= Marked_U14(isNatKind(activate(V2)), activate(V1),activate(V2)) constraint: Marked_U12(tt,V1,V2) >= Marked_U13(isNatKind(activate(V2)), activate(V1),activate(V2)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { U102(tt,M,N) >= U103(isNat(activate(N)),activate(M),activate(N)) ; isNatKind(n__0) >= tt ; isNatKind(n__plus(V1,V2)) >= U41(isNatKind(activate(V1)),activate(V2)) ; isNatKind(n__s(V1)) >= U51(isNatKind(activate(V1))) ; isNatKind(n__x(V1,V2)) >= U61(isNatKind(activate(V1)),activate(V2)) ; activate(n__0) >= 0 ; activate(n__plus(X1,X2)) >= plus(X1,X2) ; activate(n__s(X)) >= s(X) ; activate(n__x(X1,X2)) >= x(X1,X2) ; activate(X) >= X ; U101(tt,M,N) >= U102(isNatKind(activate(M)),activate(M),activate(N)) ; U103(tt,M,N) >= U104(isNatKind(activate(N)),activate(M),activate(N)) ; isNat(n__0) >= tt ; isNat(n__plus(V1,V2)) >= U11(isNatKind(activate(V1)),activate(V1), activate(V2)) ; isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) ; isNat(n__x(V1,V2)) >= U31(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U104(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ; plus(N,s(M)) >= U81(isNat(M),M,N) ; plus(N,0) >= U71(isNat(N),N) ; plus(X1,X2) >= n__plus(X1,X2) ; x(N,s(M)) >= U101(isNat(M),M,N) ; x(N,0) >= U91(isNat(N),N) ; x(X1,X2) >= n__x(X1,X2) ; U12(tt,V1,V2) >= U13(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U11(tt,V1,V2) >= U12(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U13(tt,V1,V2) >= U14(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U14(tt,V1,V2) >= U15(isNat(activate(V1)),activate(V2)) ; U15(tt,V2) >= U16(isNat(activate(V2))) ; U16(tt) >= tt ; U22(tt,V1) >= U23(isNat(activate(V1))) ; U21(tt,V1) >= U22(isNatKind(activate(V1)),activate(V1)) ; U23(tt) >= tt ; U32(tt,V1,V2) >= U33(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U31(tt,V1,V2) >= U32(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U33(tt,V1,V2) >= U34(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U34(tt,V1,V2) >= U35(isNat(activate(V1)),activate(V2)) ; U35(tt,V2) >= U36(isNat(activate(V2))) ; U36(tt) >= tt ; U42(tt) >= tt ; U41(tt,V2) >= U42(isNatKind(activate(V2))) ; U51(tt) >= tt ; U62(tt) >= tt ; U61(tt,V2) >= U62(isNatKind(activate(V2))) ; U72(tt,N) >= activate(N) ; U71(tt,N) >= U72(isNatKind(activate(N)),activate(N)) ; U82(tt,M,N) >= U83(isNat(activate(N)),activate(M),activate(N)) ; U81(tt,M,N) >= U82(isNatKind(activate(M)),activate(M),activate(N)) ; U83(tt,M,N) >= U84(isNatKind(activate(N)),activate(M),activate(N)) ; U84(tt,M,N) >= s(plus(activate(N),activate(M))) ; s(X) >= n__s(X) ; U92(tt) >= 0 ; U91(tt,N) >= U92(isNatKind(activate(N))) ; 0 >= n__0 ; Marked_isNatKind(n__plus(V1,V2)) >= Marked_isNatKind(activate(V1)) ; Marked_isNatKind(n__plus(V1,V2)) >= Marked_U41(isNatKind(activate(V1)), activate(V2)) ; Marked_isNatKind(n__x(V1,V2)) >= Marked_isNatKind(activate(V1)) ; Marked_isNatKind(n__x(V1,V2)) >= Marked_U61(isNatKind(activate(V1)), activate(V2)) ; Marked_U61(tt,V2) >= Marked_isNatKind(activate(V2)) ; Marked_U41(tt,V2) >= Marked_isNatKind(activate(V2)) ; } + Disjunctions:{ { Marked_isNatKind(n__plus(V1,V2)) > Marked_isNatKind(activate(V1)) ; } { Marked_isNatKind(n__plus(V1,V2)) > Marked_U41(isNatKind(activate(V1)), activate(V2)) ; } { Marked_isNatKind(n__x(V1,V2)) > Marked_isNatKind(activate(V1)) ; } { Marked_isNatKind(n__x(V1,V2)) > Marked_U61(isNatKind(activate(V1)), activate(V2)) ; } { Marked_U61(tt,V2) > Marked_isNatKind(activate(V2)) ; } { Marked_U41(tt,V2) > Marked_isNatKind(activate(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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: U102(tt,M,N) >= U103(isNat(activate(N)),activate(M),activate(N)) constraint: isNatKind(n__0) >= tt constraint: isNatKind(n__plus(V1,V2)) >= U41(isNatKind(activate(V1)), activate(V2)) constraint: isNatKind(n__s(V1)) >= U51(isNatKind(activate(V1))) constraint: isNatKind(n__x(V1,V2)) >= U61(isNatKind(activate(V1)),activate(V2)) constraint: activate(n__0) >= 0 constraint: activate(n__plus(X1,X2)) >= plus(X1,X2) constraint: activate(n__s(X)) >= s(X) constraint: activate(n__x(X1,X2)) >= x(X1,X2) constraint: activate(X) >= X constraint: U101(tt,M,N) >= U102(isNatKind(activate(M)),activate(M), activate(N)) constraint: U103(tt,M,N) >= U104(isNatKind(activate(N)),activate(M), activate(N)) constraint: isNat(n__0) >= tt constraint: isNat(n__plus(V1,V2)) >= U11(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) constraint: isNat(n__x(V1,V2)) >= U31(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U104(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) constraint: plus(N,s(M)) >= U81(isNat(M),M,N) constraint: plus(N,0) >= U71(isNat(N),N) constraint: plus(X1,X2) >= n__plus(X1,X2) constraint: x(N,s(M)) >= U101(isNat(M),M,N) constraint: x(N,0) >= U91(isNat(N),N) constraint: x(X1,X2) >= n__x(X1,X2) constraint: U12(tt,V1,V2) >= U13(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U11(tt,V1,V2) >= U12(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U13(tt,V1,V2) >= U14(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U14(tt,V1,V2) >= U15(isNat(activate(V1)),activate(V2)) constraint: U15(tt,V2) >= U16(isNat(activate(V2))) constraint: U16(tt) >= tt constraint: U22(tt,V1) >= U23(isNat(activate(V1))) constraint: U21(tt,V1) >= U22(isNatKind(activate(V1)),activate(V1)) constraint: U23(tt) >= tt constraint: U32(tt,V1,V2) >= U33(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U31(tt,V1,V2) >= U32(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U33(tt,V1,V2) >= U34(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U34(tt,V1,V2) >= U35(isNat(activate(V1)),activate(V2)) constraint: U35(tt,V2) >= U36(isNat(activate(V2))) constraint: U36(tt) >= tt constraint: U42(tt) >= tt constraint: U41(tt,V2) >= U42(isNatKind(activate(V2))) constraint: U51(tt) >= tt constraint: U62(tt) >= tt constraint: U61(tt,V2) >= U62(isNatKind(activate(V2))) constraint: U72(tt,N) >= activate(N) constraint: U71(tt,N) >= U72(isNatKind(activate(N)),activate(N)) constraint: U82(tt,M,N) >= U83(isNat(activate(N)),activate(M),activate(N)) constraint: U81(tt,M,N) >= U82(isNatKind(activate(M)),activate(M),activate(N)) constraint: U83(tt,M,N) >= U84(isNatKind(activate(N)),activate(M),activate(N)) constraint: U84(tt,M,N) >= s(plus(activate(N),activate(M))) constraint: s(X) >= n__s(X) constraint: U92(tt) >= 0 constraint: U91(tt,N) >= U92(isNatKind(activate(N))) constraint: 0 >= n__0 constraint: Marked_isNatKind(n__plus(V1,V2)) >= Marked_isNatKind(activate(V1)) constraint: Marked_isNatKind(n__plus(V1,V2)) >= Marked_U41(isNatKind( activate( V1)),activate(V2)) constraint: Marked_isNatKind(n__x(V1,V2)) >= Marked_isNatKind(activate(V1)) constraint: Marked_isNatKind(n__x(V1,V2)) >= Marked_U61(isNatKind(activate(V1)), activate(V2)) constraint: Marked_U61(tt,V2) >= Marked_isNatKind(activate(V2)) constraint: Marked_U41(tt,V2) >= Marked_isNatKind(activate(V2)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { U102(tt,M,N) >= U103(isNat(activate(N)),activate(M),activate(N)) ; isNatKind(n__0) >= tt ; isNatKind(n__plus(V1,V2)) >= U41(isNatKind(activate(V1)),activate(V2)) ; isNatKind(n__s(V1)) >= U51(isNatKind(activate(V1))) ; isNatKind(n__x(V1,V2)) >= U61(isNatKind(activate(V1)),activate(V2)) ; activate(n__0) >= 0 ; activate(n__plus(X1,X2)) >= plus(X1,X2) ; activate(n__s(X)) >= s(X) ; activate(n__x(X1,X2)) >= x(X1,X2) ; activate(X) >= X ; U101(tt,M,N) >= U102(isNatKind(activate(M)),activate(M),activate(N)) ; U103(tt,M,N) >= U104(isNatKind(activate(N)),activate(M),activate(N)) ; isNat(n__0) >= tt ; isNat(n__plus(V1,V2)) >= U11(isNatKind(activate(V1)),activate(V1), activate(V2)) ; isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) ; isNat(n__x(V1,V2)) >= U31(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U104(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ; plus(N,s(M)) >= U81(isNat(M),M,N) ; plus(N,0) >= U71(isNat(N),N) ; plus(X1,X2) >= n__plus(X1,X2) ; x(N,s(M)) >= U101(isNat(M),M,N) ; x(N,0) >= U91(isNat(N),N) ; x(X1,X2) >= n__x(X1,X2) ; U12(tt,V1,V2) >= U13(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U11(tt,V1,V2) >= U12(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U13(tt,V1,V2) >= U14(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U14(tt,V1,V2) >= U15(isNat(activate(V1)),activate(V2)) ; U15(tt,V2) >= U16(isNat(activate(V2))) ; U16(tt) >= tt ; U22(tt,V1) >= U23(isNat(activate(V1))) ; U21(tt,V1) >= U22(isNatKind(activate(V1)),activate(V1)) ; U23(tt) >= tt ; U32(tt,V1,V2) >= U33(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U31(tt,V1,V2) >= U32(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U33(tt,V1,V2) >= U34(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U34(tt,V1,V2) >= U35(isNat(activate(V1)),activate(V2)) ; U35(tt,V2) >= U36(isNat(activate(V2))) ; U36(tt) >= tt ; U42(tt) >= tt ; U41(tt,V2) >= U42(isNatKind(activate(V2))) ; U51(tt) >= tt ; U62(tt) >= tt ; U61(tt,V2) >= U62(isNatKind(activate(V2))) ; U72(tt,N) >= activate(N) ; U71(tt,N) >= U72(isNatKind(activate(N)),activate(N)) ; U82(tt,M,N) >= U83(isNat(activate(N)),activate(M),activate(N)) ; U81(tt,M,N) >= U82(isNatKind(activate(M)),activate(M),activate(N)) ; U83(tt,M,N) >= U84(isNatKind(activate(N)),activate(M),activate(N)) ; U84(tt,M,N) >= s(plus(activate(N),activate(M))) ; s(X) >= n__s(X) ; U92(tt) >= 0 ; U91(tt,N) >= U92(isNatKind(activate(N))) ; 0 >= n__0 ; Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNatKind(activate(V1)), activate(V1),activate(V2)) ; Marked_U11(tt,V1,V2) >= Marked_U12(isNatKind(activate(V1)),activate(V1), activate(V2)) ; Marked_U15(tt,V2) >= Marked_isNat(activate(V2)) ; Marked_U14(tt,V1,V2) >= Marked_isNat(activate(V1)) ; Marked_U14(tt,V1,V2) >= Marked_U15(isNat(activate(V1)),activate(V2)) ; Marked_U13(tt,V1,V2) >= Marked_U14(isNatKind(activate(V2)),activate(V1), activate(V2)) ; Marked_U12(tt,V1,V2) >= Marked_U13(isNatKind(activate(V2)),activate(V1), activate(V2)) ; } + Disjunctions:{ { Marked_isNat(n__plus(V1,V2)) > Marked_U11(isNatKind(activate(V1)), activate(V1),activate(V2)) ; } { Marked_U11(tt,V1,V2) > Marked_U12(isNatKind(activate(V1)),activate(V1), activate(V2)) ; } { Marked_U15(tt,V2) > Marked_isNat(activate(V2)) ; } { Marked_U14(tt,V1,V2) > Marked_isNat(activate(V1)) ; } { Marked_U14(tt,V1,V2) > Marked_U15(isNat(activate(V1)),activate(V2)) ; } { Marked_U13(tt,V1,V2) > Marked_U14(isNatKind(activate(V2)),activate(V1), activate(V2)) ; } { Marked_U12(tt,V1,V2) > Marked_U13(isNatKind(activate(V2)),activate(V1), activate(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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: U102(tt,M,N) >= U103(isNat(activate(N)),activate(M),activate(N)) constraint: isNatKind(n__0) >= tt constraint: isNatKind(n__plus(V1,V2)) >= U41(isNatKind(activate(V1)), activate(V2)) constraint: isNatKind(n__s(V1)) >= U51(isNatKind(activate(V1))) constraint: isNatKind(n__x(V1,V2)) >= U61(isNatKind(activate(V1)),activate(V2)) constraint: activate(n__0) >= 0 constraint: activate(n__plus(X1,X2)) >= plus(X1,X2) constraint: activate(n__s(X)) >= s(X) constraint: activate(n__x(X1,X2)) >= x(X1,X2) constraint: activate(X) >= X constraint: U101(tt,M,N) >= U102(isNatKind(activate(M)),activate(M), activate(N)) constraint: U103(tt,M,N) >= U104(isNatKind(activate(N)),activate(M), activate(N)) constraint: isNat(n__0) >= tt constraint: isNat(n__plus(V1,V2)) >= U11(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) constraint: isNat(n__x(V1,V2)) >= U31(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U104(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) constraint: plus(N,s(M)) >= U81(isNat(M),M,N) constraint: plus(N,0) >= U71(isNat(N),N) constraint: plus(X1,X2) >= n__plus(X1,X2) constraint: x(N,s(M)) >= U101(isNat(M),M,N) constraint: x(N,0) >= U91(isNat(N),N) constraint: x(X1,X2) >= n__x(X1,X2) constraint: U12(tt,V1,V2) >= U13(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U11(tt,V1,V2) >= U12(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U13(tt,V1,V2) >= U14(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U14(tt,V1,V2) >= U15(isNat(activate(V1)),activate(V2)) constraint: U15(tt,V2) >= U16(isNat(activate(V2))) constraint: U16(tt) >= tt constraint: U22(tt,V1) >= U23(isNat(activate(V1))) constraint: U21(tt,V1) >= U22(isNatKind(activate(V1)),activate(V1)) constraint: U23(tt) >= tt constraint: U32(tt,V1,V2) >= U33(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U31(tt,V1,V2) >= U32(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U33(tt,V1,V2) >= U34(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U34(tt,V1,V2) >= U35(isNat(activate(V1)),activate(V2)) constraint: U35(tt,V2) >= U36(isNat(activate(V2))) constraint: U36(tt) >= tt constraint: U42(tt) >= tt constraint: U41(tt,V2) >= U42(isNatKind(activate(V2))) constraint: U51(tt) >= tt constraint: U62(tt) >= tt constraint: U61(tt,V2) >= U62(isNatKind(activate(V2))) constraint: U72(tt,N) >= activate(N) constraint: U71(tt,N) >= U72(isNatKind(activate(N)),activate(N)) constraint: U82(tt,M,N) >= U83(isNat(activate(N)),activate(M),activate(N)) constraint: U81(tt,M,N) >= U82(isNatKind(activate(M)),activate(M),activate(N)) constraint: U83(tt,M,N) >= U84(isNatKind(activate(N)),activate(M),activate(N)) constraint: U84(tt,M,N) >= s(plus(activate(N),activate(M))) constraint: s(X) >= n__s(X) constraint: U92(tt) >= 0 constraint: U91(tt,N) >= U92(isNatKind(activate(N))) constraint: 0 >= n__0 constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNatKind(activate(V1)), activate(V1),activate(V2)) constraint: Marked_U11(tt,V1,V2) >= Marked_U12(isNatKind(activate(V1)), activate(V1),activate(V2)) constraint: Marked_U15(tt,V2) >= Marked_isNat(activate(V2)) constraint: Marked_U14(tt,V1,V2) >= Marked_isNat(activate(V1)) constraint: Marked_U14(tt,V1,V2) >= Marked_U15(isNat(activate(V1)), activate(V2)) constraint: Marked_U13(tt,V1,V2) >= Marked_U14(isNatKind(activate(V2)), activate(V1),activate(V2)) constraint: Marked_U12(tt,V1,V2) >= Marked_U13(isNatKind(activate(V2)), activate(V1),activate(V2)) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { U102(tt,M,N) >= U103(isNat(activate(N)),activate(M),activate(N)) ; isNatKind(n__0) >= tt ; isNatKind(n__plus(V1,V2)) >= U41(isNatKind(activate(V1)),activate(V2)) ; isNatKind(n__s(V1)) >= U51(isNatKind(activate(V1))) ; isNatKind(n__x(V1,V2)) >= U61(isNatKind(activate(V1)),activate(V2)) ; activate(n__0) >= 0 ; activate(n__plus(X1,X2)) >= plus(X1,X2) ; activate(n__s(X)) >= s(X) ; activate(n__x(X1,X2)) >= x(X1,X2) ; activate(X) >= X ; U101(tt,M,N) >= U102(isNatKind(activate(M)),activate(M),activate(N)) ; U103(tt,M,N) >= U104(isNatKind(activate(N)),activate(M),activate(N)) ; isNat(n__0) >= tt ; isNat(n__plus(V1,V2)) >= U11(isNatKind(activate(V1)),activate(V1), activate(V2)) ; isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) ; isNat(n__x(V1,V2)) >= U31(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U104(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ; plus(N,s(M)) >= U81(isNat(M),M,N) ; plus(N,0) >= U71(isNat(N),N) ; plus(X1,X2) >= n__plus(X1,X2) ; x(N,s(M)) >= U101(isNat(M),M,N) ; x(N,0) >= U91(isNat(N),N) ; x(X1,X2) >= n__x(X1,X2) ; U12(tt,V1,V2) >= U13(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U11(tt,V1,V2) >= U12(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U13(tt,V1,V2) >= U14(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U14(tt,V1,V2) >= U15(isNat(activate(V1)),activate(V2)) ; U15(tt,V2) >= U16(isNat(activate(V2))) ; U16(tt) >= tt ; U22(tt,V1) >= U23(isNat(activate(V1))) ; U21(tt,V1) >= U22(isNatKind(activate(V1)),activate(V1)) ; U23(tt) >= tt ; U32(tt,V1,V2) >= U33(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U31(tt,V1,V2) >= U32(isNatKind(activate(V1)),activate(V1),activate(V2)) ; U33(tt,V1,V2) >= U34(isNatKind(activate(V2)),activate(V1),activate(V2)) ; U34(tt,V1,V2) >= U35(isNat(activate(V1)),activate(V2)) ; U35(tt,V2) >= U36(isNat(activate(V2))) ; U36(tt) >= tt ; U42(tt) >= tt ; U41(tt,V2) >= U42(isNatKind(activate(V2))) ; U51(tt) >= tt ; U62(tt) >= tt ; U61(tt,V2) >= U62(isNatKind(activate(V2))) ; U72(tt,N) >= activate(N) ; U71(tt,N) >= U72(isNatKind(activate(N)),activate(N)) ; U82(tt,M,N) >= U83(isNat(activate(N)),activate(M),activate(N)) ; U81(tt,M,N) >= U82(isNatKind(activate(M)),activate(M),activate(N)) ; U83(tt,M,N) >= U84(isNatKind(activate(N)),activate(M),activate(N)) ; U84(tt,M,N) >= s(plus(activate(N),activate(M))) ; s(X) >= n__s(X) ; U92(tt) >= 0 ; U91(tt,N) >= U92(isNatKind(activate(N))) ; 0 >= n__0 ; Marked_isNatKind(n__plus(V1,V2)) >= Marked_isNatKind(activate(V1)) ; Marked_isNatKind(n__plus(V1,V2)) >= Marked_U41(isNatKind(activate(V1)), activate(V2)) ; Marked_U41(tt,V2) >= Marked_isNatKind(activate(V2)) ; } + Disjunctions:{ { Marked_isNatKind(n__plus(V1,V2)) > Marked_isNatKind(activate(V1)) ; } { Marked_isNatKind(n__plus(V1,V2)) > Marked_U41(isNatKind(activate(V1)), activate(V2)) ; } { Marked_U41(tt,V2) > Marked_isNatKind(activate(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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === Time out for these parameters. === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: U102(tt,M,N) >= U103(isNat(activate(N)),activate(M),activate(N)) constraint: isNatKind(n__0) >= tt constraint: isNatKind(n__plus(V1,V2)) >= U41(isNatKind(activate(V1)), activate(V2)) constraint: isNatKind(n__s(V1)) >= U51(isNatKind(activate(V1))) constraint: isNatKind(n__x(V1,V2)) >= U61(isNatKind(activate(V1)),activate(V2)) constraint: activate(n__0) >= 0 constraint: activate(n__plus(X1,X2)) >= plus(X1,X2) constraint: activate(n__s(X)) >= s(X) constraint: activate(n__x(X1,X2)) >= x(X1,X2) constraint: activate(X) >= X constraint: U101(tt,M,N) >= U102(isNatKind(activate(M)),activate(M), activate(N)) constraint: U103(tt,M,N) >= U104(isNatKind(activate(N)),activate(M), activate(N)) constraint: isNat(n__0) >= tt constraint: isNat(n__plus(V1,V2)) >= U11(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) constraint: isNat(n__x(V1,V2)) >= U31(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U104(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) constraint: plus(N,s(M)) >= U81(isNat(M),M,N) constraint: plus(N,0) >= U71(isNat(N),N) constraint: plus(X1,X2) >= n__plus(X1,X2) constraint: x(N,s(M)) >= U101(isNat(M),M,N) constraint: x(N,0) >= U91(isNat(N),N) constraint: x(X1,X2) >= n__x(X1,X2) constraint: U12(tt,V1,V2) >= U13(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U11(tt,V1,V2) >= U12(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U13(tt,V1,V2) >= U14(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U14(tt,V1,V2) >= U15(isNat(activate(V1)),activate(V2)) constraint: U15(tt,V2) >= U16(isNat(activate(V2))) constraint: U16(tt) >= tt constraint: U22(tt,V1) >= U23(isNat(activate(V1))) constraint: U21(tt,V1) >= U22(isNatKind(activate(V1)),activate(V1)) constraint: U23(tt) >= tt constraint: U32(tt,V1,V2) >= U33(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U31(tt,V1,V2) >= U32(isNatKind(activate(V1)),activate(V1), activate(V2)) constraint: U33(tt,V1,V2) >= U34(isNatKind(activate(V2)),activate(V1), activate(V2)) constraint: U34(tt,V1,V2) >= U35(isNat(activate(V1)),activate(V2)) constraint: U35(tt,V2) >= U36(isNat(activate(V2))) constraint: U36(tt) >= tt constraint: U42(tt) >= tt constraint: U41(tt,V2) >= U42(isNatKind(activate(V2))) constraint: U51(tt) >= tt constraint: U62(tt) >= tt constraint: U61(tt,V2) >= U62(isNatKind(activate(V2))) constraint: U72(tt,N) >= activate(N) constraint: U71(tt,N) >= U72(isNatKind(activate(N)),activate(N)) constraint: U82(tt,M,N) >= U83(isNat(activate(N)),activate(M),activate(N)) constraint: U81(tt,M,N) >= U82(isNatKind(activate(M)),activate(M),activate(N)) constraint: U83(tt,M,N) >= U84(isNatKind(activate(N)),activate(M),activate(N)) constraint: U84(tt,M,N) >= s(plus(activate(N),activate(M))) constraint: s(X) >= n__s(X) constraint: U92(tt) >= 0 constraint: U91(tt,N) >= U92(isNatKind(activate(N))) constraint: 0 >= n__0 constraint: Marked_isNatKind(n__plus(V1,V2)) >= Marked_isNatKind(activate(V1)) constraint: Marked_isNatKind(n__plus(V1,V2)) >= Marked_U41(isNatKind( activate( V1)),activate(V2)) constraint: Marked_U41(tt,V2) >= Marked_isNatKind(activate(V2)) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] U101(tt,M,N) -> U102(isNatKind(activate(M)),activate(M),activate(N)) [2] U102(tt,M,N) -> U103(isNat(activate(N)),activate(M),activate(N)) [3] U103(tt,M,N) -> U104(isNatKind(activate(N)),activate(M),activate(N)) [4] U104(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) [5] U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) [6] U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) [7] U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) [8] U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) [9] U15(tt,V2) -> U16(isNat(activate(V2))) [10] U16(tt) -> tt [11] U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) [12] U22(tt,V1) -> U23(isNat(activate(V1))) [13] U23(tt) -> tt [14] U31(tt,V1,V2) -> U32(isNatKind(activate(V1)),activate(V1),activate(V2)) [15] U32(tt,V1,V2) -> U33(isNatKind(activate(V2)),activate(V1),activate(V2)) [16] U33(tt,V1,V2) -> U34(isNatKind(activate(V2)),activate(V1),activate(V2)) [17] U34(tt,V1,V2) -> U35(isNat(activate(V1)),activate(V2)) [18] U35(tt,V2) -> U36(isNat(activate(V2))) [19] U36(tt) -> tt [20] U41(tt,V2) -> U42(isNatKind(activate(V2))) [21] U42(tt) -> tt [22] U51(tt) -> tt [23] U61(tt,V2) -> U62(isNatKind(activate(V2))) [24] U62(tt) -> tt [25] U71(tt,N) -> U72(isNatKind(activate(N)),activate(N)) [26] U72(tt,N) -> activate(N) [27] U81(tt,M,N) -> U82(isNatKind(activate(M)),activate(M),activate(N)) [28] U82(tt,M,N) -> U83(isNat(activate(N)),activate(M),activate(N)) [29] U83(tt,M,N) -> U84(isNatKind(activate(N)),activate(M),activate(N)) [30] U84(tt,M,N) -> s(plus(activate(N),activate(M))) [31] U91(tt,N) -> U92(isNatKind(activate(N))) [32] U92(tt) -> 0 [33] isNat(n__0) -> tt [34] isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) [35] isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) [36] isNat(n__x(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V1),activate(V2)) [37] isNatKind(n__0) -> tt [38] isNatKind(n__plus(V1,V2)) -> U41(isNatKind(activate(V1)),activate(V2)) [39] isNatKind(n__s(V1)) -> U51(isNatKind(activate(V1))) [40] isNatKind(n__x(V1,V2)) -> U61(isNatKind(activate(V1)),activate(V2)) [41] plus(N,0) -> U71(isNat(N),N) [42] plus(N,s(M)) -> U81(isNat(M),M,N) [43] x(N,0) -> U91(isNat(N),N) [44] x(N,s(M)) -> U101(isNat(M),M,N) [45] 0 -> n__0 [46] plus(X1,X2) -> n__plus(X1,X2) [47] s(X) -> n__s(X) [48] x(X1,X2) -> n__x(X1,X2) [49] activate(n__0) -> 0 [50] activate(n__plus(X1,X2)) -> plus(X1,X2) [51] activate(n__s(X)) -> s(X) [52] activate(n__x(X1,X2)) -> x(X1,X2) [53] activate(X) -> X , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ U102 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 1*X1; [ Marked_U82 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U82 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U22 ] (X0,X1) = 0; [ Marked_U104 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 1*X1 + 1; [ plus ] (X0,X1) = 1*X1 + 1*X0; [ Marked_U32 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ n__0 ] () = 1; [ U36 ] (X0) = 0; [ tt ] () = 0; [ s ] (X0) = 1*X0 + 2; [ U31 ] (X0,X1,X2) = 0; [ Marked_U81 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U13 ] (X0,X1,X2) = 0; [ Marked_U15 ] (X0,X1) = 1*X1 + 1; [ Marked_activate ] (X0) = 1*X0 + 1; [ U62 ] (X0) = 0; [ Marked_U11 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ activate ] (X0) = 1*X0; [ U83 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U23 ] (X0) = 0; [ Marked_U102 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 1*X1 + 2; [ Marked_isNat ] (X0) = 1*X0 + 1; [ U12 ] (X0,X1,X2) = 0; [ Marked_U22 ] (X0,X1) = 1*X1 + 1; [ n__s ] (X0) = 1*X0 + 2; [ U41 ] (X0,X1) = 0; [ Marked_U31 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ isNat ] (X0) = 0; [ Marked_U34 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U91 ] (X0,X1) = 1; [ U34 ] (X0,X1,X2) = 0; [ Marked_isNatKind ] (X0) = 1*X0 + 1; [ U15 ] (X0,X1) = 0; [ Marked_U13 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U72 ] (X0,X1) = 1*X1; [ Marked_U84 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ isNatKind ] (X0) = 0; [ Marked_U72 ] (X0,X1) = 1*X1 + 1; [ U81 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U21 ] (X0,X1) = 0; [ Marked_U103 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 1*X1 + 1; [ Marked_U101 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 1*X1 + 2; [ x ] (X0,X1) = 2*X1*X0 + 1*X1 + 1*X0; [ n__plus ] (X0,X1) = 1*X1 + 1*X0; [ U42 ] (X0) = 0; [ Marked_U41 ] (X0,X1) = 1*X1 + 1; [ U103 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 1*X1; [ Marked_U35 ] (X0,X1) = 1*X1 + 1; [ U92 ] (X0) = 1; [ U33 ] (X0,X1,X2) = 0; [ Marked_U71 ] (X0,X1) = 1*X1 + 1; [ U14 ] (X0,X1,X2) = 0; [ Marked_U14 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ Marked_x ] (X0,X1) = 2*X1*X0 + 1*X1; [ U61 ] (X0,X1) = 0; [ U101 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 1*X1; [ U84 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U32 ] (X0,X1,X2) = 0; [ Marked_U91 ] (X0,X1) = 2*X1 + 1; [ U11 ] (X0,X1,X2) = 0; [ n__x ] (X0,X1) = 2*X1*X0 + 1*X1 + 1*X0; [ U51 ] (X0) = 0; [ Marked_U21 ] (X0,X1) = 1*X1 + 1; [ U104 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 1*X1; [ Marked_U33 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ 0 ] () = 1; [ U35 ] (X0,X1) = 0; [ Marked_U61 ] (X0,X1) = 1*X1 + 1; [ U16 ] (X0) = 0; [ Marked_U12 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ Marked_plus ] (X0,X1) = 1*X1 + 1*X0; [ U71 ] (X0,X1) = 1*X1; [ Marked_U83 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; removing < Marked_isNat(n__s(V1)),Marked_U21(isNatKind(activate(V1)),activate(V1))>< Marked_isNat(n__s(V1)),Marked_isNatKind(activate(V1))>< Marked_plus(N,s(M)),Marked_U81(isNat(M),M,N)>< Marked_x(N,s(M)),Marked_isNat(M)>< Marked_activate(n__x(X1,X2)),Marked_x(X1,X2)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ U102 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 2*X1 + 1; [ U82 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U22 ] (X0,X1) = 0; [ plus ] (X0,X1) = 1*X1 + 1*X0; [ Marked_U32 ] (X0,X1,X2) = 1*X2 + 1*X1; [ n__0 ] () = 0; [ U36 ] (X0) = 0; [ tt ] () = 0; [ s ] (X0) = 1*X0 + 1; [ U31 ] (X0,X1,X2) = 0; [ U13 ] (X0,X1,X2) = 0; [ Marked_U15 ] (X0,X1) = 1*X1; [ U62 ] (X0) = 0; [ Marked_U11 ] (X0,X1,X2) = 1*X2 + 1*X1; [ activate ] (X0) = 1*X0; [ U83 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U23 ] (X0) = 0; [ Marked_isNat ] (X0) = 1*X0; [ U12 ] (X0,X1,X2) = 0; [ n__s ] (X0) = 1*X0 + 1; [ U41 ] (X0,X1) = 0; [ Marked_U31 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 1*X1; [ isNat ] (X0) = 0; [ Marked_U34 ] (X0,X1,X2) = 1*X2 + 1*X1; [ U91 ] (X0,X1) = 1*X1 + 1; [ U34 ] (X0,X1,X2) = 0; [ U15 ] (X0,X1) = 0; [ Marked_U13 ] (X0,X1,X2) = 1*X2 + 1*X1; [ U72 ] (X0,X1) = 1*X1; [ isNatKind ] (X0) = 0; [ U81 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U21 ] (X0,X1) = 0; [ x ] (X0,X1) = 2*X1*X0 + 2*X1 + 1*X0 + 1; [ n__plus ] (X0,X1) = 1*X1 + 1*X0; [ U42 ] (X0) = 0; [ U103 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 2*X1 + 1; [ Marked_U35 ] (X0,X1) = 1*X1; [ U92 ] (X0) = 1; [ U33 ] (X0,X1,X2) = 0; [ U14 ] (X0,X1,X2) = 0; [ Marked_U14 ] (X0,X1,X2) = 1*X2 + 1*X1; [ U61 ] (X0,X1) = 0; [ U101 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 2*X1 + 2; [ U84 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U32 ] (X0,X1,X2) = 0; [ U11 ] (X0,X1,X2) = 0; [ n__x ] (X0,X1) = 2*X1*X0 + 2*X1 + 1*X0 + 1; [ U51 ] (X0) = 0; [ U104 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 2*X1 + 1; [ Marked_U33 ] (X0,X1,X2) = 1*X2 + 1*X1; [ 0 ] () = 0; [ U35 ] (X0,X1) = 0; [ U16 ] (X0) = 0; [ Marked_U12 ] (X0,X1,X2) = 1*X2 + 1*X1; [ U71 ] (X0,X1) = 1*X1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ U102 ] (X0,X1,X2) = 2*X2*X1 + 1*X2 + 1*X1 + 1; [ U82 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U22 ] (X0,X1) = 0; [ plus ] (X0,X1) = 1*X1 + 1*X0 + 1; [ n__0 ] () = 0; [ U36 ] (X0) = 0; [ tt ] () = 0; [ s ] (X0) = 1*X0 + 1; [ U31 ] (X0,X1,X2) = 0; [ U13 ] (X0,X1,X2) = 0; [ Marked_U15 ] (X0,X1) = 1*X1; [ U62 ] (X0) = 0; [ Marked_U11 ] (X0,X1,X2) = 1*X2 + 1*X1; [ activate ] (X0) = 1*X0; [ U83 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U23 ] (X0) = 0; [ Marked_isNat ] (X0) = 1*X0; [ U12 ] (X0,X1,X2) = 0; [ n__s ] (X0) = 1*X0 + 1; [ U41 ] (X0,X1) = 0; [ isNat ] (X0) = 0; [ U91 ] (X0,X1) = 0; [ U34 ] (X0,X1,X2) = 0; [ U15 ] (X0,X1) = 0; [ Marked_U13 ] (X0,X1,X2) = 1*X2 + 1*X1; [ U72 ] (X0,X1) = 1*X1 + 1; [ isNatKind ] (X0) = 0; [ U81 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U21 ] (X0,X1) = 0; [ x ] (X0,X1) = 2*X1*X0 + 1*X1; [ n__plus ] (X0,X1) = 1*X1 + 1*X0 + 1; [ U42 ] (X0) = 0; [ U103 ] (X0,X1,X2) = 2*X2*X1 + 1*X2 + 1*X1 + 1; [ U92 ] (X0) = 0; [ U33 ] (X0,X1,X2) = 0; [ U14 ] (X0,X1,X2) = 0; [ Marked_U14 ] (X0,X1,X2) = 1*X2 + 1*X1; [ U61 ] (X0,X1) = 0; [ U101 ] (X0,X1,X2) = 2*X2*X1 + 1*X2 + 1*X1 + 1; [ U84 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U32 ] (X0,X1,X2) = 0; [ U11 ] (X0,X1,X2) = 0; [ n__x ] (X0,X1) = 2*X1*X0 + 1*X1; [ U51 ] (X0) = 0; [ U104 ] (X0,X1,X2) = 2*X2*X1 + 1*X2 + 1*X1 + 1; [ 0 ] () = 0; [ U35 ] (X0,X1) = 0; [ U16 ] (X0) = 0; [ Marked_U12 ] (X0,X1,X2) = 1*X2 + 1*X1; [ U71 ] (X0,X1) = 1*X1 + 1; removing [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ U102 ] (X0,X1,X2) = 1*X2*X1 + 2*X2 + 1*X1 + 2; [ U82 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U22 ] (X0,X1) = 0; [ plus ] (X0,X1) = 1*X1 + 1*X0; [ n__0 ] () = 0; [ U36 ] (X0) = 0; [ tt ] () = 0; [ s ] (X0) = 1*X0 + 1; [ U31 ] (X0,X1,X2) = 0; [ U13 ] (X0,X1,X2) = 0; [ U62 ] (X0) = 0; [ activate ] (X0) = 1*X0; [ U83 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U23 ] (X0) = 0; [ U12 ] (X0,X1,X2) = 0; [ n__s ] (X0) = 1*X0 + 1; [ U41 ] (X0,X1) = 0; [ isNat ] (X0) = 0; [ U91 ] (X0,X1) = 0; [ U34 ] (X0,X1,X2) = 0; [ Marked_isNatKind ] (X0) = 2*X0; [ U15 ] (X0,X1) = 0; [ U72 ] (X0,X1) = 1*X1; [ isNatKind ] (X0) = 0; [ U81 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U21 ] (X0,X1) = 0; [ x ] (X0,X1) = 1*X1*X0 + 1*X1 + 1*X0 + 1; [ n__plus ] (X0,X1) = 1*X1 + 1*X0; [ U42 ] (X0) = 0; [ Marked_U41 ] (X0,X1) = 2*X1; [ U103 ] (X0,X1,X2) = 1*X2*X1 + 2*X2 + 1*X1 + 1; [ U92 ] (X0) = 0; [ U33 ] (X0,X1,X2) = 0; [ U14 ] (X0,X1,X2) = 0; [ U61 ] (X0,X1) = 0; [ U101 ] (X0,X1,X2) = 1*X2*X1 + 2*X2 + 1*X1 + 2; [ U84 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U32 ] (X0,X1,X2) = 0; [ U11 ] (X0,X1,X2) = 0; [ n__x ] (X0,X1) = 1*X1*X0 + 1*X1 + 1*X0 + 1; [ U51 ] (X0) = 0; [ U104 ] (X0,X1,X2) = 1*X2*X1 + 2*X2 + 1*X1 + 1; [ 0 ] () = 0; [ U35 ] (X0,X1) = 0; [ Marked_U61 ] (X0,X1) = 2*X1; [ U16 ] (X0) = 0; [ U71 ] (X0,X1) = 1*X1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ U102 ] (X0,X1,X2) = 2*X2*X1 + 1*X2 + 2*X1 + 1; [ U82 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U22 ] (X0,X1) = 0; [ plus ] (X0,X1) = 1*X1 + 1*X0 + 1; [ n__0 ] () = 0; [ U36 ] (X0) = 0; [ tt ] () = 0; [ s ] (X0) = 1*X0 + 1; [ U31 ] (X0,X1,X2) = 0; [ U13 ] (X0,X1,X2) = 0; [ U62 ] (X0) = 0; [ activate ] (X0) = 1*X0; [ U83 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U23 ] (X0) = 0; [ U12 ] (X0,X1,X2) = 0; [ n__s ] (X0) = 1*X0 + 1; [ U41 ] (X0,X1) = 0; [ isNat ] (X0) = 0; [ U91 ] (X0,X1) = 0; [ U34 ] (X0,X1,X2) = 0; [ Marked_isNatKind ] (X0) = 2*X0; [ U15 ] (X0,X1) = 0; [ U72 ] (X0,X1) = 1*X1 + 1; [ isNatKind ] (X0) = 0; [ U81 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U21 ] (X0,X1) = 0; [ x ] (X0,X1) = 2*X1*X0 + 2*X1; [ n__plus ] (X0,X1) = 1*X1 + 1*X0 + 1; [ U42 ] (X0) = 0; [ Marked_U41 ] (X0,X1) = 2*X1; [ U103 ] (X0,X1,X2) = 2*X2*X1 + 1*X2 + 2*X1 + 1; [ U92 ] (X0) = 0; [ U33 ] (X0,X1,X2) = 0; [ U14 ] (X0,X1,X2) = 0; [ U61 ] (X0,X1) = 0; [ U101 ] (X0,X1,X2) = 2*X2*X1 + 1*X2 + 2*X1 + 1; [ U84 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U32 ] (X0,X1,X2) = 0; [ U11 ] (X0,X1,X2) = 0; [ n__x ] (X0,X1) = 2*X1*X0 + 2*X1; [ U51 ] (X0) = 0; [ U104 ] (X0,X1,X2) = 2*X2*X1 + 1*X2 + 2*X1 + 1; [ 0 ] () = 0; [ U35 ] (X0,X1) = 0; [ U16 ] (X0) = 0; [ U71 ] (X0,X1) = 1*X1 + 1; removing [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} ]} ]} Cime worked for 145.184679 seconds (real time) Cime Exit Status: 0