- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] U11(tt,V2) -> U12(isNat(activate(V2))) [2] U12(tt) -> tt [3] U21(tt) -> tt [4] U31(tt,V2) -> U32(isNat(activate(V2))) [5] U32(tt) -> tt [6] U41(tt,N) -> activate(N) [7] U51(tt,M,N) -> U52(isNat(activate(N)),activate(M),activate(N)) [8] U52(tt,M,N) -> s(plus(activate(N),activate(M))) [9] U61(tt) -> 0 [10] U71(tt,M,N) -> U72(isNat(activate(N)),activate(M),activate(N)) [11] U72(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) [12] isNat(n__0) -> tt [13] isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2)) [14] isNat(n__s(V1)) -> U21(isNat(activate(V1))) [15] isNat(n__x(V1,V2)) -> U31(isNat(activate(V1)),activate(V2)) [16] plus(N,0) -> U41(isNat(N),N) [17] plus(N,s(M)) -> U51(isNat(M),M,N) [18] x(N,0) -> U61(isNat(N)) [19] x(N,s(M)) -> U71(isNat(M),M,N) [20] 0 -> n__0 [21] plus(X1,X2) -> n__plus(X1,X2) [22] s(X) -> n__s(X) [23] x(X1,X2) -> n__x(X1,X2) [24] activate(n__0) -> 0 [25] activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2)) [26] activate(n__s(X)) -> s(activate(X)) [27] activate(n__x(X1,X2)) -> x(activate(X1),activate(X2)) [28] activate(X) -> X Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { U12(tt) >= tt ; isNat(n__0) >= tt ; isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2)) ; isNat(n__s(V1)) >= U21(isNat(activate(V1))) ; isNat(n__x(V1,V2)) >= U31(isNat(activate(V1)),activate(V2)) ; activate(n__0) >= 0 ; activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) ; activate(n__s(X)) >= s(activate(X)) ; activate(n__x(X1,X2)) >= x(activate(X1),activate(X2)) ; activate(X) >= X ; U11(tt,V2) >= U12(isNat(activate(V2))) ; U21(tt) >= tt ; U32(tt) >= tt ; U31(tt,V2) >= U32(isNat(activate(V2))) ; U41(tt,N) >= activate(N) ; U52(tt,M,N) >= s(plus(activate(N),activate(M))) ; U51(tt,M,N) >= U52(isNat(activate(N)),activate(M),activate(N)) ; s(X) >= n__s(X) ; plus(N,s(M)) >= U51(isNat(M),M,N) ; plus(N,0) >= U41(isNat(N),N) ; plus(X1,X2) >= n__plus(X1,X2) ; 0 >= n__0 ; U61(tt) >= 0 ; U72(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ; U71(tt,M,N) >= U72(isNat(activate(N)),activate(M),activate(N)) ; x(N,s(M)) >= U71(isNat(M),M,N) ; x(N,0) >= U61(isNat(N)) ; x(X1,X2) >= n__x(X1,X2) ; Marked_activate(n__plus(X1,X2)) >= Marked_activate(X1) ; Marked_activate(n__plus(X1,X2)) >= Marked_activate(X2) ; Marked_activate(n__plus(X1,X2)) >= Marked_plus(activate(X1),activate(X2)) ; Marked_activate(n__s(X)) >= Marked_activate(X) ; Marked_activate(n__x(X1,X2)) >= Marked_activate(X1) ; Marked_activate(n__x(X1,X2)) >= Marked_activate(X2) ; Marked_activate(n__x(X1,X2)) >= Marked_x(activate(X1),activate(X2)) ; Marked_x(N,s(M)) >= Marked_U71(isNat(M),M,N) ; Marked_x(N,s(M)) >= Marked_isNat(M) ; Marked_x(N,0) >= Marked_isNat(N) ; Marked_plus(N,s(M)) >= Marked_isNat(M) ; Marked_plus(N,s(M)) >= Marked_U51(isNat(M),M,N) ; Marked_plus(N,0) >= Marked_isNat(N) ; Marked_plus(N,0) >= Marked_U41(isNat(N),N) ; Marked_U71(tt,M,N) >= Marked_activate(N) ; Marked_U71(tt,M,N) >= Marked_activate(M) ; Marked_U71(tt,M,N) >= Marked_isNat(activate(N)) ; Marked_U71(tt,M,N) >= Marked_U72(isNat(activate(N)),activate(M),activate(N)) ; Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V2) ; Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V1) ; Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1)) ; Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNat(activate(V1)),activate(V2)) ; Marked_isNat(n__s(V1)) >= Marked_activate(V1) ; Marked_isNat(n__s(V1)) >= Marked_isNat(activate(V1)) ; Marked_isNat(n__x(V1,V2)) >= Marked_activate(V2) ; Marked_isNat(n__x(V1,V2)) >= Marked_activate(V1) ; Marked_isNat(n__x(V1,V2)) >= Marked_isNat(activate(V1)) ; Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNat(activate(V1)),activate(V2)) ; Marked_U51(tt,M,N) >= Marked_activate(N) ; Marked_U51(tt,M,N) >= Marked_activate(M) ; Marked_U51(tt,M,N) >= Marked_isNat(activate(N)) ; Marked_U51(tt,M,N) >= Marked_U52(isNat(activate(N)),activate(M),activate(N)) ; Marked_U41(tt,N) >= Marked_activate(N) ; Marked_U31(tt,V2) >= Marked_activate(V2) ; Marked_U31(tt,V2) >= Marked_isNat(activate(V2)) ; Marked_U11(tt,V2) >= Marked_activate(V2) ; Marked_U11(tt,V2) >= Marked_isNat(activate(V2)) ; Marked_U72(tt,M,N) >= Marked_activate(N) ; Marked_U72(tt,M,N) >= Marked_activate(M) ; Marked_U72(tt,M,N) >= Marked_x(activate(N),activate(M)) ; Marked_U72(tt,M,N) >= Marked_plus(x(activate(N),activate(M)),activate(N)) ; Marked_U52(tt,M,N) >= Marked_activate(N) ; Marked_U52(tt,M,N) >= Marked_activate(M) ; Marked_U52(tt,M,N) >= Marked_plus(activate(N),activate(M)) ; } + Disjunctions:{ { Marked_activate(n__plus(X1,X2)) > Marked_activate(X1) ; } { Marked_activate(n__plus(X1,X2)) > Marked_activate(X2) ; } { Marked_activate(n__plus(X1,X2)) > Marked_plus(activate(X1),activate(X2)) ; } { Marked_activate(n__s(X)) > Marked_activate(X) ; } { Marked_activate(n__x(X1,X2)) > Marked_activate(X1) ; } { Marked_activate(n__x(X1,X2)) > Marked_activate(X2) ; } { Marked_activate(n__x(X1,X2)) > Marked_x(activate(X1),activate(X2)) ; } { Marked_x(N,s(M)) > Marked_U71(isNat(M),M,N) ; } { Marked_x(N,s(M)) > Marked_isNat(M) ; } { Marked_x(N,0) > Marked_isNat(N) ; } { Marked_plus(N,s(M)) > Marked_isNat(M) ; } { Marked_plus(N,s(M)) > Marked_U51(isNat(M),M,N) ; } { Marked_plus(N,0) > Marked_isNat(N) ; } { Marked_plus(N,0) > Marked_U41(isNat(N),N) ; } { Marked_U71(tt,M,N) > Marked_activate(N) ; } { Marked_U71(tt,M,N) > Marked_activate(M) ; } { Marked_U71(tt,M,N) > Marked_isNat(activate(N)) ; } { Marked_U71(tt,M,N) > Marked_U72(isNat(activate(N)),activate(M),activate(N)) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_activate(V2) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_activate(V1) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_isNat(activate(V1)) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_U11(isNat(activate(V1)),activate(V2)) ; } { Marked_isNat(n__s(V1)) > Marked_activate(V1) ; } { Marked_isNat(n__s(V1)) > Marked_isNat(activate(V1)) ; } { Marked_isNat(n__x(V1,V2)) > Marked_activate(V2) ; } { Marked_isNat(n__x(V1,V2)) > Marked_activate(V1) ; } { Marked_isNat(n__x(V1,V2)) > Marked_isNat(activate(V1)) ; } { Marked_isNat(n__x(V1,V2)) > Marked_U31(isNat(activate(V1)),activate(V2)) ; } { Marked_U51(tt,M,N) > Marked_activate(N) ; } { Marked_U51(tt,M,N) > Marked_activate(M) ; } { Marked_U51(tt,M,N) > Marked_isNat(activate(N)) ; } { Marked_U51(tt,M,N) > Marked_U52(isNat(activate(N)),activate(M),activate(N)) ; } { Marked_U41(tt,N) > Marked_activate(N) ; } { Marked_U31(tt,V2) > Marked_activate(V2) ; } { Marked_U31(tt,V2) > Marked_isNat(activate(V2)) ; } { Marked_U11(tt,V2) > Marked_activate(V2) ; } { Marked_U11(tt,V2) > Marked_isNat(activate(V2)) ; } { Marked_U72(tt,M,N) > Marked_activate(N) ; } { Marked_U72(tt,M,N) > Marked_activate(M) ; } { Marked_U72(tt,M,N) > Marked_x(activate(N),activate(M)) ; } { Marked_U72(tt,M,N) > Marked_plus(x(activate(N),activate(M)),activate(N)) ; } { Marked_U52(tt,M,N) > Marked_activate(N) ; } { Marked_U52(tt,M,N) > Marked_activate(M) ; } { Marked_U52(tt,M,N) > Marked_plus(activate(N),activate(M)) ; } } === 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: U12(tt) >= tt constraint: isNat(n__0) >= tt constraint: isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2)) constraint: isNat(n__s(V1)) >= U21(isNat(activate(V1))) constraint: isNat(n__x(V1,V2)) >= U31(isNat(activate(V1)),activate(V2)) constraint: activate(n__0) >= 0 constraint: activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) constraint: activate(n__s(X)) >= s(activate(X)) constraint: activate(n__x(X1,X2)) >= x(activate(X1),activate(X2)) constraint: activate(X) >= X constraint: U11(tt,V2) >= U12(isNat(activate(V2))) constraint: U21(tt) >= tt constraint: U32(tt) >= tt constraint: U31(tt,V2) >= U32(isNat(activate(V2))) constraint: U41(tt,N) >= activate(N) constraint: U52(tt,M,N) >= s(plus(activate(N),activate(M))) constraint: U51(tt,M,N) >= U52(isNat(activate(N)),activate(M),activate(N)) constraint: s(X) >= n__s(X) constraint: plus(N,s(M)) >= U51(isNat(M),M,N) constraint: plus(N,0) >= U41(isNat(N),N) constraint: plus(X1,X2) >= n__plus(X1,X2) constraint: 0 >= n__0 constraint: U61(tt) >= 0 constraint: U72(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) constraint: U71(tt,M,N) >= U72(isNat(activate(N)),activate(M),activate(N)) constraint: x(N,s(M)) >= U71(isNat(M),M,N) constraint: x(N,0) >= U61(isNat(N)) constraint: x(X1,X2) >= n__x(X1,X2) constraint: Marked_activate(n__plus(X1,X2)) >= Marked_activate(X1) constraint: Marked_activate(n__plus(X1,X2)) >= Marked_activate(X2) constraint: Marked_activate(n__plus(X1,X2)) >= Marked_plus(activate(X1), activate(X2)) constraint: Marked_activate(n__s(X)) >= Marked_activate(X) constraint: Marked_activate(n__x(X1,X2)) >= Marked_activate(X1) constraint: Marked_activate(n__x(X1,X2)) >= Marked_activate(X2) constraint: Marked_activate(n__x(X1,X2)) >= Marked_x(activate(X1),activate(X2)) constraint: Marked_x(N,s(M)) >= Marked_U71(isNat(M),M,N) constraint: Marked_x(N,s(M)) >= Marked_isNat(M) constraint: Marked_x(N,0) >= Marked_isNat(N) constraint: Marked_plus(N,s(M)) >= Marked_isNat(M) constraint: Marked_plus(N,s(M)) >= Marked_U51(isNat(M),M,N) constraint: Marked_plus(N,0) >= Marked_isNat(N) constraint: Marked_plus(N,0) >= Marked_U41(isNat(N),N) constraint: Marked_U71(tt,M,N) >= Marked_activate(N) constraint: Marked_U71(tt,M,N) >= Marked_activate(M) constraint: Marked_U71(tt,M,N) >= Marked_isNat(activate(N)) constraint: Marked_U71(tt,M,N) >= Marked_U72(isNat(activate(N)),activate(M), activate(N)) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V2) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V1) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1)) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNat(activate(V1)), activate(V2)) constraint: Marked_isNat(n__s(V1)) >= Marked_activate(V1) constraint: Marked_isNat(n__s(V1)) >= Marked_isNat(activate(V1)) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_activate(V2) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_activate(V1) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_isNat(activate(V1)) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNat(activate(V1)), activate(V2)) constraint: Marked_U51(tt,M,N) >= Marked_activate(N) constraint: Marked_U51(tt,M,N) >= Marked_activate(M) constraint: Marked_U51(tt,M,N) >= Marked_isNat(activate(N)) constraint: Marked_U51(tt,M,N) >= Marked_U52(isNat(activate(N)),activate(M), activate(N)) constraint: Marked_U41(tt,N) >= Marked_activate(N) constraint: Marked_U31(tt,V2) >= Marked_activate(V2) constraint: Marked_U31(tt,V2) >= Marked_isNat(activate(V2)) constraint: Marked_U11(tt,V2) >= Marked_activate(V2) constraint: Marked_U11(tt,V2) >= Marked_isNat(activate(V2)) constraint: Marked_U72(tt,M,N) >= Marked_activate(N) constraint: Marked_U72(tt,M,N) >= Marked_activate(M) constraint: Marked_U72(tt,M,N) >= Marked_x(activate(N),activate(M)) constraint: Marked_U72(tt,M,N) >= Marked_plus(x(activate(N),activate(M)), activate(N)) constraint: Marked_U52(tt,M,N) >= Marked_activate(N) constraint: Marked_U52(tt,M,N) >= Marked_activate(M) constraint: Marked_U52(tt,M,N) >= Marked_plus(activate(N),activate(M)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { U12(tt) >= tt ; isNat(n__0) >= tt ; isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2)) ; isNat(n__s(V1)) >= U21(isNat(activate(V1))) ; isNat(n__x(V1,V2)) >= U31(isNat(activate(V1)),activate(V2)) ; activate(n__0) >= 0 ; activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) ; activate(n__s(X)) >= s(activate(X)) ; activate(n__x(X1,X2)) >= x(activate(X1),activate(X2)) ; activate(X) >= X ; U11(tt,V2) >= U12(isNat(activate(V2))) ; U21(tt) >= tt ; U32(tt) >= tt ; U31(tt,V2) >= U32(isNat(activate(V2))) ; U41(tt,N) >= activate(N) ; U52(tt,M,N) >= s(plus(activate(N),activate(M))) ; U51(tt,M,N) >= U52(isNat(activate(N)),activate(M),activate(N)) ; s(X) >= n__s(X) ; plus(N,s(M)) >= U51(isNat(M),M,N) ; plus(N,0) >= U41(isNat(N),N) ; plus(X1,X2) >= n__plus(X1,X2) ; 0 >= n__0 ; U61(tt) >= 0 ; U72(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ; U71(tt,M,N) >= U72(isNat(activate(N)),activate(M),activate(N)) ; x(N,s(M)) >= U71(isNat(M),M,N) ; x(N,0) >= U61(isNat(N)) ; x(X1,X2) >= n__x(X1,X2) ; Marked_activate(n__plus(X1,X2)) >= Marked_activate(X1) ; Marked_activate(n__plus(X1,X2)) >= Marked_activate(X2) ; Marked_activate(n__plus(X1,X2)) >= Marked_plus(activate(X1),activate(X2)) ; Marked_activate(n__x(X1,X2)) >= Marked_activate(X1) ; Marked_activate(n__x(X1,X2)) >= Marked_activate(X2) ; Marked_activate(n__x(X1,X2)) >= Marked_x(activate(X1),activate(X2)) ; Marked_x(N,0) >= Marked_isNat(N) ; Marked_plus(N,0) >= Marked_isNat(N) ; Marked_plus(N,0) >= Marked_U41(isNat(N),N) ; Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V2) ; Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V1) ; Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1)) ; Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNat(activate(V1)),activate(V2)) ; Marked_isNat(n__x(V1,V2)) >= Marked_activate(V2) ; Marked_isNat(n__x(V1,V2)) >= Marked_activate(V1) ; Marked_isNat(n__x(V1,V2)) >= Marked_isNat(activate(V1)) ; Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNat(activate(V1)),activate(V2)) ; Marked_U41(tt,N) >= Marked_activate(N) ; Marked_U31(tt,V2) >= Marked_activate(V2) ; Marked_U31(tt,V2) >= Marked_isNat(activate(V2)) ; Marked_U11(tt,V2) >= Marked_activate(V2) ; Marked_U11(tt,V2) >= Marked_isNat(activate(V2)) ; } + Disjunctions:{ { Marked_activate(n__plus(X1,X2)) > Marked_activate(X1) ; } { Marked_activate(n__plus(X1,X2)) > Marked_activate(X2) ; } { Marked_activate(n__plus(X1,X2)) > Marked_plus(activate(X1),activate(X2)) ; } { Marked_activate(n__x(X1,X2)) > Marked_activate(X1) ; } { Marked_activate(n__x(X1,X2)) > Marked_activate(X2) ; } { Marked_activate(n__x(X1,X2)) > Marked_x(activate(X1),activate(X2)) ; } { Marked_x(N,0) > Marked_isNat(N) ; } { Marked_plus(N,0) > Marked_isNat(N) ; } { Marked_plus(N,0) > Marked_U41(isNat(N),N) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_activate(V2) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_activate(V1) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_isNat(activate(V1)) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_U11(isNat(activate(V1)),activate(V2)) ; } { Marked_isNat(n__x(V1,V2)) > Marked_activate(V2) ; } { Marked_isNat(n__x(V1,V2)) > Marked_activate(V1) ; } { Marked_isNat(n__x(V1,V2)) > Marked_isNat(activate(V1)) ; } { Marked_isNat(n__x(V1,V2)) > Marked_U31(isNat(activate(V1)),activate(V2)) ; } { Marked_U41(tt,N) > Marked_activate(N) ; } { Marked_U31(tt,V2) > Marked_activate(V2) ; } { Marked_U31(tt,V2) > Marked_isNat(activate(V2)) ; } { Marked_U11(tt,V2) > Marked_activate(V2) ; } { Marked_U11(tt,V2) > Marked_isNat(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: U12(tt) >= tt constraint: isNat(n__0) >= tt constraint: isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2)) constraint: isNat(n__s(V1)) >= U21(isNat(activate(V1))) constraint: isNat(n__x(V1,V2)) >= U31(isNat(activate(V1)),activate(V2)) constraint: activate(n__0) >= 0 constraint: activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) constraint: activate(n__s(X)) >= s(activate(X)) constraint: activate(n__x(X1,X2)) >= x(activate(X1),activate(X2)) constraint: activate(X) >= X constraint: U11(tt,V2) >= U12(isNat(activate(V2))) constraint: U21(tt) >= tt constraint: U32(tt) >= tt constraint: U31(tt,V2) >= U32(isNat(activate(V2))) constraint: U41(tt,N) >= activate(N) constraint: U52(tt,M,N) >= s(plus(activate(N),activate(M))) constraint: U51(tt,M,N) >= U52(isNat(activate(N)),activate(M),activate(N)) constraint: s(X) >= n__s(X) constraint: plus(N,s(M)) >= U51(isNat(M),M,N) constraint: plus(N,0) >= U41(isNat(N),N) constraint: plus(X1,X2) >= n__plus(X1,X2) constraint: 0 >= n__0 constraint: U61(tt) >= 0 constraint: U72(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) constraint: U71(tt,M,N) >= U72(isNat(activate(N)),activate(M),activate(N)) constraint: x(N,s(M)) >= U71(isNat(M),M,N) constraint: x(N,0) >= U61(isNat(N)) constraint: x(X1,X2) >= n__x(X1,X2) constraint: Marked_activate(n__plus(X1,X2)) >= Marked_activate(X1) constraint: Marked_activate(n__plus(X1,X2)) >= Marked_activate(X2) constraint: Marked_activate(n__plus(X1,X2)) >= Marked_plus(activate(X1), activate(X2)) constraint: Marked_activate(n__x(X1,X2)) >= Marked_activate(X1) constraint: Marked_activate(n__x(X1,X2)) >= Marked_activate(X2) constraint: Marked_activate(n__x(X1,X2)) >= Marked_x(activate(X1),activate(X2)) constraint: Marked_x(N,0) >= Marked_isNat(N) constraint: Marked_plus(N,0) >= Marked_isNat(N) constraint: Marked_plus(N,0) >= Marked_U41(isNat(N),N) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V2) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V1) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1)) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNat(activate(V1)), activate(V2)) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_activate(V2) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_activate(V1) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_isNat(activate(V1)) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNat(activate(V1)), activate(V2)) constraint: Marked_U41(tt,N) >= Marked_activate(N) constraint: Marked_U31(tt,V2) >= Marked_activate(V2) constraint: Marked_U31(tt,V2) >= Marked_isNat(activate(V2)) constraint: Marked_U11(tt,V2) >= Marked_activate(V2) constraint: Marked_U11(tt,V2) >= Marked_isNat(activate(V2)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { U12(tt) >= tt ; isNat(n__0) >= tt ; isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2)) ; isNat(n__s(V1)) >= U21(isNat(activate(V1))) ; isNat(n__x(V1,V2)) >= U31(isNat(activate(V1)),activate(V2)) ; activate(n__0) >= 0 ; activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) ; activate(n__s(X)) >= s(activate(X)) ; activate(n__x(X1,X2)) >= x(activate(X1),activate(X2)) ; activate(X) >= X ; U11(tt,V2) >= U12(isNat(activate(V2))) ; U21(tt) >= tt ; U32(tt) >= tt ; U31(tt,V2) >= U32(isNat(activate(V2))) ; U41(tt,N) >= activate(N) ; U52(tt,M,N) >= s(plus(activate(N),activate(M))) ; U51(tt,M,N) >= U52(isNat(activate(N)),activate(M),activate(N)) ; s(X) >= n__s(X) ; plus(N,s(M)) >= U51(isNat(M),M,N) ; plus(N,0) >= U41(isNat(N),N) ; plus(X1,X2) >= n__plus(X1,X2) ; 0 >= n__0 ; U61(tt) >= 0 ; U72(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ; U71(tt,M,N) >= U72(isNat(activate(N)),activate(M),activate(N)) ; x(N,s(M)) >= U71(isNat(M),M,N) ; x(N,0) >= U61(isNat(N)) ; x(X1,X2) >= n__x(X1,X2) ; Marked_activate(n__plus(X1,X2)) >= Marked_activate(X1) ; Marked_activate(n__plus(X1,X2)) >= Marked_activate(X2) ; Marked_activate(n__plus(X1,X2)) >= Marked_plus(activate(X1),activate(X2)) ; Marked_activate(n__x(X1,X2)) >= Marked_activate(X1) ; Marked_activate(n__x(X1,X2)) >= Marked_activate(X2) ; Marked_plus(N,0) >= Marked_isNat(N) ; Marked_plus(N,0) >= Marked_U41(isNat(N),N) ; Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V2) ; Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V1) ; Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1)) ; Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNat(activate(V1)),activate(V2)) ; Marked_isNat(n__x(V1,V2)) >= Marked_activate(V2) ; Marked_isNat(n__x(V1,V2)) >= Marked_activate(V1) ; Marked_isNat(n__x(V1,V2)) >= Marked_isNat(activate(V1)) ; Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNat(activate(V1)),activate(V2)) ; Marked_U41(tt,N) >= Marked_activate(N) ; Marked_U31(tt,V2) >= Marked_activate(V2) ; Marked_U31(tt,V2) >= Marked_isNat(activate(V2)) ; Marked_U11(tt,V2) >= Marked_activate(V2) ; Marked_U11(tt,V2) >= Marked_isNat(activate(V2)) ; } + Disjunctions:{ { Marked_activate(n__plus(X1,X2)) > Marked_activate(X1) ; } { Marked_activate(n__plus(X1,X2)) > Marked_activate(X2) ; } { Marked_activate(n__plus(X1,X2)) > Marked_plus(activate(X1),activate(X2)) ; } { Marked_activate(n__x(X1,X2)) > Marked_activate(X1) ; } { Marked_activate(n__x(X1,X2)) > Marked_activate(X2) ; } { Marked_plus(N,0) > Marked_isNat(N) ; } { Marked_plus(N,0) > Marked_U41(isNat(N),N) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_activate(V2) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_activate(V1) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_isNat(activate(V1)) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_U11(isNat(activate(V1)),activate(V2)) ; } { Marked_isNat(n__x(V1,V2)) > Marked_activate(V2) ; } { Marked_isNat(n__x(V1,V2)) > Marked_activate(V1) ; } { Marked_isNat(n__x(V1,V2)) > Marked_isNat(activate(V1)) ; } { Marked_isNat(n__x(V1,V2)) > Marked_U31(isNat(activate(V1)),activate(V2)) ; } { Marked_U41(tt,N) > Marked_activate(N) ; } { Marked_U31(tt,V2) > Marked_activate(V2) ; } { Marked_U31(tt,V2) > Marked_isNat(activate(V2)) ; } { Marked_U11(tt,V2) > Marked_activate(V2) ; } { Marked_U11(tt,V2) > Marked_isNat(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: U12(tt) >= tt constraint: isNat(n__0) >= tt constraint: isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2)) constraint: isNat(n__s(V1)) >= U21(isNat(activate(V1))) constraint: isNat(n__x(V1,V2)) >= U31(isNat(activate(V1)),activate(V2)) constraint: activate(n__0) >= 0 constraint: activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) constraint: activate(n__s(X)) >= s(activate(X)) constraint: activate(n__x(X1,X2)) >= x(activate(X1),activate(X2)) constraint: activate(X) >= X constraint: U11(tt,V2) >= U12(isNat(activate(V2))) constraint: U21(tt) >= tt constraint: U32(tt) >= tt constraint: U31(tt,V2) >= U32(isNat(activate(V2))) constraint: U41(tt,N) >= activate(N) constraint: U52(tt,M,N) >= s(plus(activate(N),activate(M))) constraint: U51(tt,M,N) >= U52(isNat(activate(N)),activate(M),activate(N)) constraint: s(X) >= n__s(X) constraint: plus(N,s(M)) >= U51(isNat(M),M,N) constraint: plus(N,0) >= U41(isNat(N),N) constraint: plus(X1,X2) >= n__plus(X1,X2) constraint: 0 >= n__0 constraint: U61(tt) >= 0 constraint: U72(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) constraint: U71(tt,M,N) >= U72(isNat(activate(N)),activate(M),activate(N)) constraint: x(N,s(M)) >= U71(isNat(M),M,N) constraint: x(N,0) >= U61(isNat(N)) constraint: x(X1,X2) >= n__x(X1,X2) constraint: Marked_activate(n__plus(X1,X2)) >= Marked_activate(X1) constraint: Marked_activate(n__plus(X1,X2)) >= Marked_activate(X2) constraint: Marked_activate(n__plus(X1,X2)) >= Marked_plus(activate(X1), activate(X2)) constraint: Marked_activate(n__x(X1,X2)) >= Marked_activate(X1) constraint: Marked_activate(n__x(X1,X2)) >= Marked_activate(X2) constraint: Marked_plus(N,0) >= Marked_isNat(N) constraint: Marked_plus(N,0) >= Marked_U41(isNat(N),N) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V2) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_activate(V1) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1)) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNat(activate(V1)), activate(V2)) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_activate(V2) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_activate(V1) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_isNat(activate(V1)) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNat(activate(V1)), activate(V2)) constraint: Marked_U41(tt,N) >= Marked_activate(N) constraint: Marked_U31(tt,V2) >= Marked_activate(V2) constraint: Marked_U31(tt,V2) >= Marked_isNat(activate(V2)) constraint: Marked_U11(tt,V2) >= Marked_activate(V2) constraint: Marked_U11(tt,V2) >= Marked_isNat(activate(V2)) APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { U12(tt) >= tt ; isNat(n__0) >= tt ; isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2)) ; isNat(n__s(V1)) >= U21(isNat(activate(V1))) ; isNat(n__x(V1,V2)) >= U31(isNat(activate(V1)),activate(V2)) ; activate(n__0) >= 0 ; activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) ; activate(n__s(X)) >= s(activate(X)) ; activate(n__x(X1,X2)) >= x(activate(X1),activate(X2)) ; activate(X) >= X ; U11(tt,V2) >= U12(isNat(activate(V2))) ; U21(tt) >= tt ; U32(tt) >= tt ; U31(tt,V2) >= U32(isNat(activate(V2))) ; U41(tt,N) >= activate(N) ; U52(tt,M,N) >= s(plus(activate(N),activate(M))) ; U51(tt,M,N) >= U52(isNat(activate(N)),activate(M),activate(N)) ; s(X) >= n__s(X) ; plus(N,s(M)) >= U51(isNat(M),M,N) ; plus(N,0) >= U41(isNat(N),N) ; plus(X1,X2) >= n__plus(X1,X2) ; 0 >= n__0 ; U61(tt) >= 0 ; U72(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ; U71(tt,M,N) >= U72(isNat(activate(N)),activate(M),activate(N)) ; x(N,s(M)) >= U71(isNat(M),M,N) ; x(N,0) >= U61(isNat(N)) ; x(X1,X2) >= n__x(X1,X2) ; Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1)) ; Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNat(activate(V1)),activate(V2)) ; Marked_isNat(n__x(V1,V2)) >= Marked_isNat(activate(V1)) ; Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNat(activate(V1)),activate(V2)) ; Marked_U31(tt,V2) >= Marked_isNat(activate(V2)) ; Marked_U11(tt,V2) >= Marked_isNat(activate(V2)) ; } + Disjunctions:{ { Marked_isNat(n__plus(V1,V2)) > Marked_isNat(activate(V1)) ; } { Marked_isNat(n__plus(V1,V2)) > Marked_U11(isNat(activate(V1)),activate(V2)) ; } { Marked_isNat(n__x(V1,V2)) > Marked_isNat(activate(V1)) ; } { Marked_isNat(n__x(V1,V2)) > Marked_U31(isNat(activate(V1)),activate(V2)) ; } { Marked_U31(tt,V2) > Marked_isNat(activate(V2)) ; } { Marked_U11(tt,V2) > Marked_isNat(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: U12(tt) >= tt constraint: isNat(n__0) >= tt constraint: isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2)) constraint: isNat(n__s(V1)) >= U21(isNat(activate(V1))) constraint: isNat(n__x(V1,V2)) >= U31(isNat(activate(V1)),activate(V2)) constraint: activate(n__0) >= 0 constraint: activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) constraint: activate(n__s(X)) >= s(activate(X)) constraint: activate(n__x(X1,X2)) >= x(activate(X1),activate(X2)) constraint: activate(X) >= X constraint: U11(tt,V2) >= U12(isNat(activate(V2))) constraint: U21(tt) >= tt constraint: U32(tt) >= tt constraint: U31(tt,V2) >= U32(isNat(activate(V2))) constraint: U41(tt,N) >= activate(N) constraint: U52(tt,M,N) >= s(plus(activate(N),activate(M))) constraint: U51(tt,M,N) >= U52(isNat(activate(N)),activate(M),activate(N)) constraint: s(X) >= n__s(X) constraint: plus(N,s(M)) >= U51(isNat(M),M,N) constraint: plus(N,0) >= U41(isNat(N),N) constraint: plus(X1,X2) >= n__plus(X1,X2) constraint: 0 >= n__0 constraint: U61(tt) >= 0 constraint: U72(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) constraint: U71(tt,M,N) >= U72(isNat(activate(N)),activate(M),activate(N)) constraint: x(N,s(M)) >= U71(isNat(M),M,N) constraint: x(N,0) >= U61(isNat(N)) constraint: x(X1,X2) >= n__x(X1,X2) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1)) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_U11(isNat(activate(V1)), activate(V2)) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_isNat(activate(V1)) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNat(activate(V1)), activate(V2)) constraint: Marked_U31(tt,V2) >= Marked_isNat(activate(V2)) constraint: Marked_U11(tt,V2) >= Marked_isNat(activate(V2)) APPLY CRITERIA (Subterm criterion) ST: Marked_activate -> 1 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { U12(tt) >= tt ; isNat(n__0) >= tt ; isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2)) ; isNat(n__s(V1)) >= U21(isNat(activate(V1))) ; isNat(n__x(V1,V2)) >= U31(isNat(activate(V1)),activate(V2)) ; activate(n__0) >= 0 ; activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) ; activate(n__s(X)) >= s(activate(X)) ; activate(n__x(X1,X2)) >= x(activate(X1),activate(X2)) ; activate(X) >= X ; U11(tt,V2) >= U12(isNat(activate(V2))) ; U21(tt) >= tt ; U32(tt) >= tt ; U31(tt,V2) >= U32(isNat(activate(V2))) ; U41(tt,N) >= activate(N) ; U52(tt,M,N) >= s(plus(activate(N),activate(M))) ; U51(tt,M,N) >= U52(isNat(activate(N)),activate(M),activate(N)) ; s(X) >= n__s(X) ; plus(N,s(M)) >= U51(isNat(M),M,N) ; plus(N,0) >= U41(isNat(N),N) ; plus(X1,X2) >= n__plus(X1,X2) ; 0 >= n__0 ; U61(tt) >= 0 ; U72(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ; U71(tt,M,N) >= U72(isNat(activate(N)),activate(M),activate(N)) ; x(N,s(M)) >= U71(isNat(M),M,N) ; x(N,0) >= U61(isNat(N)) ; x(X1,X2) >= n__x(X1,X2) ; Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1)) ; Marked_isNat(n__x(V1,V2)) >= Marked_isNat(activate(V1)) ; Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNat(activate(V1)),activate(V2)) ; Marked_U31(tt,V2) >= Marked_isNat(activate(V2)) ; } + Disjunctions:{ { Marked_isNat(n__plus(V1,V2)) > Marked_isNat(activate(V1)) ; } { Marked_isNat(n__x(V1,V2)) > Marked_isNat(activate(V1)) ; } { Marked_isNat(n__x(V1,V2)) > Marked_U31(isNat(activate(V1)),activate(V2)) ; } { Marked_U31(tt,V2) > Marked_isNat(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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: U12(tt) >= tt constraint: isNat(n__0) >= tt constraint: isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2)) constraint: isNat(n__s(V1)) >= U21(isNat(activate(V1))) constraint: isNat(n__x(V1,V2)) >= U31(isNat(activate(V1)),activate(V2)) constraint: activate(n__0) >= 0 constraint: activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) constraint: activate(n__s(X)) >= s(activate(X)) constraint: activate(n__x(X1,X2)) >= x(activate(X1),activate(X2)) constraint: activate(X) >= X constraint: U11(tt,V2) >= U12(isNat(activate(V2))) constraint: U21(tt) >= tt constraint: U32(tt) >= tt constraint: U31(tt,V2) >= U32(isNat(activate(V2))) constraint: U41(tt,N) >= activate(N) constraint: U52(tt,M,N) >= s(plus(activate(N),activate(M))) constraint: U51(tt,M,N) >= U52(isNat(activate(N)),activate(M),activate(N)) constraint: s(X) >= n__s(X) constraint: plus(N,s(M)) >= U51(isNat(M),M,N) constraint: plus(N,0) >= U41(isNat(N),N) constraint: plus(X1,X2) >= n__plus(X1,X2) constraint: 0 >= n__0 constraint: U61(tt) >= 0 constraint: U72(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) constraint: U71(tt,M,N) >= U72(isNat(activate(N)),activate(M),activate(N)) constraint: x(N,s(M)) >= U71(isNat(M),M,N) constraint: x(N,0) >= U61(isNat(N)) constraint: x(X1,X2) >= n__x(X1,X2) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1)) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_isNat(activate(V1)) constraint: Marked_isNat(n__x(V1,V2)) >= Marked_U31(isNat(activate(V1)), activate(V2)) constraint: Marked_U31(tt,V2) >= Marked_isNat(activate(V2)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { U12(tt) >= tt ; isNat(n__0) >= tt ; isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2)) ; isNat(n__s(V1)) >= U21(isNat(activate(V1))) ; isNat(n__x(V1,V2)) >= U31(isNat(activate(V1)),activate(V2)) ; activate(n__0) >= 0 ; activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) ; activate(n__s(X)) >= s(activate(X)) ; activate(n__x(X1,X2)) >= x(activate(X1),activate(X2)) ; activate(X) >= X ; U11(tt,V2) >= U12(isNat(activate(V2))) ; U21(tt) >= tt ; U32(tt) >= tt ; U31(tt,V2) >= U32(isNat(activate(V2))) ; U41(tt,N) >= activate(N) ; U52(tt,M,N) >= s(plus(activate(N),activate(M))) ; U51(tt,M,N) >= U52(isNat(activate(N)),activate(M),activate(N)) ; s(X) >= n__s(X) ; plus(N,s(M)) >= U51(isNat(M),M,N) ; plus(N,0) >= U41(isNat(N),N) ; plus(X1,X2) >= n__plus(X1,X2) ; 0 >= n__0 ; U61(tt) >= 0 ; U72(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) ; U71(tt,M,N) >= U72(isNat(activate(N)),activate(M),activate(N)) ; x(N,s(M)) >= U71(isNat(M),M,N) ; x(N,0) >= U61(isNat(N)) ; x(X1,X2) >= n__x(X1,X2) ; Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1)) ; } + Disjunctions:{ { Marked_isNat(n__plus(V1,V2)) > Marked_isNat(activate(V1)) ; } } === 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: U12(tt) >= tt constraint: isNat(n__0) >= tt constraint: isNat(n__plus(V1,V2)) >= U11(isNat(activate(V1)),activate(V2)) constraint: isNat(n__s(V1)) >= U21(isNat(activate(V1))) constraint: isNat(n__x(V1,V2)) >= U31(isNat(activate(V1)),activate(V2)) constraint: activate(n__0) >= 0 constraint: activate(n__plus(X1,X2)) >= plus(activate(X1),activate(X2)) constraint: activate(n__s(X)) >= s(activate(X)) constraint: activate(n__x(X1,X2)) >= x(activate(X1),activate(X2)) constraint: activate(X) >= X constraint: U11(tt,V2) >= U12(isNat(activate(V2))) constraint: U21(tt) >= tt constraint: U32(tt) >= tt constraint: U31(tt,V2) >= U32(isNat(activate(V2))) constraint: U41(tt,N) >= activate(N) constraint: U52(tt,M,N) >= s(plus(activate(N),activate(M))) constraint: U51(tt,M,N) >= U52(isNat(activate(N)),activate(M),activate(N)) constraint: s(X) >= n__s(X) constraint: plus(N,s(M)) >= U51(isNat(M),M,N) constraint: plus(N,0) >= U41(isNat(N),N) constraint: plus(X1,X2) >= n__plus(X1,X2) constraint: 0 >= n__0 constraint: U61(tt) >= 0 constraint: U72(tt,M,N) >= plus(x(activate(N),activate(M)),activate(N)) constraint: U71(tt,M,N) >= U72(isNat(activate(N)),activate(M),activate(N)) constraint: x(N,s(M)) >= U71(isNat(M),M,N) constraint: x(N,0) >= U61(isNat(N)) constraint: x(X1,X2) >= n__x(X1,X2) constraint: Marked_isNat(n__plus(V1,V2)) >= Marked_isNat(activate(V1)) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] U11(tt,V2) -> U12(isNat(activate(V2))) [2] U12(tt) -> tt [3] U21(tt) -> tt [4] U31(tt,V2) -> U32(isNat(activate(V2))) [5] U32(tt) -> tt [6] U41(tt,N) -> activate(N) [7] U51(tt,M,N) -> U52(isNat(activate(N)),activate(M),activate(N)) [8] U52(tt,M,N) -> s(plus(activate(N),activate(M))) [9] U61(tt) -> 0 [10] U71(tt,M,N) -> U72(isNat(activate(N)),activate(M),activate(N)) [11] U72(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) [12] isNat(n__0) -> tt [13] isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2)) [14] isNat(n__s(V1)) -> U21(isNat(activate(V1))) [15] isNat(n__x(V1,V2)) -> U31(isNat(activate(V1)),activate(V2)) [16] plus(N,0) -> U41(isNat(N),N) [17] plus(N,s(M)) -> U51(isNat(M),M,N) [18] x(N,0) -> U61(isNat(N)) [19] x(N,s(M)) -> U71(isNat(M),M,N) [20] 0 -> n__0 [21] plus(X1,X2) -> n__plus(X1,X2) [22] s(X) -> n__s(X) [23] x(X1,X2) -> n__x(X1,X2) [24] activate(n__0) -> 0 [25] activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2)) [26] activate(n__s(X)) -> s(activate(X)) [27] activate(n__x(X1,X2)) -> x(activate(X1),activate(X2)) [28] activate(X) -> X , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ U12 ] (X0) = 0; [ Marked_U31 ] (X0,X1) = 1*X1; [ U71 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 1*X1; [ U41 ] (X0,X1) = 1*X1; [ tt ] () = 0; [ Marked_U52 ] (X0,X1,X2) = 1*X2 + 1*X1; [ n__s ] (X0) = 1*X0 + 2; [ plus ] (X0,X1) = 1*X1 + 1*X0; [ Marked_isNat ] (X0) = 1*X0; [ activate ] (X0) = 1*X0; [ Marked_U11 ] (X0,X1) = 1*X1; [ n__0 ] () = 0; [ U51 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U32 ] (X0) = 0; [ Marked_activate ] (X0) = 1*X0; [ U61 ] (X0) = 0; [ Marked_U51 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ isNat ] (X0) = 0; [ x ] (X0,X1) = 2*X1*X0 + 1*X1 + 1*X0; [ U52 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ Marked_plus ] (X0,X1) = 1*X1 + 1*X0; [ U21 ] (X0) = 0; [ n__x ] (X0,X1) = 2*X1*X0 + 1*X1 + 1*X0; [ 0 ] () = 0; [ U11 ] (X0,X1) = 0; [ Marked_U72 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 1*X1; [ n__plus ] (X0,X1) = 1*X1 + 1*X0; [ s ] (X0) = 1*X0 + 2; [ Marked_U71 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 1*X1 + 2; [ U31 ] (X0,X1) = 0; [ Marked_x ] (X0,X1) = 2*X1*X0 + 1*X1 + 1*X0; [ U72 ] (X0,X1,X2) = 2*X2*X1 + 2*X2 + 1*X1; [ Marked_U41 ] (X0,X1) = 1*X1; removing < Marked_U51(tt,M,N),Marked_activate(N)>< Marked_U51(tt,M,N),Marked_activate(N)>< Marked_U71(tt,M,N),Marked_isNat(activate(N))>< Marked_U71(tt,M,N),Marked_activate(M)>< Marked_isNat(n__s(V1)),Marked_isNat(activate(V1))> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ U12 ] (X0) = 0; [ Marked_U31 ] (X0,X1) = 2*X1; [ U71 ] (X0,X1,X2) = 1*X2*X1 + 2*X2 + 2*X1 + 2; [ U41 ] (X0,X1) = 1*X1; [ tt ] () = 0; [ n__s ] (X0) = 1*X0 + 1; [ plus ] (X0,X1) = 1*X1 + 1*X0; [ Marked_isNat ] (X0) = 1*X0; [ activate ] (X0) = 1*X0; [ Marked_U11 ] (X0,X1) = 1*X1; [ n__0 ] () = 1; [ U51 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U32 ] (X0) = 0; [ Marked_activate ] (X0) = 1*X0; [ U61 ] (X0) = 2; [ isNat ] (X0) = 0; [ x ] (X0,X1) = 1*X1*X0 + 2*X1 + 1*X0; [ U52 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ Marked_plus ] (X0,X1) = 1*X0; [ U21 ] (X0) = 0; [ n__x ] (X0,X1) = 1*X1*X0 + 2*X1 + 1*X0; [ 0 ] () = 1; [ U11 ] (X0,X1) = 0; [ n__plus ] (X0,X1) = 1*X1 + 1*X0; [ s ] (X0) = 1*X0 + 1; [ U31 ] (X0,X1) = 0; [ Marked_x ] (X0,X1) = 2*X1 + 1*X0; [ U72 ] (X0,X1,X2) = 1*X2*X1 + 2*X2 + 2*X1; [ Marked_U41 ] (X0,X1) = 1*X1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ U12 ] (X0) = 0; [ Marked_U31 ] (X0,X1) = 2*X1 + 2; [ U71 ] (X0,X1,X2) = 1*X2*X1 + 2*X2 + 2*X1; [ U41 ] (X0,X1) = 1*X1; [ tt ] () = 0; [ n__s ] (X0) = 1*X0 + 2; [ plus ] (X0,X1) = 1*X1 + 1*X0; [ Marked_isNat ] (X0) = 2*X0 + 2; [ activate ] (X0) = 1*X0; [ Marked_U11 ] (X0,X1) = 2*X1 + 2; [ n__0 ] () = 1; [ U51 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ U32 ] (X0) = 0; [ Marked_activate ] (X0) = 2*X0 + 2; [ U61 ] (X0) = 2; [ isNat ] (X0) = 0; [ x ] (X0,X1) = 1*X1*X0 + 2*X1 + 1*X0; [ U52 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ Marked_plus ] (X0,X1) = 1*X1 + 2*X0 + 1; [ U21 ] (X0) = 0; [ n__x ] (X0,X1) = 1*X1*X0 + 2*X1 + 1*X0; [ 0 ] () = 1; [ U11 ] (X0,X1) = 0; [ n__plus ] (X0,X1) = 1*X1 + 1*X0; [ s ] (X0) = 1*X0 + 2; [ U31 ] (X0,X1) = 0; [ U72 ] (X0,X1,X2) = 1*X2*X1 + 2*X2 + 2*X1; [ Marked_U41 ] (X0,X1) = 2*X1 + 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ U12 ] (X0) = 2; [ Marked_U31 ] (X0,X1) = 2*X1*X0 + 1; [ U71 ] (X0,X1,X2) = 2*X2*X1 + 2*X2; [ U41 ] (X0,X1) = 1*X1; [ tt ] () = 2; [ n__s ] (X0) = 1*X0 + 1; [ plus ] (X0,X1) = 1*X1 + 1*X0; [ Marked_isNat ] (X0) = 2*X0 + 1; [ activate ] (X0) = 1*X0; [ Marked_U11 ] (X0,X1) = 2*X1 + 2*X0 + 1; [ n__0 ] () = 2; [ U51 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U32 ] (X0) = 1*X0; [ U61 ] (X0) = 1*X0; [ isNat ] (X0) = 1*X0; [ x ] (X0,X1) = 2*X1*X0 + 1*X0; [ U52 ] (X0,X1,X2) = 1*X2 + 1*X1 + 1; [ U21 ] (X0) = 1*X0 + 1; [ n__x ] (X0,X1) = 2*X1*X0 + 1*X0; [ 0 ] () = 2; [ U11 ] (X0,X1) = 1*X0; [ n__plus ] (X0,X1) = 1*X1 + 1*X0; [ s ] (X0) = 1*X0 + 1; [ U31 ] (X0,X1) = 2*X1*X0 + 1*X0; [ U72 ] (X0,X1,X2) = 2*X2*X1 + 2*X2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ U12 ] (X0) = 2; [ Marked_U31 ] (X0,X1) = 2*X1 + 2*X0; [ U71 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2; [ U41 ] (X0,X1) = 1*X1; [ tt ] () = 2; [ n__s ] (X0) = 1*X0; [ plus ] (X0,X1) = 1*X0; [ Marked_isNat ] (X0) = 2*X0 + 2; [ activate ] (X0) = 1*X0; [ n__0 ] () = 1; [ U51 ] (X0,X1,X2) = 1*X2; [ U32 ] (X0) = 1*X0; [ U61 ] (X0) = 1; [ isNat ] (X0) = 2*X0; [ x ] (X0,X1) = 2*X1 + 2*X0 + 2; [ U52 ] (X0,X1,X2) = 1*X2; [ U21 ] (X0) = 1*X0; [ n__x ] (X0,X1) = 2*X1 + 2*X0 + 2; [ 0 ] () = 1; [ U11 ] (X0,X1) = 1*X0; [ n__plus ] (X0,X1) = 1*X0; [ s ] (X0) = 1*X0; [ U31 ] (X0,X1) = 2*X1; [ U72 ] (X0,X1,X2) = 2*X2 + 2*X1 + 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ U12 ] (X0) = 0; [ U71 ] (X0,X1,X2) = 1 + 2*X1 + 2*X2 + 2*X2*X1 + 0; [ U41 ] (X0,X1) = 1 + 1*X1 + 0; [ tt ] () = 0; [ n__s ] (X0) = 1 + 1*X0 + 0; [ plus ] (X0,X1) = 1 + 1*X0 + 2*X1 + 0; [ Marked_isNat ] (X0) = 2*X0 + 0; [ activate ] (X0) = 1*X0 + 0; [ n__0 ] () = 0; [ U51 ] (X0,X1,X2) = 2 + 2*X1 + 1*X2 + 0; [ U32 ] (X0) = 0; [ U61 ] (X0) = 0; [ isNat ] (X0) = 0; [ x ] (X0,X1) = 2*X1 + 2*X1*X0 + 0; [ U52 ] (X0,X1,X2) = 2 + 2*X1 + 1*X2 + 0; [ U21 ] (X0) = 0; [ n__x ] (X0,X1) = 2*X1 + 2*X1*X0 + 0; [ 0 ] () = 0; [ U11 ] (X0,X1) = 0; [ n__plus ] (X0,X1) = 1 + 1*X0 + 2*X1 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ U31 ] (X0,X1) = 0; [ U72 ] (X0,X1,X2) = 1 + 2*X1 + 2*X2 + 2*X2*X1 + 0; ]} ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} Cime worked for 129.162220 seconds (real time) Cime Exit Status: 0