- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__U11(tt,N) -> mark(N) [2] a__U21(tt,M,N) -> s(a__plus(mark(N),mark(M))) [3] a__and(tt,X) -> mark(X) [4] a__isNat(0) -> tt [5] a__isNat(plus(V1,V2)) -> a__and(a__isNat(V1),isNat(V2)) [6] a__isNat(s(V1)) -> a__isNat(V1) [7] a__plus(N,0) -> a__U11(a__isNat(N),N) [8] a__plus(N,s(M)) -> a__U21(a__and(a__isNat(M),isNat(N)),M,N) [9] mark(U11(X1,X2)) -> a__U11(mark(X1),X2) [10] mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) [11] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) [12] mark(and(X1,X2)) -> a__and(mark(X1),X2) [13] mark(isNat(X)) -> a__isNat(X) [14] mark(tt) -> tt [15] mark(s(X)) -> s(mark(X)) [16] mark(0) -> 0 [17] a__U11(X1,X2) -> U11(X1,X2) [18] a__U21(X1,X2,X3) -> U21(X1,X2,X3) [19] a__plus(X1,X2) -> plus(X1,X2) [20] a__and(X1,X2) -> and(X1,X2) [21] a__isNat(X) -> isNat(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: { mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(isNat(X)) >= a__isNat(X) ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,N) >= mark(N) ; a__U11(X1,X2) >= U11(X1,X2) ; a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; a__plus(N,0) >= a__U11(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U21(X1,X2,X3) >= U21(X1,X2,X3) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ; a__isNat(X) >= isNat(X) ; Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_a__plus(N,s(M)) >= Marked_a__isNat(M) ; Marked_a__plus(N,s(M)) >= Marked_a__and(a__isNat(M),isNat(N)) ; Marked_a__plus(N,s(M)) >= Marked_a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; Marked_a__plus(N,0) >= Marked_a__isNat(N) ; Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N) ; Marked_a__U21(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) ; Marked_a__U21(tt,M,N) >= Marked_mark(N) ; Marked_a__U21(tt,M,N) >= Marked_mark(M) ; Marked_a__U11(tt,N) >= Marked_mark(N) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(isNat(X)) >= Marked_a__isNat(X) ; Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) ; Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2,X3)) >= Marked_a__U21(mark(X1),X2,X3) ; Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ; } { Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ; } { Marked_a__isNat(plus(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_a__plus(N,s(M)) > Marked_a__isNat(M) ; } { Marked_a__plus(N,s(M)) > Marked_a__and(a__isNat(M),isNat(N)) ; } { Marked_a__plus(N,s(M)) > Marked_a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; } { Marked_a__plus(N,0) > Marked_a__isNat(N) ; } { Marked_a__plus(N,0) > Marked_a__U11(a__isNat(N),N) ; } { Marked_a__U21(tt,M,N) > Marked_a__plus(mark(N),mark(M)) ; } { Marked_a__U21(tt,M,N) > Marked_mark(N) ; } { Marked_a__U21(tt,M,N) > Marked_mark(M) ; } { Marked_a__U11(tt,N) > Marked_mark(N) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(isNat(X)) > Marked_a__isNat(X) ; } { Marked_mark(plus(X1,X2)) > Marked_a__plus(mark(X1),mark(X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(U11(X1,X2)) > Marked_a__U11(mark(X1),X2) ; } { Marked_mark(U11(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2,X3)) > Marked_a__U21(mark(X1),X2,X3) ; } { Marked_mark(U21(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,N) >= mark(N) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) constraint: a__plus(N,0) >= a__U11(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) constraint: a__isNat(X) >= isNat(X) constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1), isNat(V2)) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_a__plus(N,s(M)) >= Marked_a__isNat(M) constraint: Marked_a__plus(N,s(M)) >= Marked_a__and(a__isNat(M),isNat(N)) constraint: Marked_a__plus(N,s(M)) >= Marked_a__U21(a__and(a__isNat(M), isNat(N)),M,N) constraint: Marked_a__plus(N,0) >= Marked_a__isNat(N) constraint: Marked_a__plus(N,0) >= Marked_a__U11(a__isNat(N),N) constraint: Marked_a__U21(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) constraint: Marked_a__U21(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U21(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U11(tt,N) >= Marked_mark(N) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X) constraint: Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_a__U21(mark(X1),X2,X3) constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(isNat(X)) >= a__isNat(X) ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,N) >= mark(N) ; a__U11(X1,X2) >= U11(X1,X2) ; a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; a__plus(N,0) >= a__U11(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U21(X1,X2,X3) >= U21(X1,X2,X3) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ; a__isNat(X) >= isNat(X) ; Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_a__plus(N,s(M)) >= Marked_a__isNat(M) ; Marked_a__plus(N,s(M)) >= Marked_a__and(a__isNat(M),isNat(N)) ; Marked_a__plus(N,s(M)) >= Marked_a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; Marked_a__U21(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) ; Marked_a__U21(tt,M,N) >= Marked_mark(N) ; Marked_a__U21(tt,M,N) >= Marked_mark(M) ; Marked_a__U11(tt,N) >= Marked_mark(N) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(isNat(X)) >= Marked_a__isNat(X) ; Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) ; Marked_mark(U11(X1,X2)) >= Marked_mark(X1) ; Marked_mark(U21(X1,X2,X3)) >= Marked_a__U21(mark(X1),X2,X3) ; Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ; } { Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ; } { Marked_a__isNat(plus(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_a__plus(N,s(M)) > Marked_a__isNat(M) ; } { Marked_a__plus(N,s(M)) > Marked_a__and(a__isNat(M),isNat(N)) ; } { Marked_a__plus(N,s(M)) > Marked_a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; } { Marked_a__U21(tt,M,N) > Marked_a__plus(mark(N),mark(M)) ; } { Marked_a__U21(tt,M,N) > Marked_mark(N) ; } { Marked_a__U21(tt,M,N) > Marked_mark(M) ; } { Marked_a__U11(tt,N) > Marked_mark(N) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(isNat(X)) > Marked_a__isNat(X) ; } { Marked_mark(plus(X1,X2)) > Marked_a__plus(mark(X1),mark(X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(U11(X1,X2)) > Marked_a__U11(mark(X1),X2) ; } { Marked_mark(U11(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(U21(X1,X2,X3)) > Marked_a__U21(mark(X1),X2,X3) ; } { Marked_mark(U21(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,N) >= mark(N) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) constraint: a__plus(N,0) >= a__U11(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) constraint: a__isNat(X) >= isNat(X) constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1), isNat(V2)) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_a__plus(N,s(M)) >= Marked_a__isNat(M) constraint: Marked_a__plus(N,s(M)) >= Marked_a__and(a__isNat(M),isNat(N)) constraint: Marked_a__plus(N,s(M)) >= Marked_a__U21(a__and(a__isNat(M), isNat(N)),M,N) constraint: Marked_a__U21(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) constraint: Marked_a__U21(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U21(tt,M,N) >= Marked_mark(M) constraint: Marked_a__U11(tt,N) >= Marked_mark(N) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X) constraint: Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(U11(X1,X2)) >= Marked_a__U11(mark(X1),X2) constraint: Marked_mark(U11(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_a__U21(mark(X1),X2,X3) constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(isNat(X)) >= a__isNat(X) ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,N) >= mark(N) ; a__U11(X1,X2) >= U11(X1,X2) ; a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; a__plus(N,0) >= a__U11(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U21(X1,X2,X3) >= U21(X1,X2,X3) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ; a__isNat(X) >= isNat(X) ; Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_a__plus(N,s(M)) >= Marked_a__isNat(M) ; Marked_a__plus(N,s(M)) >= Marked_a__and(a__isNat(M),isNat(N)) ; Marked_a__plus(N,s(M)) >= Marked_a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; Marked_a__U21(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) ; Marked_a__U21(tt,M,N) >= Marked_mark(N) ; Marked_a__U21(tt,M,N) >= Marked_mark(M) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(isNat(X)) >= Marked_a__isNat(X) ; Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(U21(X1,X2,X3)) >= Marked_a__U21(mark(X1),X2,X3) ; Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ; } { Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ; } { Marked_a__isNat(plus(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_a__plus(N,s(M)) > Marked_a__isNat(M) ; } { Marked_a__plus(N,s(M)) > Marked_a__and(a__isNat(M),isNat(N)) ; } { Marked_a__plus(N,s(M)) > Marked_a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; } { Marked_a__U21(tt,M,N) > Marked_a__plus(mark(N),mark(M)) ; } { Marked_a__U21(tt,M,N) > Marked_mark(N) ; } { Marked_a__U21(tt,M,N) > Marked_mark(M) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(isNat(X)) > Marked_a__isNat(X) ; } { Marked_mark(plus(X1,X2)) > Marked_a__plus(mark(X1),mark(X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(U21(X1,X2,X3)) > Marked_a__U21(mark(X1),X2,X3) ; } { Marked_mark(U21(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,N) >= mark(N) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) constraint: a__plus(N,0) >= a__U11(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) constraint: a__isNat(X) >= isNat(X) constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1), isNat(V2)) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_a__plus(N,s(M)) >= Marked_a__isNat(M) constraint: Marked_a__plus(N,s(M)) >= Marked_a__and(a__isNat(M),isNat(N)) constraint: Marked_a__plus(N,s(M)) >= Marked_a__U21(a__and(a__isNat(M), isNat(N)),M,N) constraint: Marked_a__U21(tt,M,N) >= Marked_a__plus(mark(N),mark(M)) constraint: Marked_a__U21(tt,M,N) >= Marked_mark(N) constraint: Marked_a__U21(tt,M,N) >= Marked_mark(M) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X) constraint: Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_a__U21(mark(X1),X2,X3) constraint: Marked_mark(U21(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(isNat(X)) >= a__isNat(X) ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,N) >= mark(N) ; a__U11(X1,X2) >= U11(X1,X2) ; a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; a__plus(N,0) >= a__U11(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U21(X1,X2,X3) >= U21(X1,X2,X3) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ; a__isNat(X) >= isNat(X) ; Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_mark(isNat(X)) >= Marked_a__isNat(X) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNat(s(V1)) > Marked_a__isNat(V1) ; } { Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ; } { Marked_a__isNat(plus(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_mark(isNat(X)) > Marked_a__isNat(X) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,N) >= mark(N) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) constraint: a__plus(N,0) >= a__U11(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) constraint: a__isNat(X) >= isNat(X) constraint: Marked_a__isNat(s(V1)) >= Marked_a__isNat(V1) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1), isNat(V2)) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(isNat(X)) >= a__isNat(X) ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,N) >= mark(N) ; a__U11(X1,X2) >= U11(X1,X2) ; a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; a__plus(N,0) >= a__U11(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U21(X1,X2,X3) >= U21(X1,X2,X3) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ; a__isNat(X) >= isNat(X) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_mark(isNat(X)) >= Marked_a__isNat(X) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ; } { Marked_a__isNat(plus(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_mark(isNat(X)) > Marked_a__isNat(X) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,N) >= mark(N) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) constraint: a__plus(N,0) >= a__U11(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) constraint: a__isNat(X) >= isNat(X) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1), isNat(V2)) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(isNat(X)) >= a__isNat(X) ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,N) >= mark(N) ; a__U11(X1,X2) >= U11(X1,X2) ; a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; a__plus(N,0) >= a__U11(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U21(X1,X2,X3) >= U21(X1,X2,X3) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ; a__isNat(X) >= isNat(X) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1),isNat(V2)) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_mark(isNat(X)) >= Marked_a__isNat(X) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(V1) ; } { Marked_a__isNat(plus(V1,V2)) > Marked_a__and(a__isNat(V1),isNat(V2)) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_mark(isNat(X)) > Marked_a__isNat(X) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,N) >= mark(N) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) constraint: a__plus(N,0) >= a__U11(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) constraint: a__isNat(X) >= isNat(X) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__and(a__isNat(V1), isNat(V2)) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_mark(isNat(X)) >= Marked_a__isNat(X) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(isNat(X)) >= a__isNat(X) ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,N) >= mark(N) ; a__U11(X1,X2) >= U11(X1,X2) ; a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; a__plus(N,0) >= a__U11(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U21(X1,X2,X3) >= U21(X1,X2,X3) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ; a__isNat(X) >= isNat(X) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,N) >= mark(N) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) constraint: a__plus(N,0) >= a__U11(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) constraint: a__isNat(X) >= isNat(X) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(tt) >= tt ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(isNat(X)) >= a__isNat(X) ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; mark(U11(X1,X2)) >= a__U11(mark(X1),X2) ; mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; a__U11(tt,N) >= mark(N) ; a__U11(X1,X2) >= U11(X1,X2) ; a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) ; a__plus(N,0) >= a__U11(a__isNat(N),N) ; a__plus(X1,X2) >= plus(X1,X2) ; a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) ; a__U21(X1,X2,X3) >= U21(X1,X2,X3) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__isNat(s(V1)) >= a__isNat(V1) ; a__isNat(0) >= tt ; a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) ; a__isNat(X) >= isNat(X) ; Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) ; } + Disjunctions:{ { Marked_a__isNat(plus(V1,V2)) > Marked_a__isNat(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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(tt) >= tt constraint: mark(s(X)) >= s(mark(X)) constraint: mark(0) >= 0 constraint: mark(isNat(X)) >= a__isNat(X) constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: mark(U11(X1,X2)) >= a__U11(mark(X1),X2) constraint: mark(U21(X1,X2,X3)) >= a__U21(mark(X1),X2,X3) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: a__U11(tt,N) >= mark(N) constraint: a__U11(X1,X2) >= U11(X1,X2) constraint: a__plus(N,s(M)) >= a__U21(a__and(a__isNat(M),isNat(N)),M,N) constraint: a__plus(N,0) >= a__U11(a__isNat(N),N) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: a__U21(tt,M,N) >= s(a__plus(mark(N),mark(M))) constraint: a__U21(X1,X2,X3) >= U21(X1,X2,X3) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__isNat(s(V1)) >= a__isNat(V1) constraint: a__isNat(0) >= tt constraint: a__isNat(plus(V1,V2)) >= a__and(a__isNat(V1),isNat(V2)) constraint: a__isNat(X) >= isNat(X) constraint: Marked_a__isNat(plus(V1,V2)) >= Marked_a__isNat(V1) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] a__U11(tt,N) -> mark(N) [2] a__U21(tt,M,N) -> s(a__plus(mark(N),mark(M))) [3] a__and(tt,X) -> mark(X) [4] a__isNat(0) -> tt [5] a__isNat(plus(V1,V2)) -> a__and(a__isNat(V1),isNat(V2)) [6] a__isNat(s(V1)) -> a__isNat(V1) [7] a__plus(N,0) -> a__U11(a__isNat(N),N) [8] a__plus(N,s(M)) -> a__U21(a__and(a__isNat(M),isNat(N)),M,N) [9] mark(U11(X1,X2)) -> a__U11(mark(X1),X2) [10] mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) [11] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) [12] mark(and(X1,X2)) -> a__and(mark(X1),X2) [13] mark(isNat(X)) -> a__isNat(X) [14] mark(tt) -> tt [15] mark(s(X)) -> s(mark(X)) [16] mark(0) -> 0 [17] a__U11(X1,X2) -> U11(X1,X2) [18] a__U21(X1,X2,X3) -> U21(X1,X2,X3) [19] a__plus(X1,X2) -> plus(X1,X2) [20] a__and(X1,X2) -> and(X1,X2) [21] a__isNat(X) -> isNat(X) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ Marked_a__plus ] (X0,X1) = 1*X1 + 1*X0; [ 0 ] () = 1; [ a__plus ] (X0,X1) = 1*X1 + 2*X0; [ U21 ] (X0,X1,X2) = 2*X2 + 1*X1 + 2*X0; [ tt ] () = 0; [ Marked_a__U11 ] (X0,X1) = 1*X1; [ plus ] (X0,X1) = 1*X1 + 2*X0; [ a__and ] (X0,X1) = 2*X1 + 1*X0; [ Marked_a__isNat ] (X0) = 0; [ a__U11 ] (X0,X1) = 1*X1 + 1*X0; [ Marked_a__U21 ] (X0,X1,X2) = 1*X2 + 1*X1; [ isNat ] (X0) = 0; [ a__U21 ] (X0,X1,X2) = 2*X2 + 1*X1 + 2*X0; [ and ] (X0,X1) = 2*X1 + 1*X0; [ s ] (X0) = 1*X0; [ Marked_mark ] (X0) = 1*X0; [ U11 ] (X0,X1) = 1*X1 + 1*X0; [ a__isNat ] (X0) = 0; [ Marked_a__and ] (X0,X1) = 2*X1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ Marked_a__plus ] (X0,X1) = 2*X1 + 2*X0; [ 0 ] () = 2; [ a__plus ] (X0,X1) = 2*X1 + 1*X0; [ U21 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ tt ] () = 0; [ Marked_a__U11 ] (X0,X1) = 2*X1; [ plus ] (X0,X1) = 2*X1 + 1*X0; [ a__and ] (X0,X1) = 2*X1 + 1*X0; [ Marked_a__isNat ] (X0) = 0; [ a__U11 ] (X0,X1) = 1*X1 + 2*X0 + 1; [ Marked_a__U21 ] (X0,X1,X2) = 2*X2 + 2*X1; [ isNat ] (X0) = 0; [ a__U21 ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ and ] (X0,X1) = 2*X1 + 1*X0; [ s ] (X0) = 1*X0; [ Marked_mark ] (X0) = 2*X0; [ U11 ] (X0,X1) = 1*X1 + 2*X0 + 1; [ a__isNat ] (X0) = 0; [ Marked_a__and ] (X0,X1) = 2*X1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ Marked_a__plus ] (X0,X1) = 3*X1 + 2*X0; [ 0 ] () = 0; [ a__plus ] (X0,X1) = 2*X1 + 1*X0; [ U21 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1*X0 + 3; [ tt ] () = 0; [ plus ] (X0,X1) = 2*X1 + 1*X0; [ a__and ] (X0,X1) = 2*X1 + 2*X0; [ Marked_a__isNat ] (X0) = 2; [ a__U11 ] (X0,X1) = 1*X1; [ Marked_a__U21 ] (X0,X1,X2) = 2*X2 + 3*X1 + 2; [ isNat ] (X0) = 0; [ a__U21 ] (X0,X1,X2) = 1*X2 + 2*X1 + 1*X0 + 3; [ and ] (X0,X1) = 2*X1 + 2*X0; [ s ] (X0) = 1*X0 + 3; [ Marked_mark ] (X0) = 2*X0 + 2; [ U11 ] (X0,X1) = 1*X1; [ a__isNat ] (X0) = 0; [ Marked_a__and ] (X0,X1) = 2*X1 + 2; removing < Marked_mark(U21(X1,X2,X3)),Marked_a__U21(mark(X1),X2,X3)>< Marked_mark(plus(X1,X2)),Marked_a__plus(mark(X1),mark(X2))> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ 0 ] () = 0; [ a__plus ] (X0,X1) = 1*X1 + 1*X0; [ U21 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ tt ] () = 0; [ plus ] (X0,X1) = 1*X1 + 1*X0; [ a__and ] (X0,X1) = 1*X1 + 1*X0; [ Marked_a__isNat ] (X0) = 2*X0; [ a__U11 ] (X0,X1) = 1*X1; [ isNat ] (X0) = 2*X0; [ a__U21 ] (X0,X1,X2) = 1*X2 + 1*X1 + 2; [ and ] (X0,X1) = 1*X1 + 1*X0; [ s ] (X0) = 1*X0 + 2; [ Marked_mark ] (X0) = 1*X0; [ U11 ] (X0,X1) = 1*X1; [ a__isNat ] (X0) = 2*X0; [ Marked_a__and ] (X0,X1) = 1*X1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ 0 ] () = 0; [ a__plus ] (X0,X1) = 2*X1 + 2*X0 + 2; [ U21 ] (X0,X1,X2) = 0; [ tt ] () = 0; [ plus ] (X0,X1) = 2*X1 + 2*X0 + 2; [ a__and ] (X0,X1) = 2*X1 + 2*X0; [ Marked_a__isNat ] (X0) = 0; [ a__U11 ] (X0,X1) = 1*X1 + 2; [ isNat ] (X0) = 0; [ a__U21 ] (X0,X1,X2) = 0; [ and ] (X0,X1) = 2*X1 + 2*X0; [ s ] (X0) = 0; [ Marked_mark ] (X0) = 1*X0; [ U11 ] (X0,X1) = 1*X1 + 2; [ a__isNat ] (X0) = 0; [ Marked_a__and ] (X0,X1) = 1*X1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ 0 ] () = 1; [ a__plus ] (X0,X1) = 2*X1 + 2*X0; [ U21 ] (X0,X1,X2) = 2*X2 + 2*X1; [ tt ] () = 1; [ plus ] (X0,X1) = 2*X1 + 2*X0; [ a__and ] (X0,X1) = 1*X1 + 2*X0; [ Marked_a__isNat ] (X0) = 2*X0; [ a__U11 ] (X0,X1) = 1*X1; [ isNat ] (X0) = 1*X0; [ a__U21 ] (X0,X1,X2) = 2*X2 + 2*X1; [ and ] (X0,X1) = 1*X1 + 2*X0; [ s ] (X0) = 1*X0; [ Marked_mark ] (X0) = 2*X0; [ U11 ] (X0,X1) = 1*X1; [ a__isNat ] (X0) = 1*X0; [ Marked_a__and ] (X0,X1) = 2*X1 + 2*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ mark ] (X0) = 1*X0 + 0; [ 0 ] () = 0; [ a__plus ] (X0,X1) = 1 + 1*X0 + 2*X1 + 0; [ U21 ] (X0,X1,X2) = 1 + 2*X1 + 1*X2 + 0; [ tt ] () = 0; [ plus ] (X0,X1) = 1 + 1*X0 + 2*X1 + 0; [ a__and ] (X0,X1) = 1 + 1*X0 + 1*X1 + 0; [ a__U11 ] (X0,X1) = 1 + 1*X1 + 0; [ isNat ] (X0) = 1*X0 + 0; [ a__U21 ] (X0,X1,X2) = 1 + 2*X1 + 1*X2 + 0; [ and ] (X0,X1) = 1 + 1*X0 + 1*X1 + 0; [ s ] (X0) = 1*X0 + 0; [ Marked_mark ] (X0) = 3*X0 + 0; [ U11 ] (X0,X1) = 1 + 1*X1 + 0; [ a__isNat ] (X0) = 1*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ mark ] (X0) = 2*X0 + 0; [ 0 ] () = 0; [ a__plus ] (X0,X1) = 2 + 2*X0 + 0; [ U21 ] (X0,X1,X2) = 2 + 0; [ tt ] () = 0; [ plus ] (X0,X1) = 2 + 2*X0 + 0; [ a__and ] (X0,X1) = 2*X1 + 0; [ Marked_a__isNat ] (X0) = 3*X0 + 0; [ a__U11 ] (X0,X1) = 2*X1 + 0; [ isNat ] (X0) = 0; [ a__U21 ] (X0,X1,X2) = 2 + 0; [ and ] (X0,X1) = 2*X1 + 0; [ s ] (X0) = 2 + 0; [ U11 ] (X0,X1) = 1*X1 + 0; [ a__isNat ] (X0) = 0; ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} Cime worked for 0.965889 seconds (real time) Cime Exit Status: 0