- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(and(tt,X)) -> mark(X) [2] active(plus(N,0)) -> mark(N) [3] active(plus(N,s(M))) -> mark(s(plus(N,M))) [4] active(x(N,0)) -> mark(0) [5] active(x(N,s(M))) -> mark(plus(x(N,M),N)) [6] mark(and(X1,X2)) -> active(and(mark(X1),X2)) [7] mark(tt) -> active(tt) [8] mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) [9] mark(0) -> active(0) [10] mark(s(X)) -> active(s(mark(X))) [11] mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) [12] and(mark(X1),X2) -> and(X1,X2) [13] and(X1,mark(X2)) -> and(X1,X2) [14] and(active(X1),X2) -> and(X1,X2) [15] and(X1,active(X2)) -> and(X1,X2) [16] plus(mark(X1),X2) -> plus(X1,X2) [17] plus(X1,mark(X2)) -> plus(X1,X2) [18] plus(active(X1),X2) -> plus(X1,X2) [19] plus(X1,active(X2)) -> plus(X1,X2) [20] s(mark(X)) -> s(X) [21] s(active(X)) -> s(X) [22] x(mark(X1),X2) -> x(X1,X2) [23] x(X1,mark(X2)) -> x(X1,X2) [24] x(active(X1),X2) -> x(X1,X2) [25] x(X1,active(X2)) -> x(X1,X2) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 5 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(tt) >= active(tt) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(0) >= active(0) ; mark(s(X)) >= active(s(mark(X))) ; mark(x(X1,X2)) >= active(x(mark(X1),mark(X2))) ; active(and(tt,X)) >= mark(X) ; active(plus(N,0)) >= mark(N) ; active(plus(N,s(M))) >= mark(s(plus(N,M))) ; active(x(N,0)) >= mark(0) ; active(x(N,s(M))) >= mark(plus(x(N,M),N)) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; plus(mark(X1),X2) >= plus(X1,X2) ; plus(active(X1),X2) >= plus(X1,X2) ; plus(X1,mark(X2)) >= plus(X1,X2) ; plus(X1,active(X2)) >= plus(X1,X2) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; x(mark(X1),X2) >= x(X1,X2) ; x(active(X1),X2) >= x(X1,X2) ; x(X1,mark(X2)) >= x(X1,X2) ; x(X1,active(X2)) >= x(X1,X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_active(s(mark(X))) ; Marked_mark(x(X1,X2)) >= Marked_mark(X1) ; Marked_mark(x(X1,X2)) >= Marked_mark(X2) ; Marked_mark(x(X1,X2)) >= Marked_active(x(mark(X1),mark(X2))) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(plus(N,0)) >= Marked_mark(N) ; Marked_active(plus(N,s(M))) >= Marked_mark(s(plus(N,M))) ; Marked_active(x(N,s(M))) >= Marked_mark(plus(x(N,M),N)) ; } + Disjunctions:{ { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(plus(X1,X2)) > Marked_active(plus(mark(X1),mark(X2))) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_active(s(mark(X))) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(x(X1,X2)) > Marked_active(x(mark(X1),mark(X2))) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(plus(N,0)) > Marked_mark(N) ; } { Marked_active(plus(N,s(M))) > Marked_mark(s(plus(N,M))) ; } { Marked_active(x(N,s(M))) > Marked_mark(plus(x(N,M),N)) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(tt) >= active(tt) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(0) >= active(0) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(x(X1,X2)) >= active(x(mark(X1),mark(X2))) constraint: active(and(tt,X)) >= mark(X) constraint: active(plus(N,0)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(s(plus(N,M))) constraint: active(x(N,0)) >= mark(0) constraint: active(x(N,s(M))) >= mark(plus(x(N,M),N)) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: plus(mark(X1),X2) >= plus(X1,X2) constraint: plus(active(X1),X2) >= plus(X1,X2) constraint: plus(X1,mark(X2)) >= plus(X1,X2) constraint: plus(X1,active(X2)) >= plus(X1,X2) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: x(mark(X1),X2) >= x(X1,X2) constraint: x(active(X1),X2) >= x(X1,X2) constraint: x(X1,mark(X2)) >= x(X1,X2) constraint: x(X1,active(X2)) >= x(X1,X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(s(X)) >= Marked_active(s(mark(X))) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(x(X1,X2)) >= Marked_active(x(mark(X1),mark(X2))) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(plus(N,0)) >= Marked_mark(N) constraint: Marked_active(plus(N,s(M))) >= Marked_mark(s(plus(N,M))) constraint: Marked_active(x(N,s(M))) >= Marked_mark(plus(x(N,M),N)) APPLY CRITERIA (Subterm criterion) ST: Marked_and -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_plus -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_s -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_x -> 2 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(tt) >= active(tt) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(0) >= active(0) ; mark(s(X)) >= active(s(mark(X))) ; mark(x(X1,X2)) >= active(x(mark(X1),mark(X2))) ; active(and(tt,X)) >= mark(X) ; active(plus(N,0)) >= mark(N) ; active(plus(N,s(M))) >= mark(s(plus(N,M))) ; active(x(N,0)) >= mark(0) ; active(x(N,s(M))) >= mark(plus(x(N,M),N)) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; plus(mark(X1),X2) >= plus(X1,X2) ; plus(active(X1),X2) >= plus(X1,X2) ; plus(X1,mark(X2)) >= plus(X1,X2) ; plus(X1,active(X2)) >= plus(X1,X2) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; x(mark(X1),X2) >= x(X1,X2) ; x(active(X1),X2) >= x(X1,X2) ; x(X1,mark(X2)) >= x(X1,X2) ; x(X1,active(X2)) >= x(X1,X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(x(X1,X2)) >= Marked_mark(X1) ; Marked_mark(x(X1,X2)) >= Marked_mark(X2) ; Marked_mark(x(X1,X2)) >= Marked_active(x(mark(X1),mark(X2))) ; Marked_active(and(tt,X)) >= Marked_mark(X) ; Marked_active(plus(N,0)) >= Marked_mark(N) ; Marked_active(plus(N,s(M))) >= Marked_mark(s(plus(N,M))) ; Marked_active(x(N,s(M))) >= Marked_mark(plus(x(N,M),N)) ; } + Disjunctions:{ { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(plus(X1,X2)) > Marked_active(plus(mark(X1),mark(X2))) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(x(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(x(X1,X2)) > Marked_active(x(mark(X1),mark(X2))) ; } { Marked_active(and(tt,X)) > Marked_mark(X) ; } { Marked_active(plus(N,0)) > Marked_mark(N) ; } { Marked_active(plus(N,s(M))) > Marked_mark(s(plus(N,M))) ; } { Marked_active(x(N,s(M))) > Marked_mark(plus(x(N,M),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 === === STOPING TIMER virtual === constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(tt) >= active(tt) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(0) >= active(0) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(x(X1,X2)) >= active(x(mark(X1),mark(X2))) constraint: active(and(tt,X)) >= mark(X) constraint: active(plus(N,0)) >= mark(N) constraint: active(plus(N,s(M))) >= mark(s(plus(N,M))) constraint: active(x(N,0)) >= mark(0) constraint: active(x(N,s(M))) >= mark(plus(x(N,M),N)) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: plus(mark(X1),X2) >= plus(X1,X2) constraint: plus(active(X1),X2) >= plus(X1,X2) constraint: plus(X1,mark(X2)) >= plus(X1,X2) constraint: plus(X1,active(X2)) >= plus(X1,X2) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: x(mark(X1),X2) >= x(X1,X2) constraint: x(active(X1),X2) >= x(X1,X2) constraint: x(X1,mark(X2)) >= x(X1,X2) constraint: x(X1,active(X2)) >= x(X1,X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(x(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(x(X1,X2)) >= Marked_active(x(mark(X1),mark(X2))) constraint: Marked_active(and(tt,X)) >= Marked_mark(X) constraint: Marked_active(plus(N,0)) >= Marked_mark(N) constraint: Marked_active(plus(N,s(M))) >= Marked_mark(s(plus(N,M))) constraint: Marked_active(x(N,s(M))) >= Marked_mark(plus(x(N,M),N)) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_and -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_plus -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_x -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] active(and(tt,X)) -> mark(X) [2] active(plus(N,0)) -> mark(N) [3] active(plus(N,s(M))) -> mark(s(plus(N,M))) [4] active(x(N,0)) -> mark(0) [5] active(x(N,s(M))) -> mark(plus(x(N,M),N)) [6] mark(and(X1,X2)) -> active(and(mark(X1),X2)) [7] mark(tt) -> active(tt) [8] mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) [9] mark(0) -> active(0) [10] mark(s(X)) -> active(s(mark(X))) [11] mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) [12] and(mark(X1),X2) -> and(X1,X2) [13] and(X1,mark(X2)) -> and(X1,X2) [14] and(active(X1),X2) -> and(X1,X2) [15] and(X1,active(X2)) -> and(X1,X2) [16] plus(mark(X1),X2) -> plus(X1,X2) [17] plus(X1,mark(X2)) -> plus(X1,X2) [18] plus(active(X1),X2) -> plus(X1,X2) [19] plus(X1,active(X2)) -> plus(X1,X2) [20] s(mark(X)) -> s(X) [21] s(active(X)) -> s(X) [22] x(mark(X1),X2) -> x(X1,X2) [23] x(X1,mark(X2)) -> x(X1,X2) [24] x(active(X1),X2) -> x(X1,X2) [25] x(X1,active(X2)) -> x(X1,X2) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ plus ] (X0,X1) = 2; [ Marked_mark ] (X0) = 2; [ and ] (X0,X1) = 2; [ s ] (X0) = 0; [ active ] (X0) = 0; [ 0 ] () = 0; [ Marked_active ] (X0) = 1*X0; [ tt ] () = 0; [ x ] (X0,X1) = 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using RPO with AFS = AFS: mark -> 0active -> 0 and precedence: prec (All symbols are Lex.): { plus > s ; plus < x ; plus < Marked_mark ; plus < Marked_active ; s < plus ; s < x ; s < Marked_mark ; s < Marked_active ; x > plus ; x > s ; Marked_mark > plus ; Marked_mark > s ; Marked_mark = Marked_active ; Marked_active > plus ; Marked_active > s ; Marked_active = Marked_mark ; } removing < Marked_active(x(N,s(M))),Marked_mark(plus(x(N,M),N))> [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} Cime worked for 0.409148 seconds (real time) Cime Exit Status: 0