- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__and(tt,X) -> mark(X) [2] a__plus(N,0) -> mark(N) [3] a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M))) [4] mark(and(X1,X2)) -> a__and(mark(X1),X2) [5] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) [6] mark(tt) -> tt [7] mark(0) -> 0 [8] mark(s(X)) -> s(mark(X)) [9] a__and(X1,X2) -> and(X1,X2) [10] a__plus(X1,X2) -> plus(X1,X2) 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: { mark(tt) >= tt ; mark(0) >= 0 ; mark(s(X)) >= s(mark(X)) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__plus(N,0) >= mark(N) ; a__plus(N,s(M)) >= s(a__plus(mark(N),mark(M))) ; a__plus(X1,X2) >= plus(X1,X2) ; Marked_a__plus(N,0) >= Marked_mark(N) ; Marked_a__plus(N,s(M)) >= Marked_a__plus(mark(N),mark(M)) ; Marked_a__plus(N,s(M)) >= Marked_mark(N) ; Marked_a__plus(N,s(M)) >= Marked_mark(M) ; Marked_a__and(tt,X) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; 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) ; } + Disjunctions:{ { Marked_a__plus(N,0) > Marked_mark(N) ; } { Marked_a__plus(N,s(M)) > Marked_a__plus(mark(N),mark(M)) ; } { Marked_a__plus(N,s(M)) > Marked_mark(N) ; } { Marked_a__plus(N,s(M)) > Marked_mark(M) ; } { Marked_a__and(tt,X) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ; } { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { 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) ; } } === 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(0) >= 0 constraint: mark(s(X)) >= s(mark(X)) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__plus(N,0) >= mark(N) constraint: a__plus(N,s(M)) >= s(a__plus(mark(N),mark(M))) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: Marked_a__plus(N,0) >= Marked_mark(N) constraint: Marked_a__plus(N,s(M)) >= Marked_a__plus(mark(N),mark(M)) constraint: Marked_a__plus(N,s(M)) >= Marked_mark(N) constraint: Marked_a__plus(N,s(M)) >= Marked_mark(M) constraint: Marked_a__and(tt,X) >= Marked_mark(X) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) 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) APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(tt) >= tt ; mark(0) >= 0 ; mark(s(X)) >= s(mark(X)) ; mark(and(X1,X2)) >= a__and(mark(X1),X2) ; mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ; a__and(tt,X) >= mark(X) ; a__and(X1,X2) >= and(X1,X2) ; a__plus(N,0) >= mark(N) ; a__plus(N,s(M)) >= s(a__plus(mark(N),mark(M))) ; a__plus(X1,X2) >= plus(X1,X2) ; Marked_a__plus(N,s(M)) >= Marked_a__plus(mark(N),mark(M)) ; } + Disjunctions:{ { Marked_a__plus(N,s(M)) > Marked_a__plus(mark(N),mark(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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(tt) >= tt constraint: mark(0) >= 0 constraint: mark(s(X)) >= s(mark(X)) constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2) constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) constraint: a__and(tt,X) >= mark(X) constraint: a__and(X1,X2) >= and(X1,X2) constraint: a__plus(N,0) >= mark(N) constraint: a__plus(N,s(M)) >= s(a__plus(mark(N),mark(M))) constraint: a__plus(X1,X2) >= plus(X1,X2) constraint: Marked_a__plus(N,s(M)) >= Marked_a__plus(mark(N),mark(M)) APPLY CRITERIA (Subterm criterion) ST: Marked_mark -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] a__and(tt,X) -> mark(X) [2] a__plus(N,0) -> mark(N) [3] a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M))) [4] mark(and(X1,X2)) -> a__and(mark(X1),X2) [5] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) [6] mark(tt) -> tt [7] mark(0) -> 0 [8] mark(s(X)) -> s(mark(X)) [9] a__and(X1,X2) -> and(X1,X2) [10] a__plus(X1,X2) -> plus(X1,X2) , 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 + 2; [ 0 ] () = 0; [ tt ] () = 1; [ Marked_mark ] (X0) = 1*X0 + 2; [ and ] (X0,X1) = 3*X1 + 2*X0; [ a__and ] (X0,X1) = 3*X1 + 2*X0; [ Marked_a__and ] (X0,X1) = 3*X1 + 1*X0 + 1; [ s ] (X0) = 1*X0; [ a__plus ] (X0,X1) = 1*X1 + 1*X0 + 2; [ plus ] (X0,X1) = 1*X1 + 1*X0 + 2; removing < Marked_mark(plus(X1,X2)),Marked_mark(X2)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ mark ] (X0) = 1*X0 + 0; [ Marked_a__plus ] (X0,X1) = 2*X1 + 0; [ 0 ] () = 0; [ tt ] () = 0; [ and ] (X0,X1) = 3*X1 + 0; [ a__and ] (X0,X1) = 3*X1 + 0; [ s ] (X0) = 2 + 1*X0 + 0; [ a__plus ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; [ plus ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} Cime worked for 0.115740 seconds (real time) Cime Exit Status: 0