- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] plus(plus(X,Y),Z) -> plus(X,plus(Y,Z)) [2] times(X,s(Y)) -> plus(X,times(Y,X)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { plus(plus(X,Y),Z) >= plus(X,plus(Y,Z)) ; times(X,s(Y)) >= plus(X,times(Y,X)) ; Marked_times(X,s(Y)) >= Marked_times(Y,X) ; } + Disjunctions:{ { Marked_times(X,s(Y)) > Marked_times(Y,X) ; } } === 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: plus(plus(X,Y),Z) >= plus(X,plus(Y,Z)) constraint: times(X,s(Y)) >= plus(X,times(Y,X)) constraint: Marked_times(X,s(Y)) >= Marked_times(Y,X) APPLY CRITERIA (Subterm criterion) ST: Marked_plus -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] plus(plus(X,Y),Z) -> plus(X,plus(Y,Z)) [2] times(X,s(Y)) -> plus(X,times(Y,X)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ plus ] (X0,X1) = 2*X0 + 0; [ s ] (X0) = 2 + 1*X0 + 0; [ times ] (X0,X1) = 3*X0 + 3*X1 + 0; [ Marked_times ] (X0,X1) = 3*X0 + 3*X1 + 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.022423 seconds (real time) Cime Exit Status: 0