- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0))),times(x,s(z))) [2] times(x,0) -> 0 [3] times(x,s(y)) -> plus(times(x,y),x) [4] plus(x,0) -> x [5] plus(x,s(y)) -> s(plus(x,y)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> --> --> --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { plus(x,s(y)) >= s(plus(x,y)) ; plus(x,0) >= x ; times(x,plus(y,s(z))) >= plus(times(x,plus(y,times(s(z),0))),times(x,s(z))) ; times(x,s(y)) >= plus(times(x,y),x) ; times(x,0) >= 0 ; Marked_times(x,plus(y,s(z))) >= Marked_times(x,plus(y,times(s(z),0))) ; Marked_times(x,plus(y,s(z))) >= Marked_times(x,s(z)) ; Marked_times(x,s(y)) >= Marked_times(x,y) ; } + Disjunctions:{ { Marked_times(x,plus(y,s(z))) > Marked_times(x,plus(y,times(s(z),0))) ; } { Marked_times(x,plus(y,s(z))) > Marked_times(x,s(z)) ; } { Marked_times(x,s(y)) > Marked_times(x,y) ; } } === 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 === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === 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: plus(x,s(y)) >= s(plus(x,y)) constraint: plus(x,0) >= x constraint: times(x,plus(y,s(z))) >= plus(times(x,plus(y,times(s(z),0))), times(x,s(z))) constraint: times(x,s(y)) >= plus(times(x,y),x) constraint: times(x,0) >= 0 constraint: Marked_times(x,plus(y,s(z))) >= Marked_times(x, plus(y,times(s(z),0))) constraint: Marked_times(x,plus(y,s(z))) >= Marked_times(x,s(z)) constraint: Marked_times(x,s(y)) >= Marked_times(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { plus(x,s(y)) >= s(plus(x,y)) ; plus(x,0) >= x ; times(x,plus(y,s(z))) >= plus(times(x,plus(y,times(s(z),0))),times(x,s(z))) ; times(x,s(y)) >= plus(times(x,y),x) ; times(x,0) >= 0 ; Marked_plus(x,s(y)) >= Marked_plus(x,y) ; } + Disjunctions:{ { Marked_plus(x,s(y)) > Marked_plus(x,y) ; } } === 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 === === 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: plus(x,s(y)) >= s(plus(x,y)) constraint: plus(x,0) >= x constraint: times(x,plus(y,s(z))) >= plus(times(x,plus(y,times(s(z),0))), times(x,s(z))) constraint: times(x,s(y)) >= plus(times(x,y),x) constraint: times(x,0) >= 0 constraint: Marked_plus(x,s(y)) >= Marked_plus(x,y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] times(x,plus(y,s(z))) -> plus(times(x,plus(y,times(s(z),0))),times(x,s(z))) [2] times(x,0) -> 0 [3] times(x,s(y)) -> plus(times(x,y),x) [4] plus(x,0) -> x [5] plus(x,s(y)) -> s(plus(x,y)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ plus ] (X0,X1) = 1*X1 + 1*X0; [ s ] (X0) = 1*X0 + 2; [ times ] (X0,X1) = 1*X1*X0; [ Marked_times ] (X0,X1) = 2*X1; [ 0 ] () = 0; removing < Marked_times(x,s(y)),Marked_times(x,y)> [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ plus ] (X0,X1) = 1*X0 + 1*X1 + 0; [ Marked_plus ] (X0,X1) = 2*X1 + 2*X1*X0 + 0; [ s ] (X0) = 2 + 1*X0 + 0; [ times ] (X0,X1) = 2*X1 + 1*X1*X0 + 0; [ 0 ] () = 0; ]} ]} ]} Cime worked for 1.974332 seconds (real time) Cime Exit Status: 0