- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] times(x,0) -> 0 [2] times(x,s(y)) -> plus(times(x,y),x) [3] plus(x,0) -> x [4] plus(0,x) -> x [5] plus(x,s(y)) -> s(plus(x,y)) [6] plus(s(x),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: { times(x,0) >= 0 ; times(x,s(y)) >= plus(times(x,y),x) ; plus(0,x) >= x ; plus(s(x),y) >= s(plus(x,y)) ; plus(x,0) >= x ; plus(x,s(y)) >= s(plus(x,y)) ; Marked_times(x,s(y)) >= Marked_times(x,y) ; } + Disjunctions:{ { 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 === === STOPING TIMER virtual === constraint: times(x,0) >= 0 constraint: times(x,s(y)) >= plus(times(x,y),x) constraint: plus(0,x) >= x constraint: plus(s(x),y) >= s(plus(x,y)) constraint: plus(x,0) >= x constraint: plus(x,s(y)) >= s(plus(x,y)) constraint: Marked_times(x,s(y)) >= Marked_times(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { times(x,0) >= 0 ; times(x,s(y)) >= plus(times(x,y),x) ; plus(0,x) >= x ; plus(s(x),y) >= s(plus(x,y)) ; plus(x,0) >= x ; plus(x,s(y)) >= s(plus(x,y)) ; Marked_plus(s(x),y) >= Marked_plus(x,y) ; Marked_plus(x,s(y)) >= Marked_plus(x,y) ; } + Disjunctions:{ { Marked_plus(s(x),y) > Marked_plus(x,y) ; } { 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 === === STOPING TIMER virtual === constraint: times(x,0) >= 0 constraint: times(x,s(y)) >= plus(times(x,y),x) constraint: plus(0,x) >= x constraint: plus(s(x),y) >= s(plus(x,y)) constraint: plus(x,0) >= x constraint: plus(x,s(y)) >= s(plus(x,y)) constraint: Marked_plus(s(x),y) >= Marked_plus(x,y) 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,0) -> 0 [2] times(x,s(y)) -> plus(times(x,y),x) [3] plus(x,0) -> x [4] plus(0,x) -> x [5] plus(x,s(y)) -> s(plus(x,y)) [6] plus(s(x),y) -> s(plus(x,y)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { times > plus ; times > s ; plus < times ; plus > s ; s < times ; s < plus ; } ]} { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { times > plus ; times > s ; plus < times ; plus > s ; s < times ; s < plus ; } ]} ]} ]} Cime worked for 0.040129 seconds (real time) Cime Exit Status: 0