- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] +(0,y) -> y [2] +(s(x),y) -> s(+(x,y)) [3] -(0,y) -> 0 [4] -(x,0) -> x [5] -(s(x),s(y)) -> -(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: { +(0,y) >= y ; +(s(x),y) >= s(+(x,y)) ; -(0,y) >= 0 ; -(s(x),s(y)) >= -(x,y) ; -(x,0) >= x ; Marked_+(s(x),y) >= Marked_+(x,y) ; } + Disjunctions:{ { Marked_+(s(x),y) > Marked_+(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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: +(0,y) >= y constraint: +(s(x),y) >= s(+(x,y)) constraint: -(0,y) >= 0 constraint: -(s(x),s(y)) >= -(x,y) constraint: -(x,0) >= x constraint: Marked_+(s(x),y) >= Marked_+(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { +(0,y) >= y ; +(s(x),y) >= s(+(x,y)) ; -(0,y) >= 0 ; -(s(x),s(y)) >= -(x,y) ; -(x,0) >= x ; Marked_-(s(x),s(y)) >= Marked_-(x,y) ; } + Disjunctions:{ { Marked_-(s(x),s(y)) > Marked_-(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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: +(0,y) >= y constraint: +(s(x),y) >= s(+(x,y)) constraint: -(0,y) >= 0 constraint: -(s(x),s(y)) >= -(x,y) constraint: -(x,0) >= x constraint: Marked_-(s(x),s(y)) >= Marked_-(x,y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] +(0,y) -> y [2] +(s(x),y) -> s(+(x,y)) [3] -(0,y) -> 0 [4] -(x,0) -> x [5] -(s(x),s(y)) -> -(x,y) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ + ] (X0,X1) = 2*X0 + 3*X1 + 0; [ s ] (X0) = 2 + 1*X0 + 0; [ 0 ] () = 0; [ Marked_+ ] (X0,X1) = 3*X0 + 0; [ - ] (X0,X1) = 1*X0 + 3*X1 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ + ] (X0,X1) = 2*X0 + 3*X1 + 0; [ Marked_- ] (X0,X1) = 1*X1 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ 0 ] () = 0; [ - ] (X0,X1) = 2*X0 + 3*X1 + 0; ]} ]} ]} Cime worked for 0.023805 seconds (real time) Cime Exit Status: 0