- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] exp(x,0) -> s(0) [2] exp(x,s(y)) -> *(x,exp(x,y)) [3] *(0,y) -> 0 [4] *(s(x),y) -> +(y, *(x,y)) [5] -(0,y) -> 0 [6] -(x,0) -> x [7] -(s(x),s(y)) -> -(x,y) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> } { --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { exp(x,s(y)) >= *(x,exp(x,y)) ; exp(x,0) >= s(0) ; *(s(x),y) >= +(y, *(x,y)) ; *(0,y) >= 0 ; -(s(x),s(y)) >= -(x,y) ; -(0,y) >= 0 ; -(x,0) >= x ; Marked_exp(x,s(y)) >= Marked_exp(x,y) ; } + Disjunctions:{ { Marked_exp(x,s(y)) > Marked_exp(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: exp(x,s(y)) >= *(x,exp(x,y)) constraint: exp(x,0) >= s(0) constraint: *(s(x),y) >= +(y, *(x,y)) constraint: *(0,y) >= 0 constraint: -(s(x),s(y)) >= -(x,y) constraint: -(0,y) >= 0 constraint: -(x,0) >= x constraint: Marked_exp(x,s(y)) >= Marked_exp(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { exp(x,s(y)) >= *(x,exp(x,y)) ; exp(x,0) >= s(0) ; *(s(x),y) >= +(y, *(x,y)) ; *(0,y) >= 0 ; -(s(x),s(y)) >= -(x,y) ; -(0,y) >= 0 ; -(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: exp(x,s(y)) >= *(x,exp(x,y)) constraint: exp(x,0) >= s(0) constraint: *(s(x),y) >= +(y, *(x,y)) constraint: *(0,y) >= 0 constraint: -(s(x),s(y)) >= -(x,y) constraint: -(0,y) >= 0 constraint: -(x,0) >= x constraint: Marked_*(s(x),y) >= Marked_*(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { exp(x,s(y)) >= *(x,exp(x,y)) ; exp(x,0) >= s(0) ; *(s(x),y) >= +(y, *(x,y)) ; *(0,y) >= 0 ; -(s(x),s(y)) >= -(x,y) ; -(0,y) >= 0 ; -(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: exp(x,s(y)) >= *(x,exp(x,y)) constraint: exp(x,0) >= s(0) constraint: *(s(x),y) >= +(y, *(x,y)) constraint: *(0,y) >= 0 constraint: -(s(x),s(y)) >= -(x,y) constraint: -(0,y) >= 0 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: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] exp(x,0) -> s(0) [2] exp(x,s(y)) -> *(x,exp(x,y)) [3] *(0,y) -> 0 [4] *(s(x),y) -> +(y, *(x,y)) [5] -(0,y) -> 0 [6] -(x,0) -> x [7] -(s(x),s(y)) -> -(x,y) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ s ] (X0) = 2 + 3*X0 + 0; [ Marked_exp ] (X0,X1) = 3*X1 + 0; [ + ] (X0,X1) = 2 + 0; [ exp ] (X0,X1) = 2 + 3*X0 + 2*X1 + 0; [ 0 ] () = 0; [ - ] (X0,X1) = 1*X0 + 2*X1 + 0; [ * ] (X0,X1) = 2*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ s ] (X0) = 2 + 3*X0 + 0; [ + ] (X0,X1) = 2*X1 + 0; [ exp ] (X0,X1) = 2 + 3*X0 + 2*X1 + 0; [ 0 ] () = 0; [ - ] (X0,X1) = 2*X0 + 2*X1 + 0; [ * ] (X0,X1) = 3*X0 + 0; [ Marked_* ] (X0,X1) = 3*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ s ] (X0) = 1 + 1*X0 + 0; [ + ] (X0,X1) = 1*X0 + 0; [ exp ] (X0,X1) = 1 + 3*X0 + 0; [ Marked_- ] (X0,X1) = 1*X0 + 0; [ 0 ] () = 0; [ - ] (X0,X1) = 2*X0 + 3*X1 + 0; [ * ] (X0,X1) = 1*X1 + 0; ]} ]} ]} Cime worked for 0.067270 seconds (real time) Cime Exit Status: 0