- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] sum(0) -> 0 [2] sum(s(x)) -> +(sum(x),s(x)) [3] sum1(0) -> 0 [4] sum1(s(x)) -> s(+(sum1(x),+(x,x))) 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: { sum(0) >= 0 ; sum(s(x)) >= +(sum(x),s(x)) ; sum1(0) >= 0 ; sum1(s(x)) >= s(+(sum1(x),+(x,x))) ; Marked_sum(s(x)) >= Marked_sum(x) ; } + Disjunctions:{ { Marked_sum(s(x)) > Marked_sum(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: sum(0) >= 0 constraint: sum(s(x)) >= +(sum(x),s(x)) constraint: sum1(0) >= 0 constraint: sum1(s(x)) >= s(+(sum1(x),+(x,x))) constraint: Marked_sum(s(x)) >= Marked_sum(x) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { sum(0) >= 0 ; sum(s(x)) >= +(sum(x),s(x)) ; sum1(0) >= 0 ; sum1(s(x)) >= s(+(sum1(x),+(x,x))) ; Marked_sum1(s(x)) >= Marked_sum1(x) ; } + Disjunctions:{ { Marked_sum1(s(x)) > Marked_sum1(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: sum(0) >= 0 constraint: sum(s(x)) >= +(sum(x),s(x)) constraint: sum1(0) >= 0 constraint: sum1(s(x)) >= s(+(sum1(x),+(x,x))) constraint: Marked_sum1(s(x)) >= Marked_sum1(x) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] sum(0) -> 0 [2] sum(s(x)) -> +(sum(x),s(x)) [3] sum1(0) -> 0 [4] sum1(s(x)) -> s(+(sum1(x),+(x,x))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ sum1 ] (X0) = 2 + 0; [ + ] (X0,X1) = 0; [ Marked_sum ] (X0) = 3*X0 + 0; [ sum ] (X0) = 2 + 2*X0 + 0; [ s ] (X0) = 2 + 3*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ sum1 ] (X0) = 2 + 0; [ + ] (X0,X1) = 0; [ sum ] (X0) = 2 + 2*X0 + 0; [ Marked_sum1 ] (X0) = 3*X0 + 0; [ s ] (X0) = 2 + 3*X0 + 0; ]} ]} ]} Cime worked for 0.056871 seconds (real time) Cime Exit Status: 0