- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] sum(0) -> 0 [2] sum(s(x)) -> +(sqr(s(x)),sum(x)) [3] sqr(x) -> *(x,x) [4] sum(s(x)) -> +( *(s(x),s(x)),sum(x)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { sum(0) >= 0 ; sum(s(x)) >= +(sqr(s(x)),sum(x)) ; sum(s(x)) >= +( *(s(x),s(x)),sum(x)) ; sqr(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)) >= +(sqr(s(x)),sum(x)) constraint: sum(s(x)) >= +( *(s(x),s(x)),sum(x)) constraint: sqr(x) >= *(x,x) constraint: Marked_sum(s(x)) >= Marked_sum(x) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] sum(0) -> 0 [2] sum(s(x)) -> +(sqr(s(x)),sum(x)) [3] sqr(x) -> *(x,x) [4] sum(s(x)) -> +( *(s(x),s(x)),sum(x)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ s ] (X0) = 1 + 3*X0 + 0; [ + ] (X0,X1) = 2 + 0; [ Marked_sum ] (X0) = 3*X0 + 0; [ sum ] (X0) = 2*X0 + 0; [ * ] (X0,X1) = 0; [ sqr ] (X0) = 0; ]} ]} ]} Cime worked for 0.030071 seconds (real time) Cime Exit Status: 0