- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] average(s(x),y) -> average(x,s(y)) [2] average(x,s(s(s(y)))) -> s(average(s(x),y)) [3] average(0,0) -> 0 [4] average(0,s(0)) -> 0 [5] average(0,s(s(0))) -> s(0) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { average(s(x),y) >= average(x,s(y)) ; average(0,s(s(0))) >= s(0) ; average(0,s(0)) >= 0 ; average(0,0) >= 0 ; average(x,s(s(s(y)))) >= s(average(s(x),y)) ; Marked_average(s(x),y) >= Marked_average(x,s(y)) ; Marked_average(x,s(s(s(y)))) >= Marked_average(s(x),y) ; } + Disjunctions:{ { Marked_average(s(x),y) > Marked_average(x,s(y)) ; } { Marked_average(x,s(s(s(y)))) > Marked_average(s(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: average(s(x),y) >= average(x,s(y)) constraint: average(0,s(s(0))) >= s(0) constraint: average(0,s(0)) >= 0 constraint: average(0,0) >= 0 constraint: average(x,s(s(s(y)))) >= s(average(s(x),y)) constraint: Marked_average(s(x),y) >= Marked_average(x,s(y)) constraint: Marked_average(x,s(s(s(y)))) >= Marked_average(s(x),y) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] average(s(x),y) -> average(x,s(y)) [2] average(x,s(s(s(y)))) -> s(average(s(x),y)) [3] average(0,0) -> 0 [4] average(0,s(0)) -> 0 [5] average(0,s(s(0))) -> s(0) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ average ] (X0,X1) = 2 + 2*X0 + 1*X1 + 0; [ 0 ] () = 2 + 0; [ s ] (X0) = 3 + 1*X0 + 0; [ Marked_average ] (X0,X1) = 2*X0 + 1*X1 + 0; ]} ]} ]} Cime worked for 0.065381 seconds (real time) Cime Exit Status: 0