- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(f(x)) -> g(f(x)) [2] g(g(x)) -> f(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: { g(g(x)) >= f(x) ; f(f(x)) >= g(f(x)) ; Marked_g(g(x)) >= Marked_f(x) ; Marked_f(f(x)) >= Marked_g(f(x)) ; } + Disjunctions:{ { Marked_g(g(x)) > Marked_f(x) ; } { Marked_f(f(x)) > Marked_g(f(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: g(g(x)) >= f(x) constraint: f(f(x)) >= g(f(x)) constraint: Marked_g(g(x)) >= Marked_f(x) constraint: Marked_f(f(x)) >= Marked_g(f(x)) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(f(x)) -> g(f(x)) [2] g(g(x)) -> f(x) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ g ] (X0) = 1 + 1*X0 + 0; [ Marked_g ] (X0) = 1 + 3*X0 + 0; [ f ] (X0) = 2 + 1*X0 + 0; [ Marked_f ] (X0) = 2 + 3*X0 + 0; ]} ]} ]} Cime worked for 0.018877 seconds (real time) Cime Exit Status: 0