- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(g(X)) -> g(f(f(X))) [2] f(h(X)) -> h(g(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: { f(g(X)) >= g(f(f(X))) ; f(h(X)) >= h(g(X)) ; Marked_f(g(X)) >= Marked_f(f(X)) ; Marked_f(g(X)) >= Marked_f(X) ; } + Disjunctions:{ { Marked_f(g(X)) > Marked_f(f(X)) ; } { Marked_f(g(X)) > Marked_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: f(g(X)) >= g(f(f(X))) constraint: f(h(X)) >= h(g(X)) constraint: Marked_f(g(X)) >= Marked_f(f(X)) constraint: Marked_f(g(X)) >= Marked_f(X) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(g(X)) -> g(f(f(X))) [2] f(h(X)) -> h(g(X)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ g ] (X0) = 2 + 2*X0 + 0; [ h ] (X0) = 0; [ f ] (X0) = 1*X0 + 0; [ Marked_f ] (X0) = 2*X0 + 0; ]} ]} ]} Cime worked for 0.019474 seconds (real time) Cime Exit Status: 0