- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(0) -> s(0) [2] f(s(0)) -> s(0) [3] f(s(s(x))) -> f(f(s(x))) 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: { f(s(s(x))) >= f(f(s(x))) ; f(s(0)) >= s(0) ; f(0) >= s(0) ; Marked_f(s(s(x))) >= Marked_f(s(x)) ; Marked_f(s(s(x))) >= Marked_f(f(s(x))) ; } + Disjunctions:{ { Marked_f(s(s(x))) > Marked_f(s(x)) ; } { Marked_f(s(s(x))) > Marked_f(f(s(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(s(s(x))) >= f(f(s(x))) constraint: f(s(0)) >= s(0) constraint: f(0) >= s(0) constraint: Marked_f(s(s(x))) >= Marked_f(s(x)) constraint: Marked_f(s(s(x))) >= Marked_f(f(s(x))) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(0) -> s(0) [2] f(s(0)) -> s(0) [3] f(s(s(x))) -> f(f(s(x))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ s ] (X0) = 2 + 2*X0 + 0; [ f ] (X0) = 3 + 1*X0 + 0; [ 0 ] () = 1 + 0; [ Marked_f ] (X0) = 2*X0 + 0; ]} ]} ]} Cime worked for 0.034306 seconds (real time) Cime Exit Status: 0