- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] g(s(x)) -> f(x) [2] f(0) -> s(0) [3] f(s(x)) -> s(s(g(x))) [4] g(0) -> 0 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(s(x)) >= s(s(g(x))) ; f(0) >= s(0) ; g(s(x)) >= f(x) ; g(0) >= 0 ; Marked_g(s(x)) >= Marked_f(x) ; Marked_f(s(x)) >= Marked_g(x) ; } + Disjunctions:{ { Marked_g(s(x)) > Marked_f(x) ; } { Marked_f(s(x)) > Marked_g(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(x)) >= s(s(g(x))) constraint: f(0) >= s(0) constraint: g(s(x)) >= f(x) constraint: g(0) >= 0 constraint: Marked_g(s(x)) >= Marked_f(x) constraint: Marked_f(s(x)) >= Marked_g(x) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] g(s(x)) -> f(x) [2] f(0) -> s(0) [3] f(s(x)) -> s(s(g(x))) [4] g(0) -> 0 , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ f ] (X0) = 1 + 1*X0 + 0; [ Marked_g ] (X0) = 2*X0 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ g ] (X0) = 1*X0 + 0; [ Marked_f ] (X0) = 2*X0 + 0; [ 0 ] () = 0; ]} ]} ]} Cime worked for 0.022869 seconds (real time) Cime Exit Status: 0