- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(0) -> 1 [2] f(s(x)) -> g(f(x)) [3] g(x) -> +(x,s(x)) [4] f(s(x)) -> +(f(x),s(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: { f(0) >= 1 ; f(s(x)) >= g(f(x)) ; f(s(x)) >= +(f(x),s(f(x))) ; g(x) >= +(x,s(x)) ; Marked_f(s(x)) >= Marked_f(x) ; } + Disjunctions:{ { Marked_f(s(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(0) >= 1 constraint: f(s(x)) >= g(f(x)) constraint: f(s(x)) >= +(f(x),s(f(x))) constraint: g(x) >= +(x,s(x)) constraint: Marked_f(s(x)) >= Marked_f(x) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(0) -> 1 [2] f(s(x)) -> g(f(x)) [3] g(x) -> +(x,s(x)) [4] f(s(x)) -> +(f(x),s(f(x))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 1 ] () = 1 + 0; [ s ] (X0) = 2 + 3*X0 + 0; [ 0 ] () = 3 + 0; [ Marked_f ] (X0) = 3*X0 + 0; [ f ] (X0) = 3 + 2*X0 + 0; [ + ] (X0,X1) = 0; [ g ] (X0) = 0; ]} ]} ]} Cime worked for 0.022648 seconds (real time) Cime Exit Status: 0