- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(g(x),g(y)) -> f(p(f(g(x),s(y))),g(s(p(x)))) [2] p(0) -> g(0) [3] g(s(p(x))) -> p(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(g(x),g(y)) >= f(p(f(g(x),s(y))),g(s(p(x)))) ; p(0) >= g(0) ; g(s(p(x))) >= p(x) ; Marked_f(g(x),g(y)) >= Marked_f(p(f(g(x),s(y))),g(s(p(x)))) ; } + Disjunctions:{ { Marked_f(g(x),g(y)) > Marked_f(p(f(g(x),s(y))),g(s(p(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(y)) >= f(p(f(g(x),s(y))),g(s(p(x)))) constraint: p(0) >= g(0) constraint: g(s(p(x))) >= p(x) constraint: Marked_f(g(x),g(y)) >= Marked_f(p(f(g(x),s(y))),g(s(p(x)))) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(g(x),g(y)) -> f(p(f(g(x),s(y))),g(s(p(x)))) [2] p(0) -> g(0) [3] g(s(p(x))) -> p(x) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ f ] (X0,X1) = 0; [ 0 ] () = 1 + 0; [ g ] (X0) = 1 + 1*X0 + 0; [ p ] (X0) = 2*X0 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ Marked_f ] (X0,X1) = 2*X0 + 1*X1 + 0; ]} ]} ]} Cime worked for 0.078505 seconds (real time) Cime Exit Status: 0