- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(a) -> f(c(a)) [2] f(c(X)) -> X [3] f(c(a)) -> f(d(b)) [4] f(a) -> f(d(a)) [5] f(d(X)) -> X [6] f(c(b)) -> f(d(a)) [7] e(g(X)) -> e(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(c(a)) >= f(d(b)) ; f(c(b)) >= f(d(a)) ; f(c(X)) >= X ; f(a) >= f(c(a)) ; f(a) >= f(d(a)) ; f(d(X)) >= X ; e(g(X)) >= e(X) ; Marked_e(g(X)) >= Marked_e(X) ; } + Disjunctions:{ { Marked_e(g(X)) > Marked_e(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(c(a)) >= f(d(b)) constraint: f(c(b)) >= f(d(a)) constraint: f(c(X)) >= X constraint: f(a) >= f(c(a)) constraint: f(a) >= f(d(a)) constraint: f(d(X)) >= X constraint: e(g(X)) >= e(X) constraint: Marked_e(g(X)) >= Marked_e(X) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(a) -> f(c(a)) [2] f(c(X)) -> X [3] f(c(a)) -> f(d(b)) [4] f(a) -> f(d(a)) [5] f(d(X)) -> X [6] f(c(b)) -> f(d(a)) [7] e(g(X)) -> e(X) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ f ] (X0) = 3 + 2*X0 + 0; [ b ] () = 0; [ a ] () = 0; [ g ] (X0) = 3 + 3*X0 + 0; [ c ] (X0) = 1*X0 + 0; [ e ] (X0) = 2*X0 + 0; [ d ] (X0) = 2*X0 + 0; [ Marked_e ] (X0) = 2*X0 + 0; ]} ]} ]} Cime worked for 0.026438 seconds (real time) Cime Exit Status: 0