- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__f(f(a)) -> c(f(g(f(a)))) [2] mark(f(X)) -> a__f(mark(X)) [3] mark(a) -> a [4] mark(c(X)) -> c(X) [5] mark(g(X)) -> g(mark(X)) [6] a__f(X) -> 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: { a__f(f(a)) >= c(f(g(f(a)))) ; a__f(X) >= f(X) ; mark(c(X)) >= c(X) ; mark(f(X)) >= a__f(mark(X)) ; mark(g(X)) >= g(mark(X)) ; mark(a) >= a ; Marked_mark(f(X)) >= Marked_mark(X) ; Marked_mark(g(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_mark(f(X)) > Marked_mark(X) ; } { Marked_mark(g(X)) > Marked_mark(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: a__f(f(a)) >= c(f(g(f(a)))) constraint: a__f(X) >= f(X) constraint: mark(c(X)) >= c(X) constraint: mark(f(X)) >= a__f(mark(X)) constraint: mark(g(X)) >= g(mark(X)) constraint: mark(a) >= a constraint: Marked_mark(f(X)) >= Marked_mark(X) constraint: Marked_mark(g(X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] a__f(f(a)) -> c(f(g(f(a)))) [2] mark(f(X)) -> a__f(mark(X)) [3] mark(a) -> a [4] mark(c(X)) -> c(X) [5] mark(g(X)) -> g(mark(X)) [6] a__f(X) -> f(X) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ c ] (X0) = 2 + 0; [ a__f ] (X0) = 1 + 1*X0 + 0; [ g ] (X0) = 2 + 2*X0 + 0; [ f ] (X0) = 1 + 1*X0 + 0; [ mark ] (X0) = 2 + 3*X0 + 0; [ a ] () = 0; [ Marked_mark ] (X0) = 3*X0 + 0; ]} ]} ]} Cime worked for 0.040833 seconds (real time) Cime Exit Status: 0