- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a(a(x)) -> b(b(x)) [2] b(b(a(x))) -> a(b(b(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: { b(b(a(x))) >= a(b(b(x))) ; a(a(x)) >= b(b(x)) ; Marked_b(b(a(x))) >= Marked_b(b(x)) ; Marked_b(b(a(x))) >= Marked_b(x) ; Marked_b(b(a(x))) >= Marked_a(b(b(x))) ; Marked_a(a(x)) >= Marked_b(b(x)) ; Marked_a(a(x)) >= Marked_b(x) ; } + Disjunctions:{ { Marked_b(b(a(x))) > Marked_b(b(x)) ; } { Marked_b(b(a(x))) > Marked_b(x) ; } { Marked_b(b(a(x))) > Marked_a(b(b(x))) ; } { Marked_a(a(x)) > Marked_b(b(x)) ; } { Marked_a(a(x)) > Marked_b(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: b(b(a(x))) >= a(b(b(x))) constraint: a(a(x)) >= b(b(x)) constraint: Marked_b(b(a(x))) >= Marked_b(b(x)) constraint: Marked_b(b(a(x))) >= Marked_b(x) constraint: Marked_b(b(a(x))) >= Marked_a(b(b(x))) constraint: Marked_a(a(x)) >= Marked_b(b(x)) constraint: Marked_a(a(x)) >= Marked_b(x) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] a(a(x)) -> b(b(x)) [2] b(b(a(x))) -> a(b(b(x))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ b ] (X0) = 1*X0 + 0; [ Marked_b ] (X0) = 2 + 1*X0 + 0; [ a ] (X0) = 2 + 3*X0 + 0; [ Marked_a ] (X0) = 2 + 1*X0 + 0; ]} ]} ]} Cime worked for 0.030887 seconds (real time) Cime Exit Status: 0