- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y)) [2] mark(f(X1,X2)) -> a__f(mark(X1),X2) [3] mark(g(X)) -> g(mark(X)) [4] a__f(X1,X2) -> f(X1,X2) 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: { a__f(g(X),Y) >= a__f(mark(X),f(g(X),Y)) ; a__f(X1,X2) >= f(X1,X2) ; mark(f(X1,X2)) >= a__f(mark(X1),X2) ; mark(g(X)) >= g(mark(X)) ; Marked_a__f(g(X),Y) >= Marked_a__f(mark(X),f(g(X),Y)) ; Marked_a__f(g(X),Y) >= Marked_mark(X) ; Marked_mark(f(X1,X2)) >= Marked_a__f(mark(X1),X2) ; Marked_mark(f(X1,X2)) >= Marked_mark(X1) ; Marked_mark(g(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__f(g(X),Y) > Marked_a__f(mark(X),f(g(X),Y)) ; } { Marked_a__f(g(X),Y) > Marked_mark(X) ; } { Marked_mark(f(X1,X2)) > Marked_a__f(mark(X1),X2) ; } { Marked_mark(f(X1,X2)) > Marked_mark(X1) ; } { 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(g(X),Y) >= a__f(mark(X),f(g(X),Y)) constraint: a__f(X1,X2) >= f(X1,X2) constraint: mark(f(X1,X2)) >= a__f(mark(X1),X2) constraint: mark(g(X)) >= g(mark(X)) constraint: Marked_a__f(g(X),Y) >= Marked_a__f(mark(X),f(g(X),Y)) constraint: Marked_a__f(g(X),Y) >= Marked_mark(X) constraint: Marked_mark(f(X1,X2)) >= Marked_a__f(mark(X1),X2) constraint: Marked_mark(f(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(g(X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y)) [2] mark(f(X1,X2)) -> a__f(mark(X1),X2) [3] mark(g(X)) -> g(mark(X)) [4] a__f(X1,X2) -> f(X1,X2) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ a__f ] (X0,X1) = 2 + 3*X0 + 0; [ Marked_a__f ] (X0,X1) = 2 + 3*X0 + 0; [ f ] (X0,X1) = 1 + 3*X0 + 0; [ mark ] (X0) = 2*X0 + 0; [ Marked_mark ] (X0) = 2 + 3*X0 + 0; [ g ] (X0) = 2 + 2*X0 + 0; ]} ]} ]} Cime worked for 0.042853 seconds (real time) Cime Exit Status: 0