- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] minus(minus(x)) -> x [2] minus(h(x)) -> h(minus(x)) [3] minus(f(x,y)) -> f(minus(y),minus(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: { minus(minus(x)) >= x ; minus(h(x)) >= h(minus(x)) ; minus(f(x,y)) >= f(minus(y),minus(x)) ; Marked_minus(h(x)) >= Marked_minus(x) ; Marked_minus(f(x,y)) >= Marked_minus(x) ; Marked_minus(f(x,y)) >= Marked_minus(y) ; } + Disjunctions:{ { Marked_minus(h(x)) > Marked_minus(x) ; } { Marked_minus(f(x,y)) > Marked_minus(x) ; } { Marked_minus(f(x,y)) > Marked_minus(y) ; } } === 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: minus(minus(x)) >= x constraint: minus(h(x)) >= h(minus(x)) constraint: minus(f(x,y)) >= f(minus(y),minus(x)) constraint: Marked_minus(h(x)) >= Marked_minus(x) constraint: Marked_minus(f(x,y)) >= Marked_minus(x) constraint: Marked_minus(f(x,y)) >= Marked_minus(y) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(minus(x)) >= x ; minus(h(x)) >= h(minus(x)) ; minus(f(x,y)) >= f(minus(y),minus(x)) ; Marked_minus(h(x)) >= Marked_minus(x) ; } + Disjunctions:{ { Marked_minus(h(x)) > Marked_minus(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: minus(minus(x)) >= x constraint: minus(h(x)) >= h(minus(x)) constraint: minus(f(x,y)) >= f(minus(y),minus(x)) constraint: Marked_minus(h(x)) >= Marked_minus(x) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] minus(minus(x)) -> x [2] minus(h(x)) -> h(minus(x)) [3] minus(f(x,y)) -> f(minus(y),minus(x)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ minus ] (X0) = 2*X0; [ f ] (X0,X1) = 1*X1 + 1*X0 + 2; [ h ] (X0) = 1*X0; [ Marked_minus ] (X0) = 3*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ minus ] (X0) = 2 + 2*X0 + 0; [ f ] (X0,X1) = 0; [ h ] (X0) = 2 + 1*X0 + 0; [ Marked_minus ] (X0) = 3*X0 + 0; ]} ]} ]} ]} ]} Cime worked for 0.038207 seconds (real time) Cime Exit Status: 0