- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] minus(0) -> 0 [2] +(x,0) -> x [3] +(0,y) -> y [4] +(minus(1),1) -> 0 [5] minus(minus(x)) -> x [6] +(x,minus(y)) -> minus(+(minus(x),y)) [7] +(x,+(y,z)) -> +(+(x,y),z) [8] +(minus(+(x,1)),1) -> 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(0) >= 0 ; minus(minus(x)) >= x ; +(0,y) >= y ; +(minus(+(x,1)),1) >= minus(x) ; +(minus(1),1) >= 0 ; +(x,0) >= x ; +(x,minus(y)) >= minus(+(minus(x),y)) ; +(x,+(y,z)) >= +(+(x,y),z) ; Marked_+(x,minus(y)) >= Marked_+(minus(x),y) ; Marked_+(x,+(y,z)) >= Marked_+(+(x,y),z) ; Marked_+(x,+(y,z)) >= Marked_+(x,y) ; } + Disjunctions:{ { Marked_+(x,minus(y)) > Marked_+(minus(x),y) ; } { Marked_+(x,+(y,z)) > Marked_+(+(x,y),z) ; } { Marked_+(x,+(y,z)) > Marked_+(x,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(0) >= 0 constraint: minus(minus(x)) >= x constraint: +(0,y) >= y constraint: +(minus(+(x,1)),1) >= minus(x) constraint: +(minus(1),1) >= 0 constraint: +(x,0) >= x constraint: +(x,minus(y)) >= minus(+(minus(x),y)) constraint: +(x,+(y,z)) >= +(+(x,y),z) constraint: Marked_+(x,minus(y)) >= Marked_+(minus(x),y) constraint: Marked_+(x,+(y,z)) >= Marked_+(+(x,y),z) constraint: Marked_+(x,+(y,z)) >= Marked_+(x,y) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] minus(0) -> 0 [2] +(x,0) -> x [3] +(0,y) -> y [4] +(minus(1),1) -> 0 [5] minus(minus(x)) -> x [6] +(x,minus(y)) -> minus(+(minus(x),y)) [7] +(x,+(y,z)) -> +(+(x,y),z) [8] +(minus(+(x,1)),1) -> minus(x) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 3 + 0; [ Marked_+ ] (X0,X1) = 2*X1 + 0; [ + ] (X0,X1) = 3 + 1*X0 + 3*X1 + 0; [ minus ] (X0) = 3 + 1*X0 + 0; [ 1 ] () = 0; ]} ]} ]} Cime worked for 0.039457 seconds (real time) Cime Exit Status: 0