- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] +(p1,p1) -> p2 [2] +(p1,+(p2,p2)) -> p5 [3] +(p5,p5) -> p10 [4] +(+(x,y),z) -> +(x,+(y,z)) [5] +(p1,+(p1,x)) -> +(p2,x) [6] +(p1,+(p2,+(p2,x))) -> +(p5,x) [7] +(p2,p1) -> +(p1,p2) [8] +(p2,+(p1,x)) -> +(p1,+(p2,x)) [9] +(p2,+(p2,p2)) -> +(p1,p5) [10] +(p2,+(p2,+(p2,x))) -> +(p1,+(p5,x)) [11] +(p5,p1) -> +(p1,p5) [12] +(p5,+(p1,x)) -> +(p1,+(p5,x)) [13] +(p5,p2) -> +(p2,p5) [14] +(p5,+(p2,x)) -> +(p2,+(p5,x)) [15] +(p5,+(p5,x)) -> +(p10,x) [16] +(p10,p1) -> +(p1,p10) [17] +(p10,+(p1,x)) -> +(p1,+(p10,x)) [18] +(p10,p2) -> +(p2,p10) [19] +(p10,+(p2,x)) -> +(p2,+(p10,x)) [20] +(p10,p5) -> +(p5,p10) [21] +(p10,+(p5,x)) -> +(p5,+(p10,x)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { +(p2,+(p2,p2)) >= +(p1,p5) ; +(p2,+(p2,+(p2,x))) >= +(p1,+(p5,x)) ; +(p2,+(p1,x)) >= +(p1,+(p2,x)) ; +(p2,p1) >= +(p1,p2) ; +(+(x,y),z) >= +(x,+(y,z)) ; +(p1,+(p2,p2)) >= p5 ; +(p1,+(p2,+(p2,x))) >= +(p5,x) ; +(p1,+(p1,x)) >= +(p2,x) ; +(p1,p1) >= p2 ; +(p5,p2) >= +(p2,p5) ; +(p5,+(p2,x)) >= +(p2,+(p5,x)) ; +(p5,+(p1,x)) >= +(p1,+(p5,x)) ; +(p5,+(p5,x)) >= +(p10,x) ; +(p5,p1) >= +(p1,p5) ; +(p5,p5) >= p10 ; +(p10,p2) >= +(p2,p10) ; +(p10,+(p2,x)) >= +(p2,+(p10,x)) ; +(p10,+(p1,x)) >= +(p1,+(p10,x)) ; +(p10,+(p5,x)) >= +(p5,+(p10,x)) ; +(p10,p1) >= +(p1,p10) ; +(p10,p5) >= +(p5,p10) ; Marked_+(+(x,y),z) >= Marked_+(x,+(y,z)) ; Marked_+(+(x,y),z) >= Marked_+(y,z) ; } + Disjunctions:{ { Marked_+(+(x,y),z) > Marked_+(x,+(y,z)) ; } { Marked_+(+(x,y),z) > Marked_+(y,z) ; } } === 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: +(p2,+(p2,p2)) >= +(p1,p5) constraint: +(p2,+(p2,+(p2,x))) >= +(p1,+(p5,x)) constraint: +(p2,+(p1,x)) >= +(p1,+(p2,x)) constraint: +(p2,p1) >= +(p1,p2) constraint: +(+(x,y),z) >= +(x,+(y,z)) constraint: +(p1,+(p2,p2)) >= p5 constraint: +(p1,+(p2,+(p2,x))) >= +(p5,x) constraint: +(p1,+(p1,x)) >= +(p2,x) constraint: +(p1,p1) >= p2 constraint: +(p5,p2) >= +(p2,p5) constraint: +(p5,+(p2,x)) >= +(p2,+(p5,x)) constraint: +(p5,+(p1,x)) >= +(p1,+(p5,x)) constraint: +(p5,+(p5,x)) >= +(p10,x) constraint: +(p5,p1) >= +(p1,p5) constraint: +(p5,p5) >= p10 constraint: +(p10,p2) >= +(p2,p10) constraint: +(p10,+(p2,x)) >= +(p2,+(p10,x)) constraint: +(p10,+(p1,x)) >= +(p1,+(p10,x)) constraint: +(p10,+(p5,x)) >= +(p5,+(p10,x)) constraint: +(p10,p1) >= +(p1,p10) constraint: +(p10,p5) >= +(p5,p10) constraint: Marked_+(+(x,y),z) >= Marked_+(x,+(y,z)) constraint: Marked_+(+(x,y),z) >= Marked_+(y,z) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { +(p2,+(p2,p2)) >= +(p1,p5) ; +(p2,+(p2,+(p2,x))) >= +(p1,+(p5,x)) ; +(p2,+(p1,x)) >= +(p1,+(p2,x)) ; +(p2,p1) >= +(p1,p2) ; +(+(x,y),z) >= +(x,+(y,z)) ; +(p1,+(p2,p2)) >= p5 ; +(p1,+(p2,+(p2,x))) >= +(p5,x) ; +(p1,+(p1,x)) >= +(p2,x) ; +(p1,p1) >= p2 ; +(p5,p2) >= +(p2,p5) ; +(p5,+(p2,x)) >= +(p2,+(p5,x)) ; +(p5,+(p1,x)) >= +(p1,+(p5,x)) ; +(p5,+(p5,x)) >= +(p10,x) ; +(p5,p1) >= +(p1,p5) ; +(p5,p5) >= p10 ; +(p10,p2) >= +(p2,p10) ; +(p10,+(p2,x)) >= +(p2,+(p10,x)) ; +(p10,+(p1,x)) >= +(p1,+(p10,x)) ; +(p10,+(p5,x)) >= +(p5,+(p10,x)) ; +(p10,p1) >= +(p1,p10) ; +(p10,p5) >= +(p5,p10) ; Marked_+(p2,+(p2,+(p2,x))) >= Marked_+(p1,+(p5,x)) ; Marked_+(p2,+(p2,+(p2,x))) >= Marked_+(p5,x) ; Marked_+(p2,+(p1,x)) >= Marked_+(p2,x) ; Marked_+(p2,+(p1,x)) >= Marked_+(p1,+(p2,x)) ; Marked_+(p1,+(p2,+(p2,x))) >= Marked_+(p5,x) ; Marked_+(p1,+(p1,x)) >= Marked_+(p2,x) ; Marked_+(p5,+(p2,x)) >= Marked_+(p2,+(p5,x)) ; Marked_+(p5,+(p2,x)) >= Marked_+(p5,x) ; Marked_+(p5,+(p1,x)) >= Marked_+(p1,+(p5,x)) ; Marked_+(p5,+(p1,x)) >= Marked_+(p5,x) ; Marked_+(p5,+(p5,x)) >= Marked_+(p10,x) ; Marked_+(p10,+(p2,x)) >= Marked_+(p2,+(p10,x)) ; Marked_+(p10,+(p2,x)) >= Marked_+(p10,x) ; Marked_+(p10,+(p1,x)) >= Marked_+(p1,+(p10,x)) ; Marked_+(p10,+(p1,x)) >= Marked_+(p10,x) ; Marked_+(p10,+(p5,x)) >= Marked_+(p5,+(p10,x)) ; Marked_+(p10,+(p5,x)) >= Marked_+(p10,x) ; } + Disjunctions:{ { Marked_+(p2,+(p2,+(p2,x))) > Marked_+(p1,+(p5,x)) ; } { Marked_+(p2,+(p2,+(p2,x))) > Marked_+(p5,x) ; } { Marked_+(p2,+(p1,x)) > Marked_+(p2,x) ; } { Marked_+(p2,+(p1,x)) > Marked_+(p1,+(p2,x)) ; } { Marked_+(p1,+(p2,+(p2,x))) > Marked_+(p5,x) ; } { Marked_+(p1,+(p1,x)) > Marked_+(p2,x) ; } { Marked_+(p5,+(p2,x)) > Marked_+(p2,+(p5,x)) ; } { Marked_+(p5,+(p2,x)) > Marked_+(p5,x) ; } { Marked_+(p5,+(p1,x)) > Marked_+(p1,+(p5,x)) ; } { Marked_+(p5,+(p1,x)) > Marked_+(p5,x) ; } { Marked_+(p5,+(p5,x)) > Marked_+(p10,x) ; } { Marked_+(p10,+(p2,x)) > Marked_+(p2,+(p10,x)) ; } { Marked_+(p10,+(p2,x)) > Marked_+(p10,x) ; } { Marked_+(p10,+(p1,x)) > Marked_+(p1,+(p10,x)) ; } { Marked_+(p10,+(p1,x)) > Marked_+(p10,x) ; } { Marked_+(p10,+(p5,x)) > Marked_+(p5,+(p10,x)) ; } { Marked_+(p10,+(p5,x)) > Marked_+(p10,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: +(p2,+(p2,p2)) >= +(p1,p5) constraint: +(p2,+(p2,+(p2,x))) >= +(p1,+(p5,x)) constraint: +(p2,+(p1,x)) >= +(p1,+(p2,x)) constraint: +(p2,p1) >= +(p1,p2) constraint: +(+(x,y),z) >= +(x,+(y,z)) constraint: +(p1,+(p2,p2)) >= p5 constraint: +(p1,+(p2,+(p2,x))) >= +(p5,x) constraint: +(p1,+(p1,x)) >= +(p2,x) constraint: +(p1,p1) >= p2 constraint: +(p5,p2) >= +(p2,p5) constraint: +(p5,+(p2,x)) >= +(p2,+(p5,x)) constraint: +(p5,+(p1,x)) >= +(p1,+(p5,x)) constraint: +(p5,+(p5,x)) >= +(p10,x) constraint: +(p5,p1) >= +(p1,p5) constraint: +(p5,p5) >= p10 constraint: +(p10,p2) >= +(p2,p10) constraint: +(p10,+(p2,x)) >= +(p2,+(p10,x)) constraint: +(p10,+(p1,x)) >= +(p1,+(p10,x)) constraint: +(p10,+(p5,x)) >= +(p5,+(p10,x)) constraint: +(p10,p1) >= +(p1,p10) constraint: +(p10,p5) >= +(p5,p10) constraint: Marked_+(p2,+(p2,+(p2,x))) >= Marked_+(p1,+(p5,x)) constraint: Marked_+(p2,+(p2,+(p2,x))) >= Marked_+(p5,x) constraint: Marked_+(p2,+(p1,x)) >= Marked_+(p2,x) constraint: Marked_+(p2,+(p1,x)) >= Marked_+(p1,+(p2,x)) constraint: Marked_+(p1,+(p2,+(p2,x))) >= Marked_+(p5,x) constraint: Marked_+(p1,+(p1,x)) >= Marked_+(p2,x) constraint: Marked_+(p5,+(p2,x)) >= Marked_+(p2,+(p5,x)) constraint: Marked_+(p5,+(p2,x)) >= Marked_+(p5,x) constraint: Marked_+(p5,+(p1,x)) >= Marked_+(p1,+(p5,x)) constraint: Marked_+(p5,+(p1,x)) >= Marked_+(p5,x) constraint: Marked_+(p5,+(p5,x)) >= Marked_+(p10,x) constraint: Marked_+(p10,+(p2,x)) >= Marked_+(p2,+(p10,x)) constraint: Marked_+(p10,+(p2,x)) >= Marked_+(p10,x) constraint: Marked_+(p10,+(p1,x)) >= Marked_+(p1,+(p10,x)) constraint: Marked_+(p10,+(p1,x)) >= Marked_+(p10,x) constraint: Marked_+(p10,+(p5,x)) >= Marked_+(p5,+(p10,x)) constraint: Marked_+(p10,+(p5,x)) >= Marked_+(p10,x) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] +(p1,p1) -> p2 [2] +(p1,+(p2,p2)) -> p5 [3] +(p5,p5) -> p10 [4] +(+(x,y),z) -> +(x,+(y,z)) [5] +(p1,+(p1,x)) -> +(p2,x) [6] +(p1,+(p2,+(p2,x))) -> +(p5,x) [7] +(p2,p1) -> +(p1,p2) [8] +(p2,+(p1,x)) -> +(p1,+(p2,x)) [9] +(p2,+(p2,p2)) -> +(p1,p5) [10] +(p2,+(p2,+(p2,x))) -> +(p1,+(p5,x)) [11] +(p5,p1) -> +(p1,p5) [12] +(p5,+(p1,x)) -> +(p1,+(p5,x)) [13] +(p5,p2) -> +(p2,p5) [14] +(p5,+(p2,x)) -> +(p2,+(p5,x)) [15] +(p5,+(p5,x)) -> +(p10,x) [16] +(p10,p1) -> +(p1,p10) [17] +(p10,+(p1,x)) -> +(p1,+(p10,x)) [18] +(p10,p2) -> +(p2,p10) [19] +(p10,+(p2,x)) -> +(p2,+(p10,x)) [20] +(p10,p5) -> +(p5,p10) [21] +(p10,+(p5,x)) -> +(p5,+(p10,x)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ p2 ] () = 0; [ p10 ] () = 0; [ p1 ] () = 0; [ + ] (X0,X1) = 3 + 2*X0 + 1*X1 + 0; [ Marked_+ ] (X0,X1) = 3*X0 + 0; [ p5 ] () = 0; ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ p2 ] () = 0; [ p10 ] () = 0; [ p1 ] () = 0; [ + ] (X0,X1) = 1*X1 + 1*X0 + 1; [ Marked_+ ] (X0,X1) = 2*X1; [ p5 ] () = 0; removing [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.245563 seconds (real time) Cime Exit Status: 0