- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] O(0) -> 0 [2] +(0,x) -> x [3] +(x,0) -> x [4] +(O(x),O(y)) -> O(+(x,y)) [5] +(O(x),I(y)) -> I(+(x,y)) [6] +(I(x),O(y)) -> I(+(x,y)) [7] +(I(x),I(y)) -> O(+(+(x,y),I(0))) [8] *(0,x) -> 0 [9] *(x,0) -> 0 [10] *(O(x),y) -> O( *(x,y)) [11] *(I(x),y) -> +(O( *(x,y)),y) [12] -(x,0) -> x [13] -(0,x) -> 0 [14] -(O(x),O(y)) -> O(-(x,y)) [15] -(O(x),I(y)) -> I(-(-(x,y),I(1))) [16] -(I(x),O(y)) -> I(-(x,y)) [17] -(I(x),I(y)) -> O(-(x,y)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { O(0) >= 0 ; +(0,x) >= x ; +(O(x),O(y)) >= O(+(x,y)) ; +(O(x),I(y)) >= I(+(x,y)) ; +(I(x),O(y)) >= I(+(x,y)) ; +(I(x),I(y)) >= O(+(+(x,y),I(0))) ; +(x,0) >= x ; *(0,x) >= 0 ; *(O(x),y) >= O( *(x,y)) ; *(I(x),y) >= +(O( *(x,y)),y) ; *(x,0) >= 0 ; -(0,x) >= 0 ; -(O(x),O(y)) >= O(-(x,y)) ; -(O(x),I(y)) >= I(-(-(x,y),I(1))) ; -(I(x),O(y)) >= I(-(x,y)) ; -(I(x),I(y)) >= O(-(x,y)) ; -(x,0) >= x ; Marked_*(O(x),y) >= Marked_*(x,y) ; Marked_*(I(x),y) >= Marked_*(x,y) ; } + Disjunctions:{ { Marked_*(O(x),y) > Marked_*(x,y) ; } { Marked_*(I(x),y) > 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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: O(0) >= 0 constraint: +(0,x) >= x constraint: +(O(x),O(y)) >= O(+(x,y)) constraint: +(O(x),I(y)) >= I(+(x,y)) constraint: +(I(x),O(y)) >= I(+(x,y)) constraint: +(I(x),I(y)) >= O(+(+(x,y),I(0))) constraint: +(x,0) >= x constraint: *(0,x) >= 0 constraint: *(O(x),y) >= O( *(x,y)) constraint: *(I(x),y) >= +(O( *(x,y)),y) constraint: *(x,0) >= 0 constraint: -(0,x) >= 0 constraint: -(O(x),O(y)) >= O(-(x,y)) constraint: -(O(x),I(y)) >= I(-(-(x,y),I(1))) constraint: -(I(x),O(y)) >= I(-(x,y)) constraint: -(I(x),I(y)) >= O(-(x,y)) constraint: -(x,0) >= x constraint: Marked_*(O(x),y) >= Marked_*(x,y) constraint: Marked_*(I(x),y) >= Marked_*(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { O(0) >= 0 ; +(0,x) >= x ; +(O(x),O(y)) >= O(+(x,y)) ; +(O(x),I(y)) >= I(+(x,y)) ; +(I(x),O(y)) >= I(+(x,y)) ; +(I(x),I(y)) >= O(+(+(x,y),I(0))) ; +(x,0) >= x ; *(0,x) >= 0 ; *(O(x),y) >= O( *(x,y)) ; *(I(x),y) >= +(O( *(x,y)),y) ; *(x,0) >= 0 ; -(0,x) >= 0 ; -(O(x),O(y)) >= O(-(x,y)) ; -(O(x),I(y)) >= I(-(-(x,y),I(1))) ; -(I(x),O(y)) >= I(-(x,y)) ; -(I(x),I(y)) >= O(-(x,y)) ; -(x,0) >= x ; Marked_+(O(x),O(y)) >= Marked_+(x,y) ; Marked_+(O(x),I(y)) >= Marked_+(x,y) ; Marked_+(I(x),O(y)) >= Marked_+(x,y) ; Marked_+(I(x),I(y)) >= Marked_+(+(x,y),I(0)) ; Marked_+(I(x),I(y)) >= Marked_+(x,y) ; } + Disjunctions:{ { Marked_+(O(x),O(y)) > Marked_+(x,y) ; } { Marked_+(O(x),I(y)) > Marked_+(x,y) ; } { Marked_+(I(x),O(y)) > Marked_+(x,y) ; } { Marked_+(I(x),I(y)) > Marked_+(+(x,y),I(0)) ; } { Marked_+(I(x),I(y)) > 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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: O(0) >= 0 constraint: +(0,x) >= x constraint: +(O(x),O(y)) >= O(+(x,y)) constraint: +(O(x),I(y)) >= I(+(x,y)) constraint: +(I(x),O(y)) >= I(+(x,y)) constraint: +(I(x),I(y)) >= O(+(+(x,y),I(0))) constraint: +(x,0) >= x constraint: *(0,x) >= 0 constraint: *(O(x),y) >= O( *(x,y)) constraint: *(I(x),y) >= +(O( *(x,y)),y) constraint: *(x,0) >= 0 constraint: -(0,x) >= 0 constraint: -(O(x),O(y)) >= O(-(x,y)) constraint: -(O(x),I(y)) >= I(-(-(x,y),I(1))) constraint: -(I(x),O(y)) >= I(-(x,y)) constraint: -(I(x),I(y)) >= O(-(x,y)) constraint: -(x,0) >= x constraint: Marked_+(O(x),O(y)) >= Marked_+(x,y) constraint: Marked_+(O(x),I(y)) >= Marked_+(x,y) constraint: Marked_+(I(x),O(y)) >= Marked_+(x,y) constraint: Marked_+(I(x),I(y)) >= Marked_+(+(x,y),I(0)) constraint: Marked_+(I(x),I(y)) >= Marked_+(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { O(0) >= 0 ; +(0,x) >= x ; +(O(x),O(y)) >= O(+(x,y)) ; +(O(x),I(y)) >= I(+(x,y)) ; +(I(x),O(y)) >= I(+(x,y)) ; +(I(x),I(y)) >= O(+(+(x,y),I(0))) ; +(x,0) >= x ; *(0,x) >= 0 ; *(O(x),y) >= O( *(x,y)) ; *(I(x),y) >= +(O( *(x,y)),y) ; *(x,0) >= 0 ; -(0,x) >= 0 ; -(O(x),O(y)) >= O(-(x,y)) ; -(O(x),I(y)) >= I(-(-(x,y),I(1))) ; -(I(x),O(y)) >= I(-(x,y)) ; -(I(x),I(y)) >= O(-(x,y)) ; -(x,0) >= x ; Marked_-(O(x),O(y)) >= Marked_-(x,y) ; Marked_-(O(x),I(y)) >= Marked_-(-(x,y),I(1)) ; Marked_-(O(x),I(y)) >= Marked_-(x,y) ; Marked_-(I(x),O(y)) >= Marked_-(x,y) ; Marked_-(I(x),I(y)) >= Marked_-(x,y) ; } + Disjunctions:{ { Marked_-(O(x),O(y)) > Marked_-(x,y) ; } { Marked_-(O(x),I(y)) > Marked_-(-(x,y),I(1)) ; } { Marked_-(O(x),I(y)) > Marked_-(x,y) ; } { Marked_-(I(x),O(y)) > Marked_-(x,y) ; } { Marked_-(I(x),I(y)) > 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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: O(0) >= 0 constraint: +(0,x) >= x constraint: +(O(x),O(y)) >= O(+(x,y)) constraint: +(O(x),I(y)) >= I(+(x,y)) constraint: +(I(x),O(y)) >= I(+(x,y)) constraint: +(I(x),I(y)) >= O(+(+(x,y),I(0))) constraint: +(x,0) >= x constraint: *(0,x) >= 0 constraint: *(O(x),y) >= O( *(x,y)) constraint: *(I(x),y) >= +(O( *(x,y)),y) constraint: *(x,0) >= 0 constraint: -(0,x) >= 0 constraint: -(O(x),O(y)) >= O(-(x,y)) constraint: -(O(x),I(y)) >= I(-(-(x,y),I(1))) constraint: -(I(x),O(y)) >= I(-(x,y)) constraint: -(I(x),I(y)) >= O(-(x,y)) constraint: -(x,0) >= x constraint: Marked_-(O(x),O(y)) >= Marked_-(x,y) constraint: Marked_-(O(x),I(y)) >= Marked_-(-(x,y),I(1)) constraint: Marked_-(O(x),I(y)) >= Marked_-(x,y) constraint: Marked_-(I(x),O(y)) >= Marked_-(x,y) constraint: Marked_-(I(x),I(y)) >= Marked_-(x,y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { O(0) >= 0 ; +(0,x) >= x ; +(O(x),O(y)) >= O(+(x,y)) ; +(O(x),I(y)) >= I(+(x,y)) ; +(I(x),O(y)) >= I(+(x,y)) ; +(I(x),I(y)) >= O(+(+(x,y),I(0))) ; +(x,0) >= x ; *(0,x) >= 0 ; *(O(x),y) >= O( *(x,y)) ; *(I(x),y) >= +(O( *(x,y)),y) ; *(x,0) >= 0 ; -(0,x) >= 0 ; -(O(x),O(y)) >= O(-(x,y)) ; -(O(x),I(y)) >= I(-(-(x,y),I(1))) ; -(I(x),O(y)) >= I(-(x,y)) ; -(I(x),I(y)) >= O(-(x,y)) ; -(x,0) >= x ; Marked_+(I(x),I(y)) >= Marked_+(+(x,y),I(0)) ; } + Disjunctions:{ { Marked_+(I(x),I(y)) > Marked_+(+(x,y),I(0)) ; } } === 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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: O(0) >= 0 constraint: +(0,x) >= x constraint: +(O(x),O(y)) >= O(+(x,y)) constraint: +(O(x),I(y)) >= I(+(x,y)) constraint: +(I(x),O(y)) >= I(+(x,y)) constraint: +(I(x),I(y)) >= O(+(+(x,y),I(0))) constraint: +(x,0) >= x constraint: *(0,x) >= 0 constraint: *(O(x),y) >= O( *(x,y)) constraint: *(I(x),y) >= +(O( *(x,y)),y) constraint: *(x,0) >= 0 constraint: -(0,x) >= 0 constraint: -(O(x),O(y)) >= O(-(x,y)) constraint: -(O(x),I(y)) >= I(-(-(x,y),I(1))) constraint: -(I(x),O(y)) >= I(-(x,y)) constraint: -(I(x),I(y)) >= O(-(x,y)) constraint: -(x,0) >= x constraint: Marked_+(I(x),I(y)) >= Marked_+(+(x,y),I(0)) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { O(0) >= 0 ; +(0,x) >= x ; +(O(x),O(y)) >= O(+(x,y)) ; +(O(x),I(y)) >= I(+(x,y)) ; +(I(x),O(y)) >= I(+(x,y)) ; +(I(x),I(y)) >= O(+(+(x,y),I(0))) ; +(x,0) >= x ; *(0,x) >= 0 ; *(O(x),y) >= O( *(x,y)) ; *(I(x),y) >= +(O( *(x,y)),y) ; *(x,0) >= 0 ; -(0,x) >= 0 ; -(O(x),O(y)) >= O(-(x,y)) ; -(O(x),I(y)) >= I(-(-(x,y),I(1))) ; -(I(x),O(y)) >= I(-(x,y)) ; -(I(x),I(y)) >= O(-(x,y)) ; -(x,0) >= x ; Marked_-(O(x),I(y)) >= Marked_-(-(x,y),I(1)) ; } + Disjunctions:{ { Marked_-(O(x),I(y)) > Marked_-(-(x,y),I(1)) ; } } === 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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: O(0) >= 0 constraint: +(0,x) >= x constraint: +(O(x),O(y)) >= O(+(x,y)) constraint: +(O(x),I(y)) >= I(+(x,y)) constraint: +(I(x),O(y)) >= I(+(x,y)) constraint: +(I(x),I(y)) >= O(+(+(x,y),I(0))) constraint: +(x,0) >= x constraint: *(0,x) >= 0 constraint: *(O(x),y) >= O( *(x,y)) constraint: *(I(x),y) >= +(O( *(x,y)),y) constraint: *(x,0) >= 0 constraint: -(0,x) >= 0 constraint: -(O(x),O(y)) >= O(-(x,y)) constraint: -(O(x),I(y)) >= I(-(-(x,y),I(1))) constraint: -(I(x),O(y)) >= I(-(x,y)) constraint: -(I(x),I(y)) >= O(-(x,y)) constraint: -(x,0) >= x constraint: Marked_-(O(x),I(y)) >= Marked_-(-(x,y),I(1)) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] O(0) -> 0 [2] +(0,x) -> x [3] +(x,0) -> x [4] +(O(x),O(y)) -> O(+(x,y)) [5] +(O(x),I(y)) -> I(+(x,y)) [6] +(I(x),O(y)) -> I(+(x,y)) [7] +(I(x),I(y)) -> O(+(+(x,y),I(0))) [8] *(0,x) -> 0 [9] *(x,0) -> 0 [10] *(O(x),y) -> O( *(x,y)) [11] *(I(x),y) -> +(O( *(x,y)),y) [12] -(x,0) -> x [13] -(0,x) -> 0 [14] -(O(x),O(y)) -> O(-(x,y)) [15] -(O(x),I(y)) -> I(-(-(x,y),I(1))) [16] -(I(x),O(y)) -> I(-(x,y)) [17] -(I(x),I(y)) -> O(-(x,y)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ * ] (X0,X1) = 2*X0 + 2*X1 + 1*X1*X0 + 0; [ + ] (X0,X1) = 1*X0 + 2*X1 + 0; [ 1 ] () = 0; [ O ] (X0) = 2 + 1*X0 + 0; [ Marked_* ] (X0,X1) = 2*X0 + 2*X1*X0 + 0; [ - ] (X0,X1) = 1*X0 + 0; [ I ] (X0) = 2 + 1*X0 + 0; ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ 0 ] () = 0; [ * ] (X0,X1) = 1*X1*X0 + 1*X0; [ + ] (X0,X1) = 1*X1 + 1*X0; [ Marked_+ ] (X0,X1) = 2*X1; [ 1 ] () = 0; [ O ] (X0) = 1*X0 + 2; [ - ] (X0,X1) = 1*X0; [ I ] (X0) = 1*X0 + 2; removing < Marked_+(I(x),O(y)),Marked_+(x,y)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ * ] (X0,X1) = 1*X0 + 1*X1*X0 + 0; [ + ] (X0,X1) = 1*X0 + 2*X1 + 0; [ Marked_+ ] (X0,X1) = 1*X0 + 2*X1 + 0; [ 1 ] () = 0; [ O ] (X0) = 2 + 1*X0 + 0; [ - ] (X0,X1) = 1*X0 + 0; [ I ] (X0) = 2 + 1*X0 + 0; ]} ]} ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ 0 ] () = 0; [ * ] (X0,X1) = 1*X1*X0 + 1*X0; [ + ] (X0,X1) = 2*X1 + 1*X0; [ 1 ] () = 0; [ O ] (X0) = 1*X0 + 2; [ - ] (X0,X1) = 1*X0; [ I ] (X0) = 1*X0 + 2; [ Marked_- ] (X0,X1) = 1*X1; removing < Marked_-(I(x),O(y)),Marked_-(x,y)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ * ] (X0,X1) = 1*X0 + 1*X1*X0 + 0; [ + ] (X0,X1) = 1*X0 + 2*X1 + 0; [ 1 ] () = 0; [ O ] (X0) = 2 + 1*X0 + 0; [ - ] (X0,X1) = 1*X0 + 0; [ I ] (X0) = 2 + 1*X0 + 0; [ Marked_- ] (X0,X1) = 2*X1*X0 + 0; ]} ]} ]} ]} ]} Cime worked for 2.034508 seconds (real time) Cime Exit Status: 0