- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] +(a,b) -> +(b,a) [2] +(a,+(b,z)) -> +(b,+(a,z)) [3] +(+(x,y),z) -> +(x,+(y,z)) [4] f(a,y) -> a [5] f(b,y) -> b [6] f(+(x,y),z) -> +(f(x,z),f(y,z)) 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: { +(+(x,y),z) >= +(x,+(y,z)) ; +(a,+(b,z)) >= +(b,+(a,z)) ; +(a,b) >= +(b,a) ; f(+(x,y),z) >= +(f(x,z),f(y,z)) ; f(b,y) >= b ; f(a,y) >= a ; Marked_f(+(x,y),z) >= Marked_f(x,z) ; Marked_f(+(x,y),z) >= Marked_f(y,z) ; } + Disjunctions:{ { Marked_f(+(x,y),z) > Marked_f(x,z) ; } { Marked_f(+(x,y),z) > Marked_f(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: +(+(x,y),z) >= +(x,+(y,z)) constraint: +(a,+(b,z)) >= +(b,+(a,z)) constraint: +(a,b) >= +(b,a) constraint: f(+(x,y),z) >= +(f(x,z),f(y,z)) constraint: f(b,y) >= b constraint: f(a,y) >= a constraint: Marked_f(+(x,y),z) >= Marked_f(x,z) constraint: Marked_f(+(x,y),z) >= Marked_f(y,z) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { +(+(x,y),z) >= +(x,+(y,z)) ; +(a,+(b,z)) >= +(b,+(a,z)) ; +(a,b) >= +(b,a) ; f(+(x,y),z) >= +(f(x,z),f(y,z)) ; f(b,y) >= b ; f(a,y) >= a ; 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: +(+(x,y),z) >= +(x,+(y,z)) constraint: +(a,+(b,z)) >= +(b,+(a,z)) constraint: +(a,b) >= +(b,a) constraint: f(+(x,y),z) >= +(f(x,z),f(y,z)) constraint: f(b,y) >= b constraint: f(a,y) >= a 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: { +(+(x,y),z) >= +(x,+(y,z)) ; +(a,+(b,z)) >= +(b,+(a,z)) ; +(a,b) >= +(b,a) ; f(+(x,y),z) >= +(f(x,z),f(y,z)) ; f(b,y) >= b ; f(a,y) >= a ; Marked_+(a,+(b,z)) >= Marked_+(a,z) ; } + Disjunctions:{ { Marked_+(a,+(b,z)) > Marked_+(a,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: +(+(x,y),z) >= +(x,+(y,z)) constraint: +(a,+(b,z)) >= +(b,+(a,z)) constraint: +(a,b) >= +(b,a) constraint: f(+(x,y),z) >= +(f(x,z),f(y,z)) constraint: f(b,y) >= b constraint: f(a,y) >= a constraint: Marked_+(a,+(b,z)) >= Marked_+(a,z) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] +(a,b) -> +(b,a) [2] +(a,+(b,z)) -> +(b,+(a,z)) [3] +(+(x,y),z) -> +(x,+(y,z)) [4] f(a,y) -> a [5] f(b,y) -> b [6] f(+(x,y),z) -> +(f(x,z),f(y,z)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ + ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; [ Marked_f ] (X0,X1) = 3*X0 + 0; [ a ] () = 0; [ b ] () = 0; [ f ] (X0,X1) = 2*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ + ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; [ a ] () = 0; [ b ] () = 0; [ Marked_+ ] (X0,X1) = 3*X0 + 0; [ f ] (X0,X1) = 2*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ + ] (X0,X1) = 1 + 2*X0 + 1*X1 + 0; [ a ] () = 0; [ b ] () = 0; [ Marked_+ ] (X0,X1) = 1*X1 + 0; [ f ] (X0,X1) = 2*X0 + 0; ]} ]} ]} Cime worked for 0.078303 seconds (real time) Cime Exit Status: 0