- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] i(0) -> 0 [2] +(0,y) -> y [3] +(x,0) -> x [4] i(i(x)) -> x [5] +(i(x),x) -> 0 [6] +(x,i(x)) -> 0 [7] i(+(x,y)) -> +(i(x),i(y)) [8] +(x,+(y,z)) -> +(+(x,y),z) [9] +(+(x,i(y)),y) -> x [10] +(+(x,y),i(y)) -> 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: { i(0) >= 0 ; i(i(x)) >= x ; i(+(x,y)) >= +(i(x),i(y)) ; +(0,y) >= y ; +(i(x),x) >= 0 ; +(+(x,i(y)),y) >= x ; +(+(x,y),i(y)) >= x ; +(x,0) >= x ; +(x,i(x)) >= 0 ; +(x,+(y,z)) >= +(+(x,y),z) ; Marked_i(+(x,y)) >= Marked_i(x) ; Marked_i(+(x,y)) >= Marked_i(y) ; } + Disjunctions:{ { Marked_i(+(x,y)) > Marked_i(x) ; } { Marked_i(+(x,y)) > Marked_i(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: i(0) >= 0 constraint: i(i(x)) >= x constraint: i(+(x,y)) >= +(i(x),i(y)) constraint: +(0,y) >= y constraint: +(i(x),x) >= 0 constraint: +(+(x,i(y)),y) >= x constraint: +(+(x,y),i(y)) >= x constraint: +(x,0) >= x constraint: +(x,i(x)) >= 0 constraint: +(x,+(y,z)) >= +(+(x,y),z) constraint: Marked_i(+(x,y)) >= Marked_i(x) constraint: Marked_i(+(x,y)) >= Marked_i(y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { i(0) >= 0 ; i(i(x)) >= x ; i(+(x,y)) >= +(i(x),i(y)) ; +(0,y) >= y ; +(i(x),x) >= 0 ; +(+(x,i(y)),y) >= x ; +(+(x,y),i(y)) >= x ; +(x,0) >= x ; +(x,i(x)) >= 0 ; +(x,+(y,z)) >= +(+(x,y),z) ; Marked_+(x,+(y,z)) >= Marked_+(+(x,y),z) ; Marked_+(x,+(y,z)) >= Marked_+(x,y) ; } + Disjunctions:{ { 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: i(0) >= 0 constraint: i(i(x)) >= x constraint: i(+(x,y)) >= +(i(x),i(y)) constraint: +(0,y) >= y constraint: +(i(x),x) >= 0 constraint: +(+(x,i(y)),y) >= x constraint: +(+(x,y),i(y)) >= x constraint: +(x,0) >= x constraint: +(x,i(x)) >= 0 constraint: +(x,+(y,z)) >= +(+(x,y),z) constraint: Marked_+(x,+(y,z)) >= Marked_+(+(x,y),z) constraint: Marked_+(x,+(y,z)) >= Marked_+(x,y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] i(0) -> 0 [2] +(0,y) -> y [3] +(x,0) -> x [4] i(i(x)) -> x [5] +(i(x),x) -> 0 [6] +(x,i(x)) -> 0 [7] i(+(x,y)) -> +(i(x),i(y)) [8] +(x,+(y,z)) -> +(+(x,y),z) [9] +(+(x,i(y)),y) -> x [10] +(+(x,y),i(y)) -> x , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ Marked_i ] (X0) = 3*X0 + 0; [ + ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; [ i ] (X0) = 2*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ + ] (X0,X1) = 2 + 1*X0 + 2*X1 + 0; [ i ] (X0) = 2*X0 + 0; [ Marked_+ ] (X0,X1) = 3*X1 + 0; ]} ]} ]} Cime worked for 0.044673 seconds (real time) Cime Exit Status: 0