- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a(a(f(b,a(x)))) -> f(a(a(a(x))),b) [2] a(a(x)) -> f(b,a(f(a(x),b))) [3] f(a(x),b) -> f(b,a(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: { f(a(x),b) >= f(b,a(x)) ; a(a(f(b,a(x)))) >= f(a(a(a(x))),b) ; a(a(x)) >= f(b,a(f(a(x),b))) ; Marked_a(a(f(b,a(x)))) >= Marked_a(a(a(x))) ; Marked_a(a(f(b,a(x)))) >= Marked_a(a(x)) ; Marked_a(a(x)) >= Marked_a(f(a(x),b)) ; } + Disjunctions:{ { Marked_a(a(f(b,a(x)))) > Marked_a(a(a(x))) ; } { Marked_a(a(f(b,a(x)))) > Marked_a(a(x)) ; } { Marked_a(a(x)) > Marked_a(f(a(x),b)) ; } } === 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: f(a(x),b) >= f(b,a(x)) constraint: a(a(f(b,a(x)))) >= f(a(a(a(x))),b) constraint: a(a(x)) >= f(b,a(f(a(x),b))) constraint: Marked_a(a(f(b,a(x)))) >= Marked_a(a(a(x))) constraint: Marked_a(a(f(b,a(x)))) >= Marked_a(a(x)) constraint: Marked_a(a(x)) >= Marked_a(f(a(x),b)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(a(x),b) >= f(b,a(x)) ; a(a(f(b,a(x)))) >= f(a(a(a(x))),b) ; a(a(x)) >= f(b,a(f(a(x),b))) ; Marked_a(a(f(b,a(x)))) >= Marked_a(a(a(x))) ; Marked_a(a(f(b,a(x)))) >= Marked_a(a(x)) ; } + Disjunctions:{ { Marked_a(a(f(b,a(x)))) > Marked_a(a(a(x))) ; } { Marked_a(a(f(b,a(x)))) > Marked_a(a(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: f(a(x),b) >= f(b,a(x)) constraint: a(a(f(b,a(x)))) >= f(a(a(a(x))),b) constraint: a(a(x)) >= f(b,a(f(a(x),b))) constraint: Marked_a(a(f(b,a(x)))) >= Marked_a(a(a(x))) constraint: Marked_a(a(f(b,a(x)))) >= Marked_a(a(x)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(a(x),b) >= f(b,a(x)) ; a(a(f(b,a(x)))) >= f(a(a(a(x))),b) ; a(a(x)) >= f(b,a(f(a(x),b))) ; Marked_a(a(f(b,a(x)))) >= Marked_a(a(a(x))) ; } + Disjunctions:{ { Marked_a(a(f(b,a(x)))) > Marked_a(a(a(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 === 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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. === TIMER virtual : 50.000000 === trying sub matrices of size: 1 Matrix interpretation constraints generated. Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. Termination constraints generated. Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 50.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: f(a(x),b) >= f(b,a(x)) constraint: a(a(f(b,a(x)))) >= f(a(a(a(x))),b) constraint: a(a(x)) >= f(b,a(f(a(x),b))) constraint: Marked_a(a(f(b,a(x)))) >= Marked_a(a(a(x))) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] a(a(f(b,a(x)))) -> f(a(a(a(x))),b) [2] a(a(x)) -> f(b,a(f(a(x),b))) [3] f(a(x),b) -> f(b,a(x)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ f ] (X0,X1) = 0; [ Marked_a ] (X0) = 2*X0; [ b ] () = 0; [ a ] (X0) = 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ f ] (X0,X1) = 1*X1 + 1*X0; [ Marked_a ] (X0) = 2*X0; [ b ] () = 0; [ a ] (X0) = 2*X0 + 1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ f ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_a ] (X0) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ b ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; [ a ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; ]} ]} ]} ]} ]} ]} ]} Cime worked for 3.176089 seconds (real time) Cime Exit Status: 0