- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a(a(f(x,y))) -> f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) [2] f(a(x),a(y)) -> a(f(x,y)) [3] f(b(x),b(y)) -> b(f(x,y)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(a(x),a(y)) >= a(f(x,y)) ; f(b(x),b(y)) >= b(f(x,y)) ; a(a(f(x,y))) >= f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) ; Marked_f(a(x),a(y)) >= Marked_f(x,y) ; Marked_f(a(x),a(y)) >= Marked_a(f(x,y)) ; Marked_f(b(x),b(y)) >= Marked_f(x,y) ; Marked_a(a(f(x,y))) >= Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) ; Marked_a(a(f(x,y))) >= Marked_a(x) ; Marked_a(a(f(x,y))) >= Marked_a(y) ; } + Disjunctions:{ { Marked_f(a(x),a(y)) > Marked_f(x,y) ; } { Marked_f(a(x),a(y)) > Marked_a(f(x,y)) ; } { Marked_f(b(x),b(y)) > Marked_f(x,y) ; } { Marked_a(a(f(x,y))) > Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) ; } { Marked_a(a(f(x,y))) > Marked_a(x) ; } { Marked_a(a(f(x,y))) > Marked_a(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: f(a(x),a(y)) >= a(f(x,y)) constraint: f(b(x),b(y)) >= b(f(x,y)) constraint: a(a(f(x,y))) >= f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) constraint: Marked_f(a(x),a(y)) >= Marked_f(x,y) constraint: Marked_f(a(x),a(y)) >= Marked_a(f(x,y)) constraint: Marked_f(b(x),b(y)) >= Marked_f(x,y) constraint: Marked_a(a(f(x,y))) >= Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) constraint: Marked_a(a(f(x,y))) >= Marked_a(x) constraint: Marked_a(a(f(x,y))) >= Marked_a(y) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(a(x),a(y)) >= a(f(x,y)) ; f(b(x),b(y)) >= b(f(x,y)) ; a(a(f(x,y))) >= f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) ; Marked_f(a(x),a(y)) >= Marked_f(x,y) ; Marked_f(a(x),a(y)) >= Marked_a(f(x,y)) ; Marked_f(b(x),b(y)) >= Marked_f(x,y) ; Marked_a(a(f(x,y))) >= Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) ; } + Disjunctions:{ { Marked_f(a(x),a(y)) > Marked_f(x,y) ; } { Marked_f(a(x),a(y)) > Marked_a(f(x,y)) ; } { Marked_f(b(x),b(y)) > Marked_f(x,y) ; } { Marked_a(a(f(x,y))) > Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(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 : 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),a(y)) >= a(f(x,y)) constraint: f(b(x),b(y)) >= b(f(x,y)) constraint: a(a(f(x,y))) >= f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) constraint: Marked_f(a(x),a(y)) >= Marked_f(x,y) constraint: Marked_f(a(x),a(y)) >= Marked_a(f(x,y)) constraint: Marked_f(b(x),b(y)) >= Marked_f(x,y) constraint: Marked_a(a(f(x,y))) >= Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_f -> 2 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] a(a(f(x,y))) -> f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) [2] f(a(x),a(y)) -> a(f(x,y)) [3] f(b(x),b(y)) -> b(f(x,y)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ f ] (X0,X1) = 1*X1 + 1*X0 + 1; [ Marked_a ] (X0) = 2*X0; [ b ] (X0) = 1*X0; [ a ] (X0) = 1*X0; [ Marked_f ] (X0,X1) = 2*X1 + 2*X0 + 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ f ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_a ] (X0) = [ [ 1 , 0 , 1 ] [ 0 , 0 , 0 ] [ 1 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; [ b ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ a ] (X0) = [ [ 0 , 0 , 0 ] [ 1 , 1 , 0 ] [ 1 , 0 , 1 ] ]*X0 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_f ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} ]} ]} Cime worked for 48.042439 seconds (real time) Cime Exit Status: 0