- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x) [2] f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y)) [3] c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a))))) 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: { b(a,b(c(z,x,y),a)) >= b(b(z,c(y,z,a)),x) ; c(f(c(a,y,a)),x,z) >= f(b(b(z,z),f(b(y,b(x,a))))) ; f(c(a,b(b(z,a),y),x)) >= f(c(x,b(z,x),y)) ; Marked_c(f(c(a,y,a)),x,z) >= Marked_f(b(b(z,z),f(b(y,b(x,a))))) ; Marked_c(f(c(a,y,a)),x,z) >= Marked_f(b(y,b(x,a))) ; Marked_c(f(c(a,y,a)),x,z) >= Marked_b(b(z,z),f(b(y,b(x,a)))) ; Marked_c(f(c(a,y,a)),x,z) >= Marked_b(y,b(x,a)) ; Marked_c(f(c(a,y,a)),x,z) >= Marked_b(z,z) ; Marked_f(c(a,b(b(z,a),y),x)) >= Marked_c(x,b(z,x),y) ; Marked_f(c(a,b(b(z,a),y),x)) >= Marked_f(c(x,b(z,x),y)) ; Marked_f(c(a,b(b(z,a),y),x)) >= Marked_b(z,x) ; Marked_b(a,b(c(z,x,y),a)) >= Marked_c(y,z,a) ; Marked_b(a,b(c(z,x,y),a)) >= Marked_b(b(z,c(y,z,a)),x) ; Marked_b(a,b(c(z,x,y),a)) >= Marked_b(z,c(y,z,a)) ; } + Disjunctions:{ { Marked_c(f(c(a,y,a)),x,z) > Marked_f(b(b(z,z),f(b(y,b(x,a))))) ; } { Marked_c(f(c(a,y,a)),x,z) > Marked_f(b(y,b(x,a))) ; } { Marked_c(f(c(a,y,a)),x,z) > Marked_b(b(z,z),f(b(y,b(x,a)))) ; } { Marked_c(f(c(a,y,a)),x,z) > Marked_b(y,b(x,a)) ; } { Marked_c(f(c(a,y,a)),x,z) > Marked_b(z,z) ; } { Marked_f(c(a,b(b(z,a),y),x)) > Marked_c(x,b(z,x),y) ; } { Marked_f(c(a,b(b(z,a),y),x)) > Marked_f(c(x,b(z,x),y)) ; } { Marked_f(c(a,b(b(z,a),y),x)) > Marked_b(z,x) ; } { Marked_b(a,b(c(z,x,y),a)) > Marked_c(y,z,a) ; } { Marked_b(a,b(c(z,x,y),a)) > Marked_b(b(z,c(y,z,a)),x) ; } { Marked_b(a,b(c(z,x,y),a)) > Marked_b(z,c(y,z,a)) ; } } === 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: b(a,b(c(z,x,y),a)) >= b(b(z,c(y,z,a)),x) constraint: c(f(c(a,y,a)),x,z) >= f(b(b(z,z),f(b(y,b(x,a))))) constraint: f(c(a,b(b(z,a),y),x)) >= f(c(x,b(z,x),y)) constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_f(b(b(z,z),f(b(y,b(x,a))))) constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_f(b(y,b(x,a))) constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_b(b(z,z),f(b(y,b(x,a)))) constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_b(y,b(x,a)) constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_b(z,z) constraint: Marked_f(c(a,b(b(z,a),y),x)) >= Marked_c(x,b(z,x),y) constraint: Marked_f(c(a,b(b(z,a),y),x)) >= Marked_f(c(x,b(z,x),y)) constraint: Marked_f(c(a,b(b(z,a),y),x)) >= Marked_b(z,x) constraint: Marked_b(a,b(c(z,x,y),a)) >= Marked_c(y,z,a) constraint: Marked_b(a,b(c(z,x,y),a)) >= Marked_b(b(z,c(y,z,a)),x) constraint: Marked_b(a,b(c(z,x,y),a)) >= Marked_b(z,c(y,z,a)) APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { b(a,b(c(z,x,y),a)) >= b(b(z,c(y,z,a)),x) ; c(f(c(a,y,a)),x,z) >= f(b(b(z,z),f(b(y,b(x,a))))) ; f(c(a,b(b(z,a),y),x)) >= f(c(x,b(z,x),y)) ; Marked_f(c(a,b(b(z,a),y),x)) >= Marked_f(c(x,b(z,x),y)) ; } + Disjunctions:{ { Marked_f(c(a,b(b(z,a),y),x)) > Marked_f(c(x,b(z,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 : 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: b(a,b(c(z,x,y),a)) >= b(b(z,c(y,z,a)),x) constraint: c(f(c(a,y,a)),x,z) >= f(b(b(z,z),f(b(y,b(x,a))))) constraint: f(c(a,b(b(z,a),y),x)) >= f(c(x,b(z,x),y)) constraint: Marked_f(c(a,b(b(z,a),y),x)) >= Marked_f(c(x,b(z,x),y)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { b(a,b(c(z,x,y),a)) >= b(b(z,c(y,z,a)),x) ; c(f(c(a,y,a)),x,z) >= f(b(b(z,z),f(b(y,b(x,a))))) ; f(c(a,b(b(z,a),y),x)) >= f(c(x,b(z,x),y)) ; Marked_c(f(c(a,y,a)),x,z) >= Marked_b(b(z,z),f(b(y,b(x,a)))) ; Marked_c(f(c(a,y,a)),x,z) >= Marked_b(y,b(x,a)) ; Marked_c(f(c(a,y,a)),x,z) >= Marked_b(z,z) ; Marked_b(a,b(c(z,x,y),a)) >= Marked_c(y,z,a) ; Marked_b(a,b(c(z,x,y),a)) >= Marked_b(b(z,c(y,z,a)),x) ; Marked_b(a,b(c(z,x,y),a)) >= Marked_b(z,c(y,z,a)) ; } + Disjunctions:{ { Marked_c(f(c(a,y,a)),x,z) > Marked_b(b(z,z),f(b(y,b(x,a)))) ; } { Marked_c(f(c(a,y,a)),x,z) > Marked_b(y,b(x,a)) ; } { Marked_c(f(c(a,y,a)),x,z) > Marked_b(z,z) ; } { Marked_b(a,b(c(z,x,y),a)) > Marked_c(y,z,a) ; } { Marked_b(a,b(c(z,x,y),a)) > Marked_b(b(z,c(y,z,a)),x) ; } { Marked_b(a,b(c(z,x,y),a)) > Marked_b(z,c(y,z,a)) ; } } === 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: b(a,b(c(z,x,y),a)) >= b(b(z,c(y,z,a)),x) constraint: c(f(c(a,y,a)),x,z) >= f(b(b(z,z),f(b(y,b(x,a))))) constraint: f(c(a,b(b(z,a),y),x)) >= f(c(x,b(z,x),y)) constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_b(b(z,z),f(b(y,b(x,a)))) constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_b(y,b(x,a)) constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_b(z,z) constraint: Marked_b(a,b(c(z,x,y),a)) >= Marked_c(y,z,a) constraint: Marked_b(a,b(c(z,x,y),a)) >= Marked_b(b(z,c(y,z,a)),x) constraint: Marked_b(a,b(c(z,x,y),a)) >= Marked_b(z,c(y,z,a)) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x) [2] f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y)) [3] c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a))))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ b ] (X0,X1) = 0; [ Marked_c ] (X0,X1,X2) = 1; [ a ] () = 0; [ Marked_b ] (X0,X1) = 1; [ c ] (X0,X1,X2) = 2; [ Marked_f ] (X0) = 2*X0; [ f ] (X0) = 2; removing < Marked_c(f(c(a,y,a)),x,z),Marked_f(b(b(z,z),f(b(y,b(x,a)))))> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ b ] (X0,X1) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]*X1 + [ [ 0 , 1 , 1 ] [ 0 , 0 , 0 ] [ 0 , 1 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ a ] () = [ [ 0 , 0 , 0 ] [ 1 , 1 , 1 ] [ 1 , 1 , 1 ] ]; [ c ] (X0,X1,X2) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] ]*X2 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 1 , 0 , 1 ] ]*X1 + [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 1 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_f ] (X0) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ f ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ b ] (X0,X1) = 1*X1 + 2*X0; [ Marked_c ] (X0,X1,X2) = 2*X2 + 2*X1; [ a ] () = 0; [ Marked_b ] (X0,X1) = 1*X1; [ c ] (X0,X1,X2) = 3*X2 + 1*X1 + 3*X0 + 2; [ f ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} Cime worked for 8.983031 seconds (real time) Cime Exit Status: 0