- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(f(a,X,X)) -> mark(f(X,b,b)) [2] active(b) -> mark(a) [3] mark(f(X1,X2,X3)) -> active(f(X1,mark(X2),X3)) [4] mark(a) -> active(a) [5] mark(b) -> active(b) [6] f(mark(X1),X2,X3) -> f(X1,X2,X3) [7] f(X1,mark(X2),X3) -> f(X1,X2,X3) [8] f(X1,X2,mark(X3)) -> f(X1,X2,X3) [9] f(active(X1),X2,X3) -> f(X1,X2,X3) [10] f(X1,active(X2),X3) -> f(X1,X2,X3) [11] f(X1,X2,active(X3)) -> f(X1,X2,X3) 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: { mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3)) ; mark(b) >= active(b) ; mark(a) >= active(a) ; f(mark(X1),X2,X3) >= f(X1,X2,X3) ; f(active(X1),X2,X3) >= f(X1,X2,X3) ; f(X1,mark(X2),X3) >= f(X1,X2,X3) ; f(X1,active(X2),X3) >= f(X1,X2,X3) ; f(X1,X2,mark(X3)) >= f(X1,X2,X3) ; f(X1,X2,active(X3)) >= f(X1,X2,X3) ; active(f(a,X,X)) >= mark(f(X,b,b)) ; active(b) >= mark(a) ; Marked_mark(f(X1,X2,X3)) >= Marked_mark(X2) ; Marked_mark(f(X1,X2,X3)) >= Marked_active(f(X1,mark(X2),X3)) ; Marked_active(f(a,X,X)) >= Marked_mark(f(X,b,b)) ; } + Disjunctions:{ { Marked_mark(f(X1,X2,X3)) > Marked_mark(X2) ; } { Marked_mark(f(X1,X2,X3)) > Marked_active(f(X1,mark(X2),X3)) ; } { Marked_active(f(a,X,X)) > Marked_mark(f(X,b,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: mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3)) constraint: mark(b) >= active(b) constraint: mark(a) >= active(a) constraint: f(mark(X1),X2,X3) >= f(X1,X2,X3) constraint: f(active(X1),X2,X3) >= f(X1,X2,X3) constraint: f(X1,mark(X2),X3) >= f(X1,X2,X3) constraint: f(X1,active(X2),X3) >= f(X1,X2,X3) constraint: f(X1,X2,mark(X3)) >= f(X1,X2,X3) constraint: f(X1,X2,active(X3)) >= f(X1,X2,X3) constraint: active(f(a,X,X)) >= mark(f(X,b,b)) constraint: active(b) >= mark(a) constraint: Marked_mark(f(X1,X2,X3)) >= Marked_mark(X2) constraint: Marked_mark(f(X1,X2,X3)) >= Marked_active(f(X1,mark(X2),X3)) constraint: Marked_active(f(a,X,X)) >= Marked_mark(f(X,b,b)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3)) ; mark(b) >= active(b) ; mark(a) >= active(a) ; f(mark(X1),X2,X3) >= f(X1,X2,X3) ; f(active(X1),X2,X3) >= f(X1,X2,X3) ; f(X1,mark(X2),X3) >= f(X1,X2,X3) ; f(X1,active(X2),X3) >= f(X1,X2,X3) ; f(X1,X2,mark(X3)) >= f(X1,X2,X3) ; f(X1,X2,active(X3)) >= f(X1,X2,X3) ; active(f(a,X,X)) >= mark(f(X,b,b)) ; active(b) >= mark(a) ; Marked_f(mark(X1),X2,X3) >= Marked_f(X1,X2,X3) ; Marked_f(active(X1),X2,X3) >= Marked_f(X1,X2,X3) ; Marked_f(X1,mark(X2),X3) >= Marked_f(X1,X2,X3) ; Marked_f(X1,active(X2),X3) >= Marked_f(X1,X2,X3) ; Marked_f(X1,X2,mark(X3)) >= Marked_f(X1,X2,X3) ; Marked_f(X1,X2,active(X3)) >= Marked_f(X1,X2,X3) ; } + Disjunctions:{ { Marked_f(mark(X1),X2,X3) > Marked_f(X1,X2,X3) ; } { Marked_f(active(X1),X2,X3) > Marked_f(X1,X2,X3) ; } { Marked_f(X1,mark(X2),X3) > Marked_f(X1,X2,X3) ; } { Marked_f(X1,active(X2),X3) > Marked_f(X1,X2,X3) ; } { Marked_f(X1,X2,mark(X3)) > Marked_f(X1,X2,X3) ; } { Marked_f(X1,X2,active(X3)) > Marked_f(X1,X2,X3) ; } } === 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: mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3)) constraint: mark(b) >= active(b) constraint: mark(a) >= active(a) constraint: f(mark(X1),X2,X3) >= f(X1,X2,X3) constraint: f(active(X1),X2,X3) >= f(X1,X2,X3) constraint: f(X1,mark(X2),X3) >= f(X1,X2,X3) constraint: f(X1,active(X2),X3) >= f(X1,X2,X3) constraint: f(X1,X2,mark(X3)) >= f(X1,X2,X3) constraint: f(X1,X2,active(X3)) >= f(X1,X2,X3) constraint: active(f(a,X,X)) >= mark(f(X,b,b)) constraint: active(b) >= mark(a) constraint: Marked_f(mark(X1),X2,X3) >= Marked_f(X1,X2,X3) constraint: Marked_f(active(X1),X2,X3) >= Marked_f(X1,X2,X3) constraint: Marked_f(X1,mark(X2),X3) >= Marked_f(X1,X2,X3) constraint: Marked_f(X1,active(X2),X3) >= Marked_f(X1,X2,X3) constraint: Marked_f(X1,X2,mark(X3)) >= Marked_f(X1,X2,X3) constraint: Marked_f(X1,X2,active(X3)) >= Marked_f(X1,X2,X3) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3)) ; mark(b) >= active(b) ; mark(a) >= active(a) ; f(mark(X1),X2,X3) >= f(X1,X2,X3) ; f(active(X1),X2,X3) >= f(X1,X2,X3) ; f(X1,mark(X2),X3) >= f(X1,X2,X3) ; f(X1,active(X2),X3) >= f(X1,X2,X3) ; f(X1,X2,mark(X3)) >= f(X1,X2,X3) ; f(X1,X2,active(X3)) >= f(X1,X2,X3) ; active(f(a,X,X)) >= mark(f(X,b,b)) ; active(b) >= mark(a) ; Marked_mark(f(X1,X2,X3)) >= Marked_active(f(X1,mark(X2),X3)) ; Marked_active(f(a,X,X)) >= Marked_mark(f(X,b,b)) ; } + Disjunctions:{ { Marked_mark(f(X1,X2,X3)) > Marked_active(f(X1,mark(X2),X3)) ; } { Marked_active(f(a,X,X)) > Marked_mark(f(X,b,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 === 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 : 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: mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3)) constraint: mark(b) >= active(b) constraint: mark(a) >= active(a) constraint: f(mark(X1),X2,X3) >= f(X1,X2,X3) constraint: f(active(X1),X2,X3) >= f(X1,X2,X3) constraint: f(X1,mark(X2),X3) >= f(X1,X2,X3) constraint: f(X1,active(X2),X3) >= f(X1,X2,X3) constraint: f(X1,X2,mark(X3)) >= f(X1,X2,X3) constraint: f(X1,X2,active(X3)) >= f(X1,X2,X3) constraint: active(f(a,X,X)) >= mark(f(X,b,b)) constraint: active(b) >= mark(a) constraint: Marked_mark(f(X1,X2,X3)) >= Marked_active(f(X1,mark(X2),X3)) constraint: Marked_active(f(a,X,X)) >= Marked_mark(f(X,b,b)) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3)) ; mark(b) >= active(b) ; mark(a) >= active(a) ; f(mark(X1),X2,X3) >= f(X1,X2,X3) ; f(active(X1),X2,X3) >= f(X1,X2,X3) ; f(X1,mark(X2),X3) >= f(X1,X2,X3) ; f(X1,active(X2),X3) >= f(X1,X2,X3) ; f(X1,X2,mark(X3)) >= f(X1,X2,X3) ; f(X1,X2,active(X3)) >= f(X1,X2,X3) ; active(f(a,X,X)) >= mark(f(X,b,b)) ; active(b) >= mark(a) ; Marked_f(active(X1),X2,X3) >= Marked_f(X1,X2,X3) ; Marked_f(X1,active(X2),X3) >= Marked_f(X1,X2,X3) ; Marked_f(X1,X2,active(X3)) >= Marked_f(X1,X2,X3) ; } + Disjunctions:{ { Marked_f(active(X1),X2,X3) > Marked_f(X1,X2,X3) ; } { Marked_f(X1,active(X2),X3) > Marked_f(X1,X2,X3) ; } { Marked_f(X1,X2,active(X3)) > Marked_f(X1,X2,X3) ; } } === 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: mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3)) constraint: mark(b) >= active(b) constraint: mark(a) >= active(a) constraint: f(mark(X1),X2,X3) >= f(X1,X2,X3) constraint: f(active(X1),X2,X3) >= f(X1,X2,X3) constraint: f(X1,mark(X2),X3) >= f(X1,X2,X3) constraint: f(X1,active(X2),X3) >= f(X1,X2,X3) constraint: f(X1,X2,mark(X3)) >= f(X1,X2,X3) constraint: f(X1,X2,active(X3)) >= f(X1,X2,X3) constraint: active(f(a,X,X)) >= mark(f(X,b,b)) constraint: active(b) >= mark(a) constraint: Marked_f(active(X1),X2,X3) >= Marked_f(X1,X2,X3) constraint: Marked_f(X1,active(X2),X3) >= Marked_f(X1,X2,X3) constraint: Marked_f(X1,X2,active(X3)) >= Marked_f(X1,X2,X3) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] active(f(a,X,X)) -> mark(f(X,b,b)) [2] active(b) -> mark(a) [3] mark(f(X1,X2,X3)) -> active(f(X1,mark(X2),X3)) [4] mark(a) -> active(a) [5] mark(b) -> active(b) [6] f(mark(X1),X2,X3) -> f(X1,X2,X3) [7] f(X1,mark(X2),X3) -> f(X1,X2,X3) [8] f(X1,X2,mark(X3)) -> f(X1,X2,X3) [9] f(active(X1),X2,X3) -> f(X1,X2,X3) [10] f(X1,active(X2),X3) -> f(X1,X2,X3) [11] f(X1,X2,active(X3)) -> f(X1,X2,X3) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ a ] () = 0; [ b ] () = 0; [ Marked_mark ] (X0) = 1*X0; [ f ] (X0,X1,X2) = 2*X1 + 2; [ active ] (X0) = 1*X0; [ Marked_active ] (X0) = 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ mark ] (X0) = [ [ 1 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ a ] () = [ [ 1 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ b ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 1 , 0 ] ]; [ Marked_mark ] (X0) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ f ] (X0,X1,X2) = [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X2 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ active ] (X0) = [ [ 1 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_active ] (X0) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; removing [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 2*X0 + 2; [ a ] () = 0; [ b ] () = 1; [ f ] (X0,X1,X2) = 2; [ Marked_f ] (X0,X1,X2) = 3*X2 + 3*X1 + 3*X0; [ active ] (X0) = 3*X0; removing < Marked_f(X1,X2,mark(X3)),Marked_f(X1,X2,X3)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ mark ] (X0) = 1 + 0; [ a ] () = 0; [ b ] () = 0; [ f ] (X0,X1,X2) = 0; [ Marked_f ] (X0,X1,X2) = 3*X0 + 3*X1 + 3*X2 + 0; [ active ] (X0) = 1 + 2*X0 + 0; ]} ]} ]} ]} ]} Cime worked for 0.926881 seconds (real time) Cime Exit Status: 0