- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(f(b,X,c)) -> mark(f(X,c,X)) [2] active(c) -> mark(b) [3] active(f(X1,X2,X3)) -> f(X1,active(X2),X3) [4] f(X1,mark(X2),X3) -> mark(f(X1,X2,X3)) [5] proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) [6] proper(b) -> ok(b) [7] proper(c) -> ok(c) [8] f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) [9] top(mark(X)) -> top(proper(X)) [10] top(ok(X)) -> top(active(X)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 4 components: { --> --> --> --> } { --> --> --> --> --> --> --> --> --> } { --> } { --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(ok(X1),ok(X2),ok(X3)) >= ok(f(X1,X2,X3)) ; f(X1,mark(X2),X3) >= mark(f(X1,X2,X3)) ; active(f(b,X,c)) >= mark(f(X,c,X)) ; active(f(X1,X2,X3)) >= f(X1,active(X2),X3) ; active(c) >= mark(b) ; proper(f(X1,X2,X3)) >= f(proper(X1),proper(X2),proper(X3)) ; proper(c) >= ok(c) ; proper(b) >= ok(b) ; top(mark(X)) >= top(proper(X)) ; top(ok(X)) >= top(active(X)) ; Marked_top(mark(X)) >= Marked_top(proper(X)) ; Marked_top(ok(X)) >= Marked_top(active(X)) ; } + Disjunctions:{ { Marked_top(mark(X)) > Marked_top(proper(X)) ; } { Marked_top(ok(X)) > Marked_top(active(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 : 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(ok(X1),ok(X2),ok(X3)) >= ok(f(X1,X2,X3)) constraint: f(X1,mark(X2),X3) >= mark(f(X1,X2,X3)) constraint: active(f(b,X,c)) >= mark(f(X,c,X)) constraint: active(f(X1,X2,X3)) >= f(X1,active(X2),X3) constraint: active(c) >= mark(b) constraint: proper(f(X1,X2,X3)) >= f(proper(X1),proper(X2),proper(X3)) constraint: proper(c) >= ok(c) constraint: proper(b) >= ok(b) constraint: top(mark(X)) >= top(proper(X)) constraint: top(ok(X)) >= top(active(X)) constraint: Marked_top(mark(X)) >= Marked_top(proper(X)) constraint: Marked_top(ok(X)) >= Marked_top(active(X)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(ok(X1),ok(X2),ok(X3)) >= ok(f(X1,X2,X3)) ; f(X1,mark(X2),X3) >= mark(f(X1,X2,X3)) ; active(f(b,X,c)) >= mark(f(X,c,X)) ; active(f(X1,X2,X3)) >= f(X1,active(X2),X3) ; active(c) >= mark(b) ; proper(f(X1,X2,X3)) >= f(proper(X1),proper(X2),proper(X3)) ; proper(c) >= ok(c) ; proper(b) >= ok(b) ; top(mark(X)) >= top(proper(X)) ; top(ok(X)) >= top(active(X)) ; Marked_proper(f(X1,X2,X3)) >= Marked_proper(X1) ; Marked_proper(f(X1,X2,X3)) >= Marked_proper(X2) ; Marked_proper(f(X1,X2,X3)) >= Marked_proper(X3) ; } + Disjunctions:{ { Marked_proper(f(X1,X2,X3)) > Marked_proper(X1) ; } { Marked_proper(f(X1,X2,X3)) > Marked_proper(X2) ; } { Marked_proper(f(X1,X2,X3)) > Marked_proper(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: f(ok(X1),ok(X2),ok(X3)) >= ok(f(X1,X2,X3)) constraint: f(X1,mark(X2),X3) >= mark(f(X1,X2,X3)) constraint: active(f(b,X,c)) >= mark(f(X,c,X)) constraint: active(f(X1,X2,X3)) >= f(X1,active(X2),X3) constraint: active(c) >= mark(b) constraint: proper(f(X1,X2,X3)) >= f(proper(X1),proper(X2),proper(X3)) constraint: proper(c) >= ok(c) constraint: proper(b) >= ok(b) constraint: top(mark(X)) >= top(proper(X)) constraint: top(ok(X)) >= top(active(X)) constraint: Marked_proper(f(X1,X2,X3)) >= Marked_proper(X1) constraint: Marked_proper(f(X1,X2,X3)) >= Marked_proper(X2) constraint: Marked_proper(f(X1,X2,X3)) >= Marked_proper(X3) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(ok(X1),ok(X2),ok(X3)) >= ok(f(X1,X2,X3)) ; f(X1,mark(X2),X3) >= mark(f(X1,X2,X3)) ; active(f(b,X,c)) >= mark(f(X,c,X)) ; active(f(X1,X2,X3)) >= f(X1,active(X2),X3) ; active(c) >= mark(b) ; proper(f(X1,X2,X3)) >= f(proper(X1),proper(X2),proper(X3)) ; proper(c) >= ok(c) ; proper(b) >= ok(b) ; top(mark(X)) >= top(proper(X)) ; top(ok(X)) >= top(active(X)) ; Marked_active(f(X1,X2,X3)) >= Marked_active(X2) ; } + Disjunctions:{ { Marked_active(f(X1,X2,X3)) > Marked_active(X2) ; } } === 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(ok(X1),ok(X2),ok(X3)) >= ok(f(X1,X2,X3)) constraint: f(X1,mark(X2),X3) >= mark(f(X1,X2,X3)) constraint: active(f(b,X,c)) >= mark(f(X,c,X)) constraint: active(f(X1,X2,X3)) >= f(X1,active(X2),X3) constraint: active(c) >= mark(b) constraint: proper(f(X1,X2,X3)) >= f(proper(X1),proper(X2),proper(X3)) constraint: proper(c) >= ok(c) constraint: proper(b) >= ok(b) constraint: top(mark(X)) >= top(proper(X)) constraint: top(ok(X)) >= top(active(X)) constraint: Marked_active(f(X1,X2,X3)) >= Marked_active(X2) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(ok(X1),ok(X2),ok(X3)) >= ok(f(X1,X2,X3)) ; f(X1,mark(X2),X3) >= mark(f(X1,X2,X3)) ; active(f(b,X,c)) >= mark(f(X,c,X)) ; active(f(X1,X2,X3)) >= f(X1,active(X2),X3) ; active(c) >= mark(b) ; proper(f(X1,X2,X3)) >= f(proper(X1),proper(X2),proper(X3)) ; proper(c) >= ok(c) ; proper(b) >= ok(b) ; top(mark(X)) >= top(proper(X)) ; top(ok(X)) >= top(active(X)) ; Marked_f(ok(X1),ok(X2),ok(X3)) >= Marked_f(X1,X2,X3) ; Marked_f(X1,mark(X2),X3) >= Marked_f(X1,X2,X3) ; } + Disjunctions:{ { Marked_f(ok(X1),ok(X2),ok(X3)) > Marked_f(X1,X2,X3) ; } { Marked_f(X1,mark(X2),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: f(ok(X1),ok(X2),ok(X3)) >= ok(f(X1,X2,X3)) constraint: f(X1,mark(X2),X3) >= mark(f(X1,X2,X3)) constraint: active(f(b,X,c)) >= mark(f(X,c,X)) constraint: active(f(X1,X2,X3)) >= f(X1,active(X2),X3) constraint: active(c) >= mark(b) constraint: proper(f(X1,X2,X3)) >= f(proper(X1),proper(X2),proper(X3)) constraint: proper(c) >= ok(c) constraint: proper(b) >= ok(b) constraint: top(mark(X)) >= top(proper(X)) constraint: top(ok(X)) >= top(active(X)) constraint: Marked_f(ok(X1),ok(X2),ok(X3)) >= Marked_f(X1,X2,X3) constraint: Marked_f(X1,mark(X2),X3) >= Marked_f(X1,X2,X3) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(ok(X1),ok(X2),ok(X3)) >= ok(f(X1,X2,X3)) ; f(X1,mark(X2),X3) >= mark(f(X1,X2,X3)) ; active(f(b,X,c)) >= mark(f(X,c,X)) ; active(f(X1,X2,X3)) >= f(X1,active(X2),X3) ; active(c) >= mark(b) ; proper(f(X1,X2,X3)) >= f(proper(X1),proper(X2),proper(X3)) ; proper(c) >= ok(c) ; proper(b) >= ok(b) ; top(mark(X)) >= top(proper(X)) ; top(ok(X)) >= top(active(X)) ; Marked_top(ok(X)) >= Marked_top(active(X)) ; } + Disjunctions:{ { Marked_top(ok(X)) > Marked_top(active(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(ok(X1),ok(X2),ok(X3)) >= ok(f(X1,X2,X3)) constraint: f(X1,mark(X2),X3) >= mark(f(X1,X2,X3)) constraint: active(f(b,X,c)) >= mark(f(X,c,X)) constraint: active(f(X1,X2,X3)) >= f(X1,active(X2),X3) constraint: active(c) >= mark(b) constraint: proper(f(X1,X2,X3)) >= f(proper(X1),proper(X2),proper(X3)) constraint: proper(c) >= ok(c) constraint: proper(b) >= ok(b) constraint: top(mark(X)) >= top(proper(X)) constraint: top(ok(X)) >= top(active(X)) constraint: Marked_top(ok(X)) >= Marked_top(active(X)) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(ok(X1),ok(X2),ok(X3)) >= ok(f(X1,X2,X3)) ; f(X1,mark(X2),X3) >= mark(f(X1,X2,X3)) ; active(f(b,X,c)) >= mark(f(X,c,X)) ; active(f(X1,X2,X3)) >= f(X1,active(X2),X3) ; active(c) >= mark(b) ; proper(f(X1,X2,X3)) >= f(proper(X1),proper(X2),proper(X3)) ; proper(c) >= ok(c) ; proper(b) >= ok(b) ; top(mark(X)) >= top(proper(X)) ; top(ok(X)) >= top(active(X)) ; Marked_f(X1,mark(X2),X3) >= Marked_f(X1,X2,X3) ; } + Disjunctions:{ { Marked_f(X1,mark(X2),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: f(ok(X1),ok(X2),ok(X3)) >= ok(f(X1,X2,X3)) constraint: f(X1,mark(X2),X3) >= mark(f(X1,X2,X3)) constraint: active(f(b,X,c)) >= mark(f(X,c,X)) constraint: active(f(X1,X2,X3)) >= f(X1,active(X2),X3) constraint: active(c) >= mark(b) constraint: proper(f(X1,X2,X3)) >= f(proper(X1),proper(X2),proper(X3)) constraint: proper(c) >= ok(c) constraint: proper(b) >= ok(b) constraint: top(mark(X)) >= top(proper(X)) constraint: top(ok(X)) >= top(active(X)) constraint: Marked_f(X1,mark(X2),X3) >= Marked_f(X1,X2,X3) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] active(f(b,X,c)) -> mark(f(X,c,X)) [2] active(c) -> mark(b) [3] active(f(X1,X2,X3)) -> f(X1,active(X2),X3) [4] f(X1,mark(X2),X3) -> mark(f(X1,X2,X3)) [5] proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) [6] proper(b) -> ok(b) [7] proper(c) -> ok(c) [8] f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) [9] top(mark(X)) -> top(proper(X)) [10] top(ok(X)) -> top(active(X)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ mark ] (X0) = [ [ 0 , 0 , 0 ] [ 1 , 0 , 1 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; [ Marked_top ] (X0) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ b ] () = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ c ] () = [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 1 , 0 , 0 ] ]; [ ok ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ f ] (X0,X1,X2) = [ [ 0 , 0 , 0 ] [ 0 , 1 , 1 ] [ 0 , 1 , 1 ] ]*X2 + [ [ 0 , 0 , 0 ] [ 1 , 1 , 1 ] [ 1 , 1 , 1 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 1 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ proper ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 1 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ active ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ top ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ mark ] (X0) = 0; [ Marked_top ] (X0) = 3*X0 + 0; [ b ] () = 2 + 0; [ c ] () = 2 + 0; [ ok ] (X0) = 2 + 0; [ f ] (X0,X1,X2) = 2*X1 + 0; [ proper ] (X0) = 1*X0 + 0; [ active ] (X0) = 0; [ top ] (X0) = 0; ]} ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ mark ] (X0) = 0; [ b ] () = 0; [ c ] () = 2 + 0; [ Marked_proper ] (X0) = 3*X0 + 0; [ ok ] (X0) = 0; [ f ] (X0,X1,X2) = 2 + 1*X0 + 1*X1 + 1*X2 + 0; [ proper ] (X0) = 2*X0 + 0; [ active ] (X0) = 2 + 2*X0 + 0; [ top ] (X0) = 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ mark ] (X0) = 2 + 0; [ b ] () = 0; [ c ] () = 2 + 0; [ ok ] (X0) = 2 + 2*X0 + 0; [ f ] (X0,X1,X2) = 2 + 2*X0 + 1*X1 + 0; [ Marked_active ] (X0) = 3*X0 + 0; [ proper ] (X0) = 2 + 3*X0 + 0; [ active ] (X0) = 1*X0 + 0; [ top ] (X0) = 0; ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ b ] () = 2; [ c ] () = 2; [ ok ] (X0) = 2*X0 + 1; [ f ] (X0,X1,X2) = 2*X1; [ proper ] (X0) = 3*X0; [ active ] (X0) = 0; [ Marked_f ] (X0,X1,X2) = 1*X0; [ top ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ mark ] (X0) = 1 + 1*X0 + 0; [ b ] () = 3 + 0; [ c ] () = 2 + 0; [ ok ] (X0) = 2 + 2*X0 + 0; [ f ] (X0,X1,X2) = 2 + 2*X0 + 1*X1 + 0; [ proper ] (X0) = 3*X0 + 0; [ active ] (X0) = 2*X0 + 0; [ Marked_f ] (X0,X1,X2) = 3*X1 + 0; [ top ] (X0) = 0; ]} ]} ]} ]} ]} Cime worked for 1.120126 seconds (real time) Cime Exit Status: 0