- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(a,f(a,f(a,f(x,b)))) -> f(f(a,f(a,f(a,x))),b) [2] f(f(f(a,x),b),b) -> f(f(a,f(f(x,b),b)),b) 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(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b) ; f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b) ; Marked_f(f(f(a,x),b),b) >= Marked_f(f(a,f(f(x,b),b)),b) ; Marked_f(f(f(a,x),b),b) >= Marked_f(f(x,b),b) ; Marked_f(f(f(a,x),b),b) >= Marked_f(a,f(f(x,b),b)) ; Marked_f(f(f(a,x),b),b) >= Marked_f(x,b) ; Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(f(a,f(a,f(a,x))),b) ; Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,f(a,x))) ; Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,x)) ; Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,x) ; } + Disjunctions:{ { Marked_f(f(f(a,x),b),b) > Marked_f(f(a,f(f(x,b),b)),b) ; } { Marked_f(f(f(a,x),b),b) > Marked_f(f(x,b),b) ; } { Marked_f(f(f(a,x),b),b) > Marked_f(a,f(f(x,b),b)) ; } { Marked_f(f(f(a,x),b),b) > Marked_f(x,b) ; } { Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(f(a,f(a,f(a,x))),b) ; } { Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(a,f(a,f(a,x))) ; } { Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(a,f(a,x)) ; } { Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(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(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b) constraint: f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b) constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(f(a,f(f(x,b),b)),b) constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(f(x,b),b) constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(a,f(f(x,b),b)) constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(x,b) constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(f(a,f(a,f(a,x))),b) constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,f(a,x))) constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,x)) constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,x) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b) ; f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b) ; Marked_f(f(f(a,x),b),b) >= Marked_f(f(a,f(f(x,b),b)),b) ; Marked_f(f(f(a,x),b),b) >= Marked_f(a,f(f(x,b),b)) ; Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(f(a,f(a,f(a,x))),b) ; Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,f(a,x))) ; } + Disjunctions:{ { Marked_f(f(f(a,x),b),b) > Marked_f(f(a,f(f(x,b),b)),b) ; } { Marked_f(f(f(a,x),b),b) > Marked_f(a,f(f(x,b),b)) ; } { Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(f(a,f(a,f(a,x))),b) ; } { Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(a,f(a,f(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 : 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(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b) constraint: f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b) constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(f(a,f(f(x,b),b)),b) constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(a,f(f(x,b),b)) constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(f(a,f(a,f(a,x))),b) constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,f(a,x))) APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b) ; f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b) ; Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,f(a,x))) ; } + Disjunctions:{ { Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(a,f(a,f(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(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b) constraint: f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b) constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,f(a,x))) APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b) ; f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b) ; Marked_f(f(f(a,x),b),b) >= Marked_f(f(a,f(f(x,b),b)),b) ; } + Disjunctions:{ { Marked_f(f(f(a,x),b),b) > Marked_f(f(a,f(f(x,b),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 : 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(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b) constraint: f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b) constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(f(a,f(f(x,b),b)),b) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(a,f(a,f(a,f(x,b)))) -> f(f(a,f(a,f(a,x))),b) [2] f(f(f(a,x),b),b) -> f(f(a,f(f(x,b),b)),b) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ f ] (X0,X1) = 1*X1 + 1*X0; [ b ] () = 0; [ a ] () = 1; [ Marked_f ] (X0,X1) = 1*X1 + 1*X0; 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 + [ [ 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 ] ]; [ a ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; [ Marked_f ] (X0,X1) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 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: Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ f ] (X0,X1) = [ [ 0 , 0 , 1 ] [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 1 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ b ] () = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ a ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_f ] (X0,X1) = [ [ 1 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; ]} { DP termination of: , CRITERION: ORD [ Solution found: Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ f ] (X0,X1) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; [ b ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ a ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_f ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; ]} ]} ]} ]} ]} ]} ]} Cime worked for 28.298504 seconds (real time) Cime Exit Status: 0