- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] p(a(x0),p(b(a(x1)),x2)) -> p(x1,p(a(b(a(x1))),x2)) [2] a(b(a(x0))) -> b(a(b(x0))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { p(a(x0),p(b(a(x1)),x2)) >= p(x1,p(a(b(a(x1))),x2)) ; a(b(a(x0))) >= b(a(b(x0))) ; Marked_p(a(x0),p(b(a(x1)),x2)) >= Marked_p(a(b(a(x1))),x2) ; Marked_p(a(x0),p(b(a(x1)),x2)) >= Marked_p(x1,p(a(b(a(x1))),x2)) ; } + Disjunctions:{ { Marked_p(a(x0),p(b(a(x1)),x2)) > Marked_p(a(b(a(x1))),x2) ; } { Marked_p(a(x0),p(b(a(x1)),x2)) > Marked_p(x1,p(a(b(a(x1))),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: p(a(x0),p(b(a(x1)),x2)) >= p(x1,p(a(b(a(x1))),x2)) constraint: a(b(a(x0))) >= b(a(b(x0))) constraint: Marked_p(a(x0),p(b(a(x1)),x2)) >= Marked_p(a(b(a(x1))),x2) constraint: Marked_p(a(x0),p(b(a(x1)),x2)) >= Marked_p(x1,p(a(b(a(x1))),x2)) APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { p(a(x0),p(b(a(x1)),x2)) >= p(x1,p(a(b(a(x1))),x2)) ; a(b(a(x0))) >= b(a(b(x0))) ; Marked_a(b(a(x0))) >= Marked_a(b(x0)) ; } + Disjunctions:{ { Marked_a(b(a(x0))) > Marked_a(b(x0)) ; } } === 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: p(a(x0),p(b(a(x1)),x2)) >= p(x1,p(a(b(a(x1))),x2)) constraint: a(b(a(x0))) >= b(a(b(x0))) constraint: Marked_a(b(a(x0))) >= Marked_a(b(x0)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { p(a(x0),p(b(a(x1)),x2)) >= p(x1,p(a(b(a(x1))),x2)) ; a(b(a(x0))) >= b(a(b(x0))) ; Marked_p(a(x0),p(b(a(x1)),x2)) >= Marked_p(x1,p(a(b(a(x1))),x2)) ; } + Disjunctions:{ { Marked_p(a(x0),p(b(a(x1)),x2)) > Marked_p(x1,p(a(b(a(x1))),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 === 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: p(a(x0),p(b(a(x1)),x2)) >= p(x1,p(a(b(a(x1))),x2)) constraint: a(b(a(x0))) >= b(a(b(x0))) constraint: Marked_p(a(x0),p(b(a(x1)),x2)) >= Marked_p(x1,p(a(b(a(x1))),x2)) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] p(a(x0),p(b(a(x1)),x2)) -> p(x1,p(a(b(a(x1))),x2)) [2] a(b(a(x0))) -> b(a(b(x0))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ p ] (X0,X1) = 1*X1 + 1; [ Marked_p ] (X0,X1) = 1*X1; [ b ] (X0) = 2; [ a ] (X0) = 3*X0 + 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ p ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_p ] (X0,X1) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ b ] (X0) = [ [ 0 , 0 , 1 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ a ] (X0) = [ [ 1 , 1 , 1 ] [ 1 , 0 , 0 ] [ 1 , 0 , 1 ] ]*X0 + [ [ 1 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; ]} ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ p ] (X0,X1) = 0; [ b ] (X0) = 2*X0 + 0; [ a ] (X0) = 1 + 2*X0 + 0; [ Marked_a ] (X0) = 2*X0 + 0; ]} ]} ]} Cime worked for 9.928153 seconds (real time) Cime Exit Status: 0