- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z))))) [2] c(f(f(c(x,a,z))),a,y) -> b(y,f(b(a,z))) [3] b(b(c(b(a,a),a,z),f(a)),y) -> z 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: { b(f(b(x,z)),y) >= f(f(f(b(z,b(y,z))))) ; b(b(c(b(a,a),a,z),f(a)),y) >= z ; c(f(f(c(x,a,z))),a,y) >= b(y,f(b(a,z))) ; Marked_b(f(b(x,z)),y) >= Marked_b(y,z) ; Marked_b(f(b(x,z)),y) >= Marked_b(z,b(y,z)) ; } + Disjunctions:{ { Marked_b(f(b(x,z)),y) > Marked_b(y,z) ; } { Marked_b(f(b(x,z)),y) > Marked_b(z,b(y,z)) ; } } === 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: b(f(b(x,z)),y) >= f(f(f(b(z,b(y,z))))) constraint: b(b(c(b(a,a),a,z),f(a)),y) >= z constraint: c(f(f(c(x,a,z))),a,y) >= b(y,f(b(a,z))) constraint: Marked_b(f(b(x,z)),y) >= Marked_b(y,z) constraint: Marked_b(f(b(x,z)),y) >= Marked_b(z,b(y,z)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_b -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z))))) [2] c(f(f(c(x,a,z))),a,y) -> b(y,f(b(a,z))) [3] b(b(c(b(a,a),a,z),f(a)),y) -> z , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ f ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] [ 1 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; [ Marked_b ] (X0,X1) = [ [ 0 , 0 , 1 ] [ 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 ] ]; [ a ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ b ] (X0,X1) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 1 ] [ 0 , 0 , 1 ] ]*X1 + [ [ 0 , 0 , 1 ] [ 0 , 0 , 1 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; [ c ] (X0,X1,X2) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 1 ] [ 1 , 1 , 1 ] ]*X2 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 1 , 1 ] [ 0 , 1 , 1 ] [ 0 , 1 , 1 ] ]*X0 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} Cime worked for 4.306317 seconds (real time) Cime Exit Status: 0