- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] g(c(x,s(y))) -> g(c(s(x),y)) [2] f(c(s(x),y)) -> f(c(x,s(y))) [3] f(f(x)) -> f(d(f(x))) [4] f(x) -> x 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: { g(c(x,s(y))) >= g(c(s(x),y)) ; f(c(s(x),y)) >= f(c(x,s(y))) ; f(f(x)) >= f(d(f(x))) ; f(x) >= x ; Marked_g(c(x,s(y))) >= Marked_g(c(s(x),y)) ; } + Disjunctions:{ { Marked_g(c(x,s(y))) > Marked_g(c(s(x),y)) ; } } === 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: g(c(x,s(y))) >= g(c(s(x),y)) constraint: f(c(s(x),y)) >= f(c(x,s(y))) constraint: f(f(x)) >= f(d(f(x))) constraint: f(x) >= x constraint: Marked_g(c(x,s(y))) >= Marked_g(c(s(x),y)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { g(c(x,s(y))) >= g(c(s(x),y)) ; f(c(s(x),y)) >= f(c(x,s(y))) ; f(f(x)) >= f(d(f(x))) ; f(x) >= x ; Marked_f(c(s(x),y)) >= Marked_f(c(x,s(y))) ; } + Disjunctions:{ { Marked_f(c(s(x),y)) > Marked_f(c(x,s(y))) ; } } === 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: g(c(x,s(y))) >= g(c(s(x),y)) constraint: f(c(s(x),y)) >= f(c(x,s(y))) constraint: f(f(x)) >= f(d(f(x))) constraint: f(x) >= x constraint: Marked_f(c(s(x),y)) >= Marked_f(c(x,s(y))) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] g(c(x,s(y))) -> g(c(s(x),y)) [2] f(c(s(x),y)) -> f(c(x,s(y))) [3] f(f(x)) -> f(d(f(x))) [4] f(x) -> x , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ g ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ d ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ s ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; [ Marked_g ] (X0) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ c ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ f ] (X0) = [ [ 1 , 0 , 0 ] [ 1 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ g ] (X0) = 0; [ d ] (X0) = 0; [ s ] (X0) = 1 + 2*X0 + 0; [ c ] (X0,X1) = 3*X0 + 0; [ Marked_f ] (X0) = 2*X0 + 0; [ f ] (X0) = 2*X0 + 0; ]} ]} ]} Cime worked for 0.477669 seconds (real time) Cime Exit Status: 0