- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(g(x)) -> g(f(f(x))) [2] f(h(x)) -> h(g(x)) [3] f'(s(x),y,y) -> f'(y,x,s(x)) 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: { f(g(x)) >= g(f(f(x))) ; f(h(x)) >= h(g(x)) ; f'(s(x),y,y) >= f'(y,x,s(x)) ; Marked_f(g(x)) >= Marked_f(f(x)) ; Marked_f(g(x)) >= Marked_f(x) ; } + Disjunctions:{ { Marked_f(g(x)) > Marked_f(f(x)) ; } { Marked_f(g(x)) > Marked_f(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(g(x)) >= g(f(f(x))) constraint: f(h(x)) >= h(g(x)) constraint: f'(s(x),y,y) >= f'(y,x,s(x)) constraint: Marked_f(g(x)) >= Marked_f(f(x)) constraint: Marked_f(g(x)) >= Marked_f(x) APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(g(x)) >= g(f(f(x))) ; f(h(x)) >= h(g(x)) ; f'(s(x),y,y) >= f'(y,x,s(x)) ; Marked_f'(s(x),y,y) >= Marked_f'(y,x,s(x)) ; } + Disjunctions:{ { Marked_f'(s(x),y,y) > Marked_f'(y,x,s(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(g(x)) >= g(f(f(x))) constraint: f(h(x)) >= h(g(x)) constraint: f'(s(x),y,y) >= f'(y,x,s(x)) constraint: Marked_f'(s(x),y,y) >= Marked_f'(y,x,s(x)) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(g(x)) -> g(f(f(x))) [2] f(h(x)) -> h(g(x)) [3] f'(s(x),y,y) -> f'(y,x,s(x)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ g ] (X0) = 2 + 1*X0 + 0; [ s ] (X0) = 2 + 2*X0 + 0; [ h ] (X0) = 0; [ Marked_f ] (X0) = 2*X0 + 0; [ f ] (X0) = 1*X0 + 0; [ f' ] (X0,X1,X2) = 2*X0 + 2*X1 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ g ] (X0) = 2 + 0; [ s ] (X0) = 2 + 2*X0 + 0; [ h ] (X0) = 1 + 2*X0 + 0; [ f ] (X0) = 2 + 3*X0 + 0; [ Marked_f' ] (X0,X1,X2) = 3*X0 + 3*X1 + 0; [ f' ] (X0,X1,X2) = 2*X0 + 2*X1 + 0; ]} ]} ]} Cime worked for 0.048334 seconds (real time) Cime Exit Status: 0