- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(c(s(x),y)) -> f(c(x,s(y))) [2] f(c(s(x),s(y))) -> g(c(x,y)) [3] g(c(x,s(y))) -> g(c(s(x),y)) [4] g(c(s(x),s(y))) -> f(c(x,y)) 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(c(s(x),s(y))) >= g(c(x,y)) ; f(c(s(x),y)) >= f(c(x,s(y))) ; g(c(s(x),s(y))) >= f(c(x,y)) ; g(c(x,s(y))) >= g(c(s(x),y)) ; Marked_g(c(s(x),s(y))) >= Marked_f(c(x,y)) ; Marked_g(c(x,s(y))) >= Marked_g(c(s(x),y)) ; Marked_f(c(s(x),s(y))) >= Marked_g(c(x,y)) ; Marked_f(c(s(x),y)) >= Marked_f(c(x,s(y))) ; } + Disjunctions:{ { Marked_g(c(s(x),s(y))) > Marked_f(c(x,y)) ; } { Marked_g(c(x,s(y))) > Marked_g(c(s(x),y)) ; } { Marked_f(c(s(x),s(y))) > Marked_g(c(x,y)) ; } { 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: f(c(s(x),s(y))) >= g(c(x,y)) constraint: f(c(s(x),y)) >= f(c(x,s(y))) constraint: g(c(s(x),s(y))) >= f(c(x,y)) constraint: g(c(x,s(y))) >= g(c(s(x),y)) constraint: Marked_g(c(s(x),s(y))) >= Marked_f(c(x,y)) constraint: Marked_g(c(x,s(y))) >= Marked_g(c(s(x),y)) constraint: Marked_f(c(s(x),s(y))) >= Marked_g(c(x,y)) constraint: Marked_f(c(s(x),y)) >= Marked_f(c(x,s(y))) APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(c(s(x),s(y))) >= g(c(x,y)) ; f(c(s(x),y)) >= f(c(x,s(y))) ; g(c(s(x),s(y))) >= f(c(x,y)) ; g(c(x,s(y))) >= g(c(s(x),y)) ; 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: f(c(s(x),s(y))) >= g(c(x,y)) constraint: f(c(s(x),y)) >= f(c(x,s(y))) constraint: g(c(s(x),s(y))) >= f(c(x,y)) constraint: g(c(x,s(y))) >= g(c(s(x),y)) constraint: Marked_f(c(s(x),y)) >= Marked_f(c(x,s(y))) APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(c(s(x),s(y))) >= g(c(x,y)) ; f(c(s(x),y)) >= f(c(x,s(y))) ; g(c(s(x),s(y))) >= f(c(x,y)) ; g(c(x,s(y))) >= g(c(s(x),y)) ; 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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: f(c(s(x),s(y))) >= g(c(x,y)) constraint: f(c(s(x),y)) >= f(c(x,s(y))) constraint: g(c(s(x),s(y))) >= f(c(x,y)) constraint: g(c(x,s(y))) >= g(c(s(x),y)) constraint: Marked_g(c(x,s(y))) >= Marked_g(c(s(x),y)) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(c(s(x),y)) -> f(c(x,s(y))) [2] f(c(s(x),s(y))) -> g(c(x,y)) [3] g(c(x,s(y))) -> g(c(s(x),y)) [4] g(c(s(x),s(y))) -> f(c(x,y)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ f ] (X0) = 0; [ Marked_g ] (X0) = 1*X0; [ s ] (X0) = 1*X0 + 2; [ c ] (X0,X1) = 2*X1 + 2*X0; [ Marked_f ] (X0) = 1*X0; [ g ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ f ] (X0) = 0; [ s ] (X0) = 3 + 1*X0 + 0; [ c ] (X0,X1) = 2*X0 + 0; [ Marked_f ] (X0) = 2*X0 + 0; [ g ] (X0) = 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ f ] (X0) = 0; [ Marked_g ] (X0) = 3*X0 + 0; [ s ] (X0) = 3 + 1*X0 + 0; [ c ] (X0,X1) = 1*X0 + 2*X1 + 0; [ g ] (X0) = 0; ]} ]} ]} ]} ]} Cime worked for 0.159405 seconds (real time) Cime Exit Status: 0