- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(0,y) -> 0 [2] f(s(x),y) -> f(f(x,y),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(0,y) >= 0 ; f(s(x),y) >= f(f(x,y),y) ; Marked_f(s(x),y) >= Marked_f(f(x,y),y) ; Marked_f(s(x),y) >= Marked_f(x,y) ; } + Disjunctions:{ { Marked_f(s(x),y) > Marked_f(f(x,y),y) ; } { Marked_f(s(x),y) > Marked_f(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(0,y) >= 0 constraint: f(s(x),y) >= f(f(x,y),y) constraint: Marked_f(s(x),y) >= Marked_f(f(x,y),y) constraint: Marked_f(s(x),y) >= Marked_f(x,y) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(0,y) -> 0 [2] f(s(x),y) -> f(f(x,y),y) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ s ] (X0) = 3 + 3*X0 + 0; [ f ] (X0,X1) = 2*X0 + 0; [ Marked_f ] (X0,X1) = 2*X0 + 0; ]} ]} ]} Cime worked for 0.016362 seconds (real time) Cime Exit Status: 0