- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] +(0,y) -> y [2] +(s(x),0) -> s(x) [3] +(s(x),s(y)) -> s(+(s(x),+(y,0))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { +(0,y) >= y ; +(s(x),0) >= s(x) ; +(s(x),s(y)) >= s(+(s(x),+(y,0))) ; Marked_+(s(x),s(y)) >= Marked_+(s(x),+(y,0)) ; } + Disjunctions:{ { Marked_+(s(x),s(y)) > Marked_+(s(x),+(y,0)) ; } } === 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: +(0,y) >= y constraint: +(s(x),0) >= s(x) constraint: +(s(x),s(y)) >= s(+(s(x),+(y,0))) constraint: Marked_+(s(x),s(y)) >= Marked_+(s(x),+(y,0)) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] +(0,y) -> y [2] +(s(x),0) -> s(x) [3] +(s(x),s(y)) -> s(+(s(x),+(y,0))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ + ] (X0,X1) = 1*X0 + 2*X1 + 0; [ s ] (X0) = 2 + 1*X0 + 0; [ 0 ] () = 0; [ Marked_+ ] (X0,X1) = 2*X1 + 0; ]} ]} ]} Cime worked for 0.028938 seconds (real time) Cime Exit Status: 0