- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] pred(s(x)) -> x [2] minus(x,0) -> x [3] minus(x,s(y)) -> pred(minus(x,y)) [4] quot(0,s(y)) -> 0 [5] quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) 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: { pred(s(x)) >= x ; minus(x,s(y)) >= pred(minus(x,y)) ; minus(x,0) >= x ; quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ; quot(0,s(y)) >= 0 ; Marked_quot(s(x),s(y)) >= Marked_quot(minus(x,y),s(y)) ; } + Disjunctions:{ { Marked_quot(s(x),s(y)) > Marked_quot(minus(x,y),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: pred(s(x)) >= x constraint: minus(x,s(y)) >= pred(minus(x,y)) constraint: minus(x,0) >= x constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) constraint: quot(0,s(y)) >= 0 constraint: Marked_quot(s(x),s(y)) >= Marked_quot(minus(x,y),s(y)) APPLY CRITERIA (Subterm criterion) ST: Marked_minus -> 2 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] pred(s(x)) -> x [2] minus(x,0) -> x [3] minus(x,s(y)) -> pred(minus(x,y)) [4] quot(0,s(y)) -> 0 [5] quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ pred ] (X0) = 1*X0 + 0; [ quot ] (X0,X1) = 2*X0 + 0; [ minus ] (X0,X1) = 1*X0 + 0; [ s ] (X0) = 2 + 1*X0 + 0; [ Marked_quot ] (X0,X1) = 3*X0 + 0; [ 0 ] () = 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.035393 seconds (real time) Cime Exit Status: 0