- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] quot(0,s(y),s(z)) -> 0 [2] quot(s(x),s(y),z) -> quot(x,y,z) [3] plus(0,y) -> y [4] plus(s(x),y) -> s(plus(x,y)) [5] quot(x,0,s(z)) -> s(quot(x,plus(z,s(0)),s(z))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> } { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_quot -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_plus -> 1 APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { quot(0,s(y),s(z)) >= 0 ; quot(s(x),s(y),z) >= quot(x,y,z) ; quot(x,0,s(z)) >= s(quot(x,plus(z,s(0)),s(z))) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(x,y)) ; Marked_quot(x,0,s(z)) >= Marked_quot(x,plus(z,s(0)),s(z)) ; } + Disjunctions:{ { Marked_quot(x,0,s(z)) > Marked_quot(x,plus(z,s(0)),s(z)) ; } } === 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: quot(0,s(y),s(z)) >= 0 constraint: quot(s(x),s(y),z) >= quot(x,y,z) constraint: quot(x,0,s(z)) >= s(quot(x,plus(z,s(0)),s(z))) constraint: plus(0,y) >= y constraint: plus(s(x),y) >= s(plus(x,y)) constraint: Marked_quot(x,0,s(z)) >= Marked_quot(x,plus(z,s(0)),s(z)) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] quot(0,s(y),s(z)) -> 0 [2] quot(s(x),s(y),z) -> quot(x,y,z) [3] plus(0,y) -> y [4] plus(s(x),y) -> s(plus(x,y)) [5] quot(x,0,s(z)) -> s(quot(x,plus(z,s(0)),s(z))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 1 + 0; [ Marked_quot ] (X0,X1,X2) = 1*X1 + 0; [ s ] (X0) = 0; [ quot ] (X0,X1,X2) = 2 + 0; [ plus ] (X0,X1) = 2*X1 + 0; ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.063435 seconds (real time) Cime Exit Status: 0