- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] div(0,y) -> 0 [2] div(x,y) -> quot(x,y,y) [3] quot(0,s(y),z) -> 0 [4] quot(s(x),s(y),z) -> quot(x,y,z) [5] quot(x,0,s(z)) -> s(div(x,s(z))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_quot -> 1 Marked_div -> 1 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { div(0,y) >= 0 ; div(x,y) >= quot(x,y,y) ; quot(0,s(y),z) >= 0 ; quot(s(x),s(y),z) >= quot(x,y,z) ; quot(x,0,s(z)) >= s(div(x,s(z))) ; Marked_quot(x,0,s(z)) >= Marked_div(x,s(z)) ; Marked_div(x,y) >= Marked_quot(x,y,y) ; } + Disjunctions:{ { Marked_quot(x,0,s(z)) > Marked_div(x,s(z)) ; } { Marked_div(x,y) > Marked_quot(x,y,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: div(0,y) >= 0 constraint: div(x,y) >= quot(x,y,y) constraint: quot(0,s(y),z) >= 0 constraint: quot(s(x),s(y),z) >= quot(x,y,z) constraint: quot(x,0,s(z)) >= s(div(x,s(z))) constraint: Marked_quot(x,0,s(z)) >= Marked_div(x,s(z)) constraint: Marked_div(x,y) >= Marked_quot(x,y,y) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] div(0,y) -> 0 [2] div(x,y) -> quot(x,y,y) [3] quot(0,s(y),z) -> 0 [4] quot(s(x),s(y),z) -> quot(x,y,z) [5] quot(x,0,s(z)) -> s(div(x,s(z))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ 0 ] () = 3; [ Marked_quot ] (X0,X1,X2) = 3*X1 + 3*X0 + 3; [ quot ] (X0,X1,X2) = 3; [ div ] (X0,X1) = 3; [ Marked_div ] (X0,X1) = 3*X1 + 3*X0 + 3; [ s ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} Cime worked for 0.035783 seconds (real time) Cime Exit Status: 0