- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] -(x,0) -> x [2] -(0,s(y)) -> 0 [3] -(s(x),s(y)) -> -(x,y) [4] lt(x,0) -> false [5] lt(0,s(y)) -> true [6] lt(s(x),s(y)) -> lt(x,y) [7] if(true,x,y) -> x [8] if(false,x,y) -> y [9] div(x,0) -> 0 [10] div(0,y) -> 0 [11] div(s(x),s(y)) -> if(lt(x,y),0,s(div(-(x,y),s(y)))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> } { --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { -(0,s(y)) >= 0 ; -(s(x),s(y)) >= -(x,y) ; -(x,0) >= x ; lt(0,s(y)) >= true ; lt(s(x),s(y)) >= lt(x,y) ; lt(x,0) >= false ; if(false,x,y) >= y ; if(true,x,y) >= x ; div(0,y) >= 0 ; div(s(x),s(y)) >= if(lt(x,y),0,s(div(-(x,y),s(y)))) ; div(x,0) >= 0 ; Marked_div(s(x),s(y)) >= Marked_div(-(x,y),s(y)) ; } + Disjunctions:{ { Marked_div(s(x),s(y)) > Marked_div(-(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: -(0,s(y)) >= 0 constraint: -(s(x),s(y)) >= -(x,y) constraint: -(x,0) >= x constraint: lt(0,s(y)) >= true constraint: lt(s(x),s(y)) >= lt(x,y) constraint: lt(x,0) >= false constraint: if(false,x,y) >= y constraint: if(true,x,y) >= x constraint: div(0,y) >= 0 constraint: div(s(x),s(y)) >= if(lt(x,y),0,s(div(-(x,y),s(y)))) constraint: div(x,0) >= 0 constraint: Marked_div(s(x),s(y)) >= Marked_div(-(x,y),s(y)) APPLY CRITERIA (Subterm criterion) ST: Marked_lt -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_- -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] -(x,0) -> x [2] -(0,s(y)) -> 0 [3] -(s(x),s(y)) -> -(x,y) [4] lt(x,0) -> false [5] lt(0,s(y)) -> true [6] lt(s(x),s(y)) -> lt(x,y) [7] if(true,x,y) -> x [8] if(false,x,y) -> y [9] div(x,0) -> 0 [10] div(0,y) -> 0 [11] div(s(x),s(y)) -> if(lt(x,y),0,s(div(-(x,y),s(y)))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ - ] (X0,X1) = 1*X0 + 0; [ Marked_div ] (X0,X1) = 3*X0 + 0; [ lt ] (X0,X1) = 0; [ s ] (X0) = 2 + 1*X0 + 0; [ if ] (X0,X1,X2) = 2*X1 + 1*X2 + 0; [ 0 ] () = 0; [ true ] () = 0; [ false ] () = 0; [ div ] (X0,X1) = 1*X0 + 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.068013 seconds (real time) Cime Exit Status: 0