- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] purge(nil) -> nil [2] purge(.(x,y)) -> .(x,purge(remove(x,y))) [3] remove(x,nil) -> nil [4] remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z))) 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: { purge(nil) >= nil ; purge(.(x,y)) >= .(x,purge(remove(x,y))) ; remove(x,nil) >= nil ; remove(x,.(y,z)) >= if(=(x,y),remove(x,z),.(y,remove(x,z))) ; Marked_purge(.(x,y)) >= Marked_purge(remove(x,y)) ; } + Disjunctions:{ { Marked_purge(.(x,y)) > Marked_purge(remove(x,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: purge(nil) >= nil constraint: purge(.(x,y)) >= .(x,purge(remove(x,y))) constraint: remove(x,nil) >= nil constraint: remove(x,.(y,z)) >= if(=(x,y),remove(x,z),.(y,remove(x,z))) constraint: Marked_purge(.(x,y)) >= Marked_purge(remove(x,y)) APPLY CRITERIA (Subterm criterion) ST: Marked_remove -> 2 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] purge(nil) -> nil [2] purge(.(x,y)) -> .(x,purge(remove(x,y))) [3] remove(x,nil) -> nil [4] remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ nil ] () = 0; [ if ] (X0,X1,X2) = 0; [ . ] (X0,X1) = 3 + 2*X0 + 3*X1 + 0; [ purge ] (X0) = 2*X0 + 0; [ = ] (X0,X1) = 0; [ remove ] (X0,X1) = 0; [ Marked_purge ] (X0) = 2*X0 + 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.049618 seconds (real time) Cime Exit Status: 0