- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] ++(nil,y) -> y [2] ++(x,nil) -> x [3] ++(.(x,y),z) -> .(x,++(y,z)) [4] ++(++(x,y),z) -> ++(x,++(y,z)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { ++(++(x,y),z) >= ++(x,++(y,z)) ; ++(nil,y) >= y ; ++(.(x,y),z) >= .(x,++(y,z)) ; ++(x,nil) >= x ; Marked_++(++(x,y),z) >= Marked_++(x,++(y,z)) ; Marked_++(++(x,y),z) >= Marked_++(y,z) ; Marked_++(.(x,y),z) >= Marked_++(y,z) ; } + Disjunctions:{ { Marked_++(++(x,y),z) > Marked_++(x,++(y,z)) ; } { Marked_++(++(x,y),z) > Marked_++(y,z) ; } { Marked_++(.(x,y),z) > Marked_++(y,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: ++(++(x,y),z) >= ++(x,++(y,z)) constraint: ++(nil,y) >= y constraint: ++(.(x,y),z) >= .(x,++(y,z)) constraint: ++(x,nil) >= x constraint: Marked_++(++(x,y),z) >= Marked_++(x,++(y,z)) constraint: Marked_++(++(x,y),z) >= Marked_++(y,z) constraint: Marked_++(.(x,y),z) >= Marked_++(y,z) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { ++(++(x,y),z) >= ++(x,++(y,z)) ; ++(nil,y) >= y ; ++(.(x,y),z) >= .(x,++(y,z)) ; ++(x,nil) >= x ; Marked_++(.(x,y),z) >= Marked_++(y,z) ; } + Disjunctions:{ { Marked_++(.(x,y),z) > Marked_++(y,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: ++(++(x,y),z) >= ++(x,++(y,z)) constraint: ++(nil,y) >= y constraint: ++(.(x,y),z) >= .(x,++(y,z)) constraint: ++(x,nil) >= x constraint: Marked_++(.(x,y),z) >= Marked_++(y,z) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] ++(nil,y) -> y [2] ++(x,nil) -> x [3] ++(.(x,y),z) -> .(x,++(y,z)) [4] ++(++(x,y),z) -> ++(x,++(y,z)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ ++ ] (X0,X1) = 1*X1 + 1*X0 + 2; [ . ] (X0,X1) = 1*X1 + 3*X0; [ nil ] () = 2; [ Marked_++ ] (X0,X1) = 1*X1 + 2*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ ++ ] (X0,X1) = 2*X0 + 1*X1 + 0; [ . ] (X0,X1) = 2 + 3*X0 + 1*X1 + 0; [ nil ] () = 3 + 0; [ Marked_++ ] (X0,X1) = 3*X0 + 0; ]} ]} ]} ]} ]} Cime worked for 0.029280 seconds (real time) Cime Exit Status: 0