- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] rev(nil) -> nil [2] rev(.(x,y)) -> ++(rev(y),.(x,nil)) [3] car(.(x,y)) -> x [4] cdr(.(x,y)) -> y [5] null(nil) -> true [6] null(.(x,y)) -> false [7] ++(nil,y) -> y [8] ++(.(x,y),z) -> .(x,++(y,z)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { rev(nil) >= nil ; rev(.(x,y)) >= ++(rev(y),.(x,nil)) ; ++(nil,y) >= y ; ++(.(x,y),z) >= .(x,++(y,z)) ; car(.(x,y)) >= x ; cdr(.(x,y)) >= y ; null(nil) >= true ; null(.(x,y)) >= false ; Marked_rev(.(x,y)) >= Marked_rev(y) ; } + Disjunctions:{ { Marked_rev(.(x,y)) > Marked_rev(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: rev(nil) >= nil constraint: rev(.(x,y)) >= ++(rev(y),.(x,nil)) constraint: ++(nil,y) >= y constraint: ++(.(x,y),z) >= .(x,++(y,z)) constraint: car(.(x,y)) >= x constraint: cdr(.(x,y)) >= y constraint: null(nil) >= true constraint: null(.(x,y)) >= false constraint: Marked_rev(.(x,y)) >= Marked_rev(y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { rev(nil) >= nil ; rev(.(x,y)) >= ++(rev(y),.(x,nil)) ; ++(nil,y) >= y ; ++(.(x,y),z) >= .(x,++(y,z)) ; car(.(x,y)) >= x ; cdr(.(x,y)) >= y ; null(nil) >= true ; null(.(x,y)) >= false ; 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: rev(nil) >= nil constraint: rev(.(x,y)) >= ++(rev(y),.(x,nil)) constraint: ++(nil,y) >= y constraint: ++(.(x,y),z) >= .(x,++(y,z)) constraint: car(.(x,y)) >= x constraint: cdr(.(x,y)) >= y constraint: null(nil) >= true constraint: null(.(x,y)) >= false constraint: Marked_++(.(x,y),z) >= Marked_++(y,z) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] rev(nil) -> nil [2] rev(.(x,y)) -> ++(rev(y),.(x,nil)) [3] car(.(x,y)) -> x [4] cdr(.(x,y)) -> y [5] null(nil) -> true [6] null(.(x,y)) -> false [7] ++(nil,y) -> y [8] ++(.(x,y),z) -> .(x,++(y,z)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ nil ] () = 0; [ false ] () = 0; [ car ] (X0) = 3 + 3*X0 + 0; [ ++ ] (X0,X1) = 1*X0 + 2*X1 + 0; [ true ] () = 3 + 0; [ rev ] (X0) = 2*X0 + 0; [ cdr ] (X0) = 3 + 3*X0 + 0; [ Marked_rev ] (X0) = 3*X0 + 0; [ . ] (X0,X1) = 2 + 2*X0 + 1*X1 + 0; [ null ] (X0) = 3 + 3*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ nil ] () = 0; [ false ] () = 3 + 0; [ car ] (X0) = 2 + 3*X0 + 0; [ ++ ] (X0,X1) = 1*X0 + 2*X1 + 0; [ true ] () = 3 + 0; [ rev ] (X0) = 2*X0 + 0; [ Marked_++ ] (X0,X1) = 3*X0 + 0; [ cdr ] (X0) = 2 + 3*X0 + 0; [ . ] (X0,X1) = 1 + 1*X0 + 1*X1 + 0; [ null ] (X0) = 3 + 3*X0 + 0; ]} ]} ]} Cime worked for 0.042649 seconds (real time) Cime Exit Status: 0