- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] flatten(nil) -> nil [2] flatten(unit(x)) -> flatten(x) [3] flatten(++(x,y)) -> ++(flatten(x),flatten(y)) [4] flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) [5] flatten(flatten(x)) -> flatten(x) [6] rev(nil) -> nil [7] rev(unit(x)) -> unit(x) [8] rev(++(x,y)) -> ++(rev(y),rev(x)) [9] rev(rev(x)) -> x [10] ++(x,nil) -> x [11] ++(nil,y) -> y [12] ++(++(x,y),z) -> ++(x,++(y,z)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { flatten(nil) >= nil ; flatten(flatten(x)) >= flatten(x) ; flatten(unit(x)) >= flatten(x) ; flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y)) ; flatten(++(x,y)) >= ++(flatten(x),flatten(y)) ; ++(nil,y) >= y ; ++(++(x,y),z) >= ++(x,++(y,z)) ; ++(x,nil) >= x ; rev(nil) >= nil ; rev(unit(x)) >= unit(x) ; rev(++(x,y)) >= ++(rev(y),rev(x)) ; rev(rev(x)) >= x ; Marked_flatten(unit(x)) >= Marked_flatten(x) ; Marked_flatten(++(unit(x),y)) >= Marked_flatten(x) ; Marked_flatten(++(unit(x),y)) >= Marked_flatten(y) ; Marked_flatten(++(x,y)) >= Marked_flatten(x) ; Marked_flatten(++(x,y)) >= Marked_flatten(y) ; } + Disjunctions:{ { Marked_flatten(unit(x)) > Marked_flatten(x) ; } { Marked_flatten(++(unit(x),y)) > Marked_flatten(x) ; } { Marked_flatten(++(unit(x),y)) > Marked_flatten(y) ; } { Marked_flatten(++(x,y)) > Marked_flatten(x) ; } { Marked_flatten(++(x,y)) > Marked_flatten(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: flatten(nil) >= nil constraint: flatten(flatten(x)) >= flatten(x) constraint: flatten(unit(x)) >= flatten(x) constraint: flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y)) constraint: flatten(++(x,y)) >= ++(flatten(x),flatten(y)) constraint: ++(nil,y) >= y constraint: ++(++(x,y),z) >= ++(x,++(y,z)) constraint: ++(x,nil) >= x constraint: rev(nil) >= nil constraint: rev(unit(x)) >= unit(x) constraint: rev(++(x,y)) >= ++(rev(y),rev(x)) constraint: rev(rev(x)) >= x constraint: Marked_flatten(unit(x)) >= Marked_flatten(x) constraint: Marked_flatten(++(unit(x),y)) >= Marked_flatten(x) constraint: Marked_flatten(++(unit(x),y)) >= Marked_flatten(y) constraint: Marked_flatten(++(x,y)) >= Marked_flatten(x) constraint: Marked_flatten(++(x,y)) >= Marked_flatten(y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { flatten(nil) >= nil ; flatten(flatten(x)) >= flatten(x) ; flatten(unit(x)) >= flatten(x) ; flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y)) ; flatten(++(x,y)) >= ++(flatten(x),flatten(y)) ; ++(nil,y) >= y ; ++(++(x,y),z) >= ++(x,++(y,z)) ; ++(x,nil) >= x ; rev(nil) >= nil ; rev(unit(x)) >= unit(x) ; rev(++(x,y)) >= ++(rev(y),rev(x)) ; rev(rev(x)) >= x ; Marked_rev(++(x,y)) >= Marked_rev(x) ; Marked_rev(++(x,y)) >= Marked_rev(y) ; } + Disjunctions:{ { Marked_rev(++(x,y)) > Marked_rev(x) ; } { 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: flatten(nil) >= nil constraint: flatten(flatten(x)) >= flatten(x) constraint: flatten(unit(x)) >= flatten(x) constraint: flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y)) constraint: flatten(++(x,y)) >= ++(flatten(x),flatten(y)) constraint: ++(nil,y) >= y constraint: ++(++(x,y),z) >= ++(x,++(y,z)) constraint: ++(x,nil) >= x constraint: rev(nil) >= nil constraint: rev(unit(x)) >= unit(x) constraint: rev(++(x,y)) >= ++(rev(y),rev(x)) constraint: rev(rev(x)) >= x constraint: Marked_rev(++(x,y)) >= Marked_rev(x) constraint: Marked_rev(++(x,y)) >= Marked_rev(y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { flatten(nil) >= nil ; flatten(flatten(x)) >= flatten(x) ; flatten(unit(x)) >= flatten(x) ; flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y)) ; flatten(++(x,y)) >= ++(flatten(x),flatten(y)) ; ++(nil,y) >= y ; ++(++(x,y),z) >= ++(x,++(y,z)) ; ++(x,nil) >= x ; rev(nil) >= nil ; rev(unit(x)) >= unit(x) ; rev(++(x,y)) >= ++(rev(y),rev(x)) ; rev(rev(x)) >= x ; Marked_++(++(x,y),z) >= Marked_++(x,++(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) ; } } === 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: flatten(nil) >= nil constraint: flatten(flatten(x)) >= flatten(x) constraint: flatten(unit(x)) >= flatten(x) constraint: flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y)) constraint: flatten(++(x,y)) >= ++(flatten(x),flatten(y)) constraint: ++(nil,y) >= y constraint: ++(++(x,y),z) >= ++(x,++(y,z)) constraint: ++(x,nil) >= x constraint: rev(nil) >= nil constraint: rev(unit(x)) >= unit(x) constraint: rev(++(x,y)) >= ++(rev(y),rev(x)) constraint: rev(rev(x)) >= x constraint: Marked_++(++(x,y),z) >= Marked_++(x,++(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: { flatten(nil) >= nil ; flatten(flatten(x)) >= flatten(x) ; flatten(unit(x)) >= flatten(x) ; flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y)) ; flatten(++(x,y)) >= ++(flatten(x),flatten(y)) ; ++(nil,y) >= y ; ++(++(x,y),z) >= ++(x,++(y,z)) ; ++(x,nil) >= x ; rev(nil) >= nil ; rev(unit(x)) >= unit(x) ; rev(++(x,y)) >= ++(rev(y),rev(x)) ; rev(rev(x)) >= x ; Marked_flatten(unit(x)) >= Marked_flatten(x) ; } + Disjunctions:{ { Marked_flatten(unit(x)) > Marked_flatten(x) ; } } === 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: flatten(nil) >= nil constraint: flatten(flatten(x)) >= flatten(x) constraint: flatten(unit(x)) >= flatten(x) constraint: flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y)) constraint: flatten(++(x,y)) >= ++(flatten(x),flatten(y)) constraint: ++(nil,y) >= y constraint: ++(++(x,y),z) >= ++(x,++(y,z)) constraint: ++(x,nil) >= x constraint: rev(nil) >= nil constraint: rev(unit(x)) >= unit(x) constraint: rev(++(x,y)) >= ++(rev(y),rev(x)) constraint: rev(rev(x)) >= x constraint: Marked_flatten(unit(x)) >= Marked_flatten(x) 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] flatten(nil) -> nil [2] flatten(unit(x)) -> flatten(x) [3] flatten(++(x,y)) -> ++(flatten(x),flatten(y)) [4] flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) [5] flatten(flatten(x)) -> flatten(x) [6] rev(nil) -> nil [7] rev(unit(x)) -> unit(x) [8] rev(++(x,y)) -> ++(rev(y),rev(x)) [9] rev(rev(x)) -> x [10] ++(x,nil) -> x [11] ++(nil,y) -> y [12] ++(++(x,y),z) -> ++(x,++(y,z)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ nil ] () = 0; [ rev ] (X0) = 2*X0; [ unit ] (X0) = 1*X0; [ flatten ] (X0) = 2*X0; [ ++ ] (X0,X1) = 1*X1 + 1*X0 + 2; [ Marked_flatten ] (X0) = 2*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ nil ] () = 0; [ rev ] (X0) = 1*X0 + 0; [ unit ] (X0) = 2 + 3*X0 + 0; [ flatten ] (X0) = 3*X0 + 0; [ ++ ] (X0,X1) = 1*X0 + 1*X1 + 0; [ Marked_flatten ] (X0) = 3*X0 + 0; ]} ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ nil ] () = 0; [ rev ] (X0) = 2*X0 + 0; [ unit ] (X0) = 1*X0 + 0; [ Marked_rev ] (X0) = 3*X0 + 0; [ flatten ] (X0) = 2*X0 + 0; [ ++ ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ nil ] () = 0; [ rev ] (X0) = 2*X0 + 0; [ unit ] (X0) = 1*X0 + 0; [ flatten ] (X0) = 2*X0 + 0; [ Marked_++ ] (X0,X1) = 3*X0 + 0; [ ++ ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; ]} ]} ]} Cime worked for 0.120934 seconds (real time) Cime Exit Status: 0