- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] rev(nil) -> nil [2] rev(rev(x)) -> x [3] rev(++(x,y)) -> ++(rev(y),rev(x)) [4] ++(nil,y) -> y [5] ++(x,nil) -> x [6] ++(.(x,y),z) -> .(x,++(y,z)) [7] ++(x,++(y,z)) -> ++(++(x,y),z) [8] make(x) -> .(x,nil) 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(rev(x)) >= x ; rev(++(x,y)) >= ++(rev(y),rev(x)) ; ++(nil,y) >= y ; ++(.(x,y),z) >= .(x,++(y,z)) ; ++(x,nil) >= x ; ++(x,++(y,z)) >= ++(++(x,y),z) ; make(x) >= .(x,nil) ; 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: rev(nil) >= nil constraint: rev(rev(x)) >= x constraint: rev(++(x,y)) >= ++(rev(y),rev(x)) constraint: ++(nil,y) >= y constraint: ++(.(x,y),z) >= .(x,++(y,z)) constraint: ++(x,nil) >= x constraint: ++(x,++(y,z)) >= ++(++(x,y),z) constraint: make(x) >= .(x,nil) 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: { rev(nil) >= nil ; rev(rev(x)) >= x ; rev(++(x,y)) >= ++(rev(y),rev(x)) ; ++(nil,y) >= y ; ++(.(x,y),z) >= .(x,++(y,z)) ; ++(x,nil) >= x ; ++(x,++(y,z)) >= ++(++(x,y),z) ; make(x) >= .(x,nil) ; Marked_++(.(x,y),z) >= Marked_++(y,z) ; Marked_++(x,++(y,z)) >= Marked_++(++(x,y),z) ; Marked_++(x,++(y,z)) >= Marked_++(x,y) ; } + Disjunctions:{ { Marked_++(.(x,y),z) > Marked_++(y,z) ; } { Marked_++(x,++(y,z)) > Marked_++(++(x,y),z) ; } { Marked_++(x,++(y,z)) > Marked_++(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: rev(nil) >= nil constraint: rev(rev(x)) >= x constraint: rev(++(x,y)) >= ++(rev(y),rev(x)) constraint: ++(nil,y) >= y constraint: ++(.(x,y),z) >= .(x,++(y,z)) constraint: ++(x,nil) >= x constraint: ++(x,++(y,z)) >= ++(++(x,y),z) constraint: make(x) >= .(x,nil) constraint: Marked_++(.(x,y),z) >= Marked_++(y,z) constraint: Marked_++(x,++(y,z)) >= Marked_++(++(x,y),z) constraint: Marked_++(x,++(y,z)) >= Marked_++(x,y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { rev(nil) >= nil ; rev(rev(x)) >= x ; rev(++(x,y)) >= ++(rev(y),rev(x)) ; ++(nil,y) >= y ; ++(.(x,y),z) >= .(x,++(y,z)) ; ++(x,nil) >= x ; ++(x,++(y,z)) >= ++(++(x,y),z) ; make(x) >= .(x,nil) ; 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(rev(x)) >= x constraint: rev(++(x,y)) >= ++(rev(y),rev(x)) constraint: ++(nil,y) >= y constraint: ++(.(x,y),z) >= .(x,++(y,z)) constraint: ++(x,nil) >= x constraint: ++(x,++(y,z)) >= ++(++(x,y),z) constraint: make(x) >= .(x,nil) constraint: Marked_++(.(x,y),z) >= Marked_++(y,z) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] rev(nil) -> nil [2] rev(rev(x)) -> x [3] rev(++(x,y)) -> ++(rev(y),rev(x)) [4] ++(nil,y) -> y [5] ++(x,nil) -> x [6] ++(.(x,y),z) -> .(x,++(y,z)) [7] ++(x,++(y,z)) -> ++(++(x,y),z) [8] make(x) -> .(x,nil) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ nil ] () = 0; [ make ] (X0) = 3*X0 + 0; [ ++ ] (X0,X1) = 1 + 1*X0 + 1*X1 + 0; [ rev ] (X0) = 1 + 3*X0 + 0; [ . ] (X0,X1) = 3*X0 + 1*X1 + 0; [ Marked_rev ] (X0) = 3*X0 + 0; ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ nil ] () = 0; [ make ] (X0) = 3*X0 + 1; [ ++ ] (X0,X1) = 1*X1 + 1*X0 + 2; [ Marked_++ ] (X0,X1) = 3*X1; [ rev ] (X0) = 2*X0; [ . ] (X0,X1) = 2*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ nil ] () = 0; [ make ] (X0) = 2 + 3*X0 + 0; [ ++ ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; [ Marked_++ ] (X0,X1) = 3*X0 + 0; [ rev ] (X0) = 2*X0 + 0; [ . ] (X0,X1) = 2 + 3*X0 + 1*X1 + 0; ]} ]} ]} ]} ]} Cime worked for 0.078614 seconds (real time) Cime Exit Status: 0