- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] first(0,X) -> nil [2] first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) [3] from(X) -> cons(X,n__from(n__s(X))) [4] first(X1,X2) -> n__first(X1,X2) [5] from(X) -> n__from(X) [6] s(X) -> n__s(X) [7] activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) [8] activate(n__from(X)) -> from(activate(X)) [9] activate(n__s(X)) -> s(activate(X)) [10] activate(X) -> X Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { first(0,X) >= nil ; first(s(X),cons(Y,Z)) >= cons(Y,n__first(X,activate(Z))) ; first(X1,X2) >= n__first(X1,X2) ; activate(n__first(X1,X2)) >= first(activate(X1),activate(X2)) ; activate(n__from(X)) >= from(activate(X)) ; activate(n__s(X)) >= s(activate(X)) ; activate(X) >= X ; s(X) >= n__s(X) ; from(X) >= cons(X,n__from(n__s(X))) ; from(X) >= n__from(X) ; Marked_activate(n__first(X1,X2)) >= Marked_activate(X1) ; Marked_activate(n__first(X1,X2)) >= Marked_activate(X2) ; Marked_activate(n__first(X1,X2)) >= Marked_first(activate(X1),activate(X2)) ; Marked_activate(n__from(X)) >= Marked_activate(X) ; Marked_activate(n__s(X)) >= Marked_activate(X) ; Marked_first(s(X),cons(Y,Z)) >= Marked_activate(Z) ; } + Disjunctions:{ { Marked_activate(n__first(X1,X2)) > Marked_activate(X1) ; } { Marked_activate(n__first(X1,X2)) > Marked_activate(X2) ; } { Marked_activate(n__first(X1,X2)) > Marked_first(activate(X1),activate(X2)) ; } { Marked_activate(n__from(X)) > Marked_activate(X) ; } { Marked_activate(n__s(X)) > Marked_activate(X) ; } { Marked_first(s(X),cons(Y,Z)) > Marked_activate(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: first(0,X) >= nil constraint: first(s(X),cons(Y,Z)) >= cons(Y,n__first(X,activate(Z))) constraint: first(X1,X2) >= n__first(X1,X2) constraint: activate(n__first(X1,X2)) >= first(activate(X1),activate(X2)) constraint: activate(n__from(X)) >= from(activate(X)) constraint: activate(n__s(X)) >= s(activate(X)) constraint: activate(X) >= X constraint: s(X) >= n__s(X) constraint: from(X) >= cons(X,n__from(n__s(X))) constraint: from(X) >= n__from(X) constraint: Marked_activate(n__first(X1,X2)) >= Marked_activate(X1) constraint: Marked_activate(n__first(X1,X2)) >= Marked_activate(X2) constraint: Marked_activate(n__first(X1,X2)) >= Marked_first(activate(X1), activate(X2)) constraint: Marked_activate(n__from(X)) >= Marked_activate(X) constraint: Marked_activate(n__s(X)) >= Marked_activate(X) constraint: Marked_first(s(X),cons(Y,Z)) >= Marked_activate(Z) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_activate -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] first(0,X) -> nil [2] first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) [3] from(X) -> cons(X,n__from(n__s(X))) [4] first(X1,X2) -> n__first(X1,X2) [5] from(X) -> n__from(X) [6] s(X) -> n__s(X) [7] activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) [8] activate(n__from(X)) -> from(activate(X)) [9] activate(n__s(X)) -> s(activate(X)) [10] activate(X) -> X , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ nil ] () = 2; [ n__s ] (X0) = 1*X0; [ n__first ] (X0,X1) = 1*X1 + 1*X0 + 3; [ 0 ] () = 3; [ Marked_activate ] (X0) = 1*X0 + 1; [ s ] (X0) = 1*X0; [ first ] (X0,X1) = 1*X1 + 1*X0 + 3; [ from ] (X0) = 1*X0; [ activate ] (X0) = 1*X0; [ Marked_first ] (X0,X1) = 1*X1 + 1*X0 + 2; [ cons ] (X0,X1) = 1*X1; [ n__from ] (X0) = 1*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} Cime worked for 0.058847 seconds (real time) Cime Exit Status: 0