- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] __(__(X,Y),Z) -> __(X,__(Y,Z)) [2] __(X,nil) -> X [3] __(nil,X) -> X [4] and(tt,X) -> activate(X) [5] isList(V) -> isNeList(activate(V)) [6] isList(n__nil) -> tt [7] isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) [8] isNeList(V) -> isQid(activate(V)) [9] isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) [10] isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) [11] isNePal(V) -> isQid(activate(V)) [12] isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) [13] isPal(V) -> isNePal(activate(V)) [14] isPal(n__nil) -> tt [15] isQid(n__a) -> tt [16] isQid(n__e) -> tt [17] isQid(n__i) -> tt [18] isQid(n__o) -> tt [19] isQid(n__u) -> tt [20] nil -> n__nil [21] __(X1,X2) -> n____(X1,X2) [22] isList(X) -> n__isList(X) [23] isNeList(X) -> n__isNeList(X) [24] isPal(X) -> n__isPal(X) [25] a -> n__a [26] e -> n__e [27] i -> n__i [28] o -> n__o [29] u -> n__u [30] activate(n__nil) -> nil [31] activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) [32] activate(n__isList(X)) -> isList(X) [33] activate(n__isNeList(X)) -> isNeList(X) [34] activate(n__isPal(X)) -> isPal(X) [35] activate(n__a) -> a [36] activate(n__e) -> e [37] activate(n__i) -> i [38] activate(n__o) -> o [39] activate(n__u) -> u [40] activate(X) -> X Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { __(__(X,Y),Z) >= __(X,__(Y,Z)) ; __(nil,X) >= X ; __(X,nil) >= X ; __(X1,X2) >= n____(X1,X2) ; nil >= n__nil ; activate(n__nil) >= nil ; activate(n__isList(X)) >= isList(X) ; activate(n____(X1,X2)) >= __(activate(X1),activate(X2)) ; activate(n__isNeList(X)) >= isNeList(X) ; activate(n__isPal(X)) >= isPal(X) ; activate(n__a) >= a ; activate(n__e) >= e ; activate(n__i) >= i ; activate(n__o) >= o ; activate(n__u) >= u ; activate(X) >= X ; and(tt,X) >= activate(X) ; isNeList(n____(V1,V2)) >= and(isNeList(activate(V1)),n__isList(activate(V2))) ; isNeList(n____(V1,V2)) >= and(isList(activate(V1)),n__isNeList(activate(V2))) ; isNeList(X) >= n__isNeList(X) ; isNeList(V) >= isQid(activate(V)) ; isList(n__nil) >= tt ; isList(n____(V1,V2)) >= and(isList(activate(V1)),n__isList(activate(V2))) ; isList(X) >= n__isList(X) ; isList(V) >= isNeList(activate(V)) ; isQid(n__a) >= tt ; isQid(n__e) >= tt ; isQid(n__i) >= tt ; isQid(n__o) >= tt ; isQid(n__u) >= tt ; isNePal(n____(I,n____(P,I))) >= and(isQid(activate(I)),n__isPal(activate(P))) ; isNePal(V) >= isQid(activate(V)) ; isPal(n__nil) >= tt ; isPal(X) >= n__isPal(X) ; isPal(V) >= isNePal(activate(V)) ; a >= n__a ; e >= n__e ; i >= n__i ; o >= n__o ; u >= n__u ; Marked_activate(n__isList(X)) >= Marked_isList(X) ; Marked_activate(n____(X1,X2)) >= Marked_activate(X1) ; Marked_activate(n____(X1,X2)) >= Marked_activate(X2) ; Marked_activate(n__isNeList(X)) >= Marked_isNeList(X) ; Marked_activate(n__isPal(X)) >= Marked_isPal(X) ; Marked_isPal(V) >= Marked_activate(V) ; Marked_isPal(V) >= Marked_isNePal(activate(V)) ; Marked_isNeList(n____(V1,V2)) >= Marked_activate(V1) ; Marked_isNeList(n____(V1,V2)) >= Marked_activate(V2) ; Marked_isNeList(n____(V1,V2)) >= Marked_isNeList(activate(V1)) ; Marked_isNeList(n____(V1,V2)) >= Marked_isList(activate(V1)) ; Marked_isNeList(n____(V1,V2)) >= Marked_and(isNeList(activate(V1)), n__isList(activate(V2))) ; Marked_isNeList(n____(V1,V2)) >= Marked_and(isList(activate(V1)), n__isNeList(activate(V2))) ; Marked_isNeList(V) >= Marked_activate(V) ; Marked_isList(n____(V1,V2)) >= Marked_activate(V1) ; Marked_isList(n____(V1,V2)) >= Marked_activate(V2) ; Marked_isList(n____(V1,V2)) >= Marked_isList(activate(V1)) ; Marked_isList(n____(V1,V2)) >= Marked_and(isList(activate(V1)), n__isList(activate(V2))) ; Marked_isList(V) >= Marked_activate(V) ; Marked_isList(V) >= Marked_isNeList(activate(V)) ; Marked_isNePal(n____(I,n____(P,I))) >= Marked_activate(I) ; Marked_isNePal(n____(I,n____(P,I))) >= Marked_activate(P) ; Marked_isNePal(n____(I,n____(P,I))) >= Marked_and(isQid(activate(I)), n__isPal(activate(P))) ; Marked_isNePal(V) >= Marked_activate(V) ; Marked_and(tt,X) >= Marked_activate(X) ; } + Disjunctions:{ { Marked_activate(n__isList(X)) > Marked_isList(X) ; } { Marked_activate(n____(X1,X2)) > Marked_activate(X1) ; } { Marked_activate(n____(X1,X2)) > Marked_activate(X2) ; } { Marked_activate(n__isNeList(X)) > Marked_isNeList(X) ; } { Marked_activate(n__isPal(X)) > Marked_isPal(X) ; } { Marked_isPal(V) > Marked_activate(V) ; } { Marked_isPal(V) > Marked_isNePal(activate(V)) ; } { Marked_isNeList(n____(V1,V2)) > Marked_activate(V1) ; } { Marked_isNeList(n____(V1,V2)) > Marked_activate(V2) ; } { Marked_isNeList(n____(V1,V2)) > Marked_isNeList(activate(V1)) ; } { Marked_isNeList(n____(V1,V2)) > Marked_isList(activate(V1)) ; } { Marked_isNeList(n____(V1,V2)) > Marked_and(isNeList(activate(V1)), n__isList(activate(V2))) ; } { Marked_isNeList(n____(V1,V2)) > Marked_and(isList(activate(V1)), n__isNeList(activate(V2))) ; } { Marked_isNeList(V) > Marked_activate(V) ; } { Marked_isList(n____(V1,V2)) > Marked_activate(V1) ; } { Marked_isList(n____(V1,V2)) > Marked_activate(V2) ; } { Marked_isList(n____(V1,V2)) > Marked_isList(activate(V1)) ; } { Marked_isList(n____(V1,V2)) > Marked_and(isList(activate(V1)), n__isList(activate(V2))) ; } { Marked_isList(V) > Marked_activate(V) ; } { Marked_isList(V) > Marked_isNeList(activate(V)) ; } { Marked_isNePal(n____(I,n____(P,I))) > Marked_activate(I) ; } { Marked_isNePal(n____(I,n____(P,I))) > Marked_activate(P) ; } { Marked_isNePal(n____(I,n____(P,I))) > Marked_and(isQid(activate(I)), n__isPal(activate(P))) ; } { Marked_isNePal(V) > Marked_activate(V) ; } { Marked_and(tt,X) > Marked_activate(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: __(__(X,Y),Z) >= __(X,__(Y,Z)) constraint: __(nil,X) >= X constraint: __(X,nil) >= X constraint: __(X1,X2) >= n____(X1,X2) constraint: nil >= n__nil constraint: activate(n__nil) >= nil constraint: activate(n__isList(X)) >= isList(X) constraint: activate(n____(X1,X2)) >= __(activate(X1),activate(X2)) constraint: activate(n__isNeList(X)) >= isNeList(X) constraint: activate(n__isPal(X)) >= isPal(X) constraint: activate(n__a) >= a constraint: activate(n__e) >= e constraint: activate(n__i) >= i constraint: activate(n__o) >= o constraint: activate(n__u) >= u constraint: activate(X) >= X constraint: and(tt,X) >= activate(X) constraint: isNeList(n____(V1,V2)) >= and(isNeList(activate(V1)), n__isList(activate(V2))) constraint: isNeList(n____(V1,V2)) >= and(isList(activate(V1)), n__isNeList(activate(V2))) constraint: isNeList(X) >= n__isNeList(X) constraint: isNeList(V) >= isQid(activate(V)) constraint: isList(n__nil) >= tt constraint: isList(n____(V1,V2)) >= and(isList(activate(V1)), n__isList(activate(V2))) constraint: isList(X) >= n__isList(X) constraint: isList(V) >= isNeList(activate(V)) constraint: isQid(n__a) >= tt constraint: isQid(n__e) >= tt constraint: isQid(n__i) >= tt constraint: isQid(n__o) >= tt constraint: isQid(n__u) >= tt constraint: isNePal(n____(I,n____(P,I))) >= and(isQid(activate(I)), n__isPal(activate(P))) constraint: isNePal(V) >= isQid(activate(V)) constraint: isPal(n__nil) >= tt constraint: isPal(X) >= n__isPal(X) constraint: isPal(V) >= isNePal(activate(V)) constraint: a >= n__a constraint: e >= n__e constraint: i >= n__i constraint: o >= n__o constraint: u >= n__u constraint: Marked_activate(n__isList(X)) >= Marked_isList(X) constraint: Marked_activate(n____(X1,X2)) >= Marked_activate(X1) constraint: Marked_activate(n____(X1,X2)) >= Marked_activate(X2) constraint: Marked_activate(n__isNeList(X)) >= Marked_isNeList(X) constraint: Marked_activate(n__isPal(X)) >= Marked_isPal(X) constraint: Marked_isPal(V) >= Marked_activate(V) constraint: Marked_isPal(V) >= Marked_isNePal(activate(V)) constraint: Marked_isNeList(n____(V1,V2)) >= Marked_activate(V1) constraint: Marked_isNeList(n____(V1,V2)) >= Marked_activate(V2) constraint: Marked_isNeList(n____(V1,V2)) >= Marked_isNeList(activate(V1)) constraint: Marked_isNeList(n____(V1,V2)) >= Marked_isList(activate(V1)) constraint: Marked_isNeList(n____(V1,V2)) >= Marked_and(isNeList(activate(V1)), n__isList(activate(V2))) constraint: Marked_isNeList(n____(V1,V2)) >= Marked_and(isList(activate(V1)), n__isNeList(activate(V2))) constraint: Marked_isNeList(V) >= Marked_activate(V) constraint: Marked_isList(n____(V1,V2)) >= Marked_activate(V1) constraint: Marked_isList(n____(V1,V2)) >= Marked_activate(V2) constraint: Marked_isList(n____(V1,V2)) >= Marked_isList(activate(V1)) constraint: Marked_isList(n____(V1,V2)) >= Marked_and(isList(activate(V1)), n__isList(activate(V2))) constraint: Marked_isList(V) >= Marked_activate(V) constraint: Marked_isList(V) >= Marked_isNeList(activate(V)) constraint: Marked_isNePal(n____(I,n____(P,I))) >= Marked_activate(I) constraint: Marked_isNePal(n____(I,n____(P,I))) >= Marked_activate(P) constraint: Marked_isNePal(n____(I,n____(P,I))) >= Marked_and(isQid(activate(I)), n__isPal(activate(P))) constraint: Marked_isNePal(V) >= Marked_activate(V) constraint: Marked_and(tt,X) >= Marked_activate(X) APPLY CRITERIA (Subterm criterion) ST: Marked___ -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] __(__(X,Y),Z) -> __(X,__(Y,Z)) [2] __(X,nil) -> X [3] __(nil,X) -> X [4] and(tt,X) -> activate(X) [5] isList(V) -> isNeList(activate(V)) [6] isList(n__nil) -> tt [7] isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2))) [8] isNeList(V) -> isQid(activate(V)) [9] isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2))) [10] isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2))) [11] isNePal(V) -> isQid(activate(V)) [12] isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) [13] isPal(V) -> isNePal(activate(V)) [14] isPal(n__nil) -> tt [15] isQid(n__a) -> tt [16] isQid(n__e) -> tt [17] isQid(n__i) -> tt [18] isQid(n__o) -> tt [19] isQid(n__u) -> tt [20] nil -> n__nil [21] __(X1,X2) -> n____(X1,X2) [22] isList(X) -> n__isList(X) [23] isNeList(X) -> n__isNeList(X) [24] isPal(X) -> n__isPal(X) [25] a -> n__a [26] e -> n__e [27] i -> n__i [28] o -> n__o [29] u -> n__u [30] activate(n__nil) -> nil [31] activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) [32] activate(n__isList(X)) -> isList(X) [33] activate(n__isNeList(X)) -> isNeList(X) [34] activate(n__isPal(X)) -> isPal(X) [35] activate(n__a) -> a [36] activate(n__e) -> e [37] activate(n__i) -> i [38] activate(n__o) -> o [39] activate(n__u) -> u [40] activate(X) -> X , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ __ ] (X0,X1) = 1*X1 + 2*X0 + 2; [ Marked_isNeList ] (X0) = 2*X0; [ n__e ] () = 3; [ n__isList ] (X0) = 1*X0 + 1; [ u ] () = 2; [ tt ] () = 3; [ a ] () = 2; [ isNePal ] (X0) = 2*X0 + 1; [ activate ] (X0) = 1*X0; [ n__o ] () = 2; [ isQid ] (X0) = 1*X0 + 1; [ isList ] (X0) = 1*X0 + 1; [ Marked_and ] (X0,X1) = 2*X1 + 2*X0; [ i ] () = 2; [ isPal ] (X0) = 2*X0 + 3; [ nil ] () = 2; [ Marked_isList ] (X0) = 2*X0; [ n__i ] () = 2; [ n____ ] (X0,X1) = 1*X1 + 2*X0 + 2; [ Marked_activate ] (X0) = 2*X0; [ isNeList ] (X0) = 1*X0 + 1; [ Marked_isNePal ] (X0) = 3*X0 + 2; [ e ] () = 3; [ n__isPal ] (X0) = 2*X0 + 3; [ and ] (X0,X1) = 1*X1 + 1*X0 + 1; [ n__u ] () = 2; [ n__isNeList ] (X0) = 1*X0 + 1; [ n__nil ] () = 2; [ o ] () = 2; [ n__a ] () = 2; [ Marked_isPal ] (X0) = 3*X0 + 2; removing < Marked_isList(n____(V1,V2)),Marked_activate(V2)>< Marked_isNeList(n____(V1,V2)),Marked_activate(V2)>< Marked_isPal(V),Marked_activate(V)>< Marked_activate(n____(X1,X2)),Marked_activate(X2)>< Marked_activate(n__isPal(X)),Marked_isPal(X)> [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.218458 seconds (real time) Cime Exit Status: 0