YES
Problem:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
Proof:
DP Processor:
DPs:
__#(__(X,Y),Z) -> __#(Y,Z)
__#(__(X,Y),Z) -> __#(X,__(Y,Z))
and#(tt(),X) -> activate#(X)
isList#(V) -> activate#(V)
isList#(V) -> isNeList#(activate(V))
isList#(n____(V1,V2)) -> activate#(V2)
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> isList#(activate(V1))
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
isNeList#(V) -> activate#(V)
isNeList#(V) -> isQid#(activate(V))
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> isList#(activate(V1))
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1))
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal#(V) -> activate#(V)
isNePal#(V) -> isQid#(activate(V))
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> isQid#(activate(I))
isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPal(activate(P)))
isPal#(V) -> activate#(V)
isPal#(V) -> isNePal#(activate(V))
activate#(n__nil()) -> nil#()
activate#(n____(X1,X2)) -> activate#(X2)
activate#(n____(X1,X2)) -> activate#(X1)
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
activate#(n__isList(X)) -> isList#(X)
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#()
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
TDG Processor:
DPs:
__#(__(X,Y),Z) -> __#(Y,Z)
__#(__(X,Y),Z) -> __#(X,__(Y,Z))
and#(tt(),X) -> activate#(X)
isList#(V) -> activate#(V)
isList#(V) -> isNeList#(activate(V))
isList#(n____(V1,V2)) -> activate#(V2)
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> isList#(activate(V1))
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
isNeList#(V) -> activate#(V)
isNeList#(V) -> isQid#(activate(V))
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> isList#(activate(V1))
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1))
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal#(V) -> activate#(V)
isNePal#(V) -> isQid#(activate(V))
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> isQid#(activate(I))
isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPal(activate(P)))
isPal#(V) -> activate#(V)
isPal#(V) -> isNePal#(activate(V))
activate#(n__nil()) -> nil#()
activate#(n____(X1,X2)) -> activate#(X2)
activate#(n____(X1,X2)) -> activate#(X1)
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
activate#(n__isList(X)) -> isList#(X)
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#()
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
graph:
isPal#(V) -> isNePal#(activate(V)) ->
isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPal(activate(P)))
isPal#(V) -> isNePal#(activate(V)) ->
isNePal#(n____(I,n____(P,I))) -> isQid#(activate(I))
isPal#(V) -> isNePal#(activate(V)) ->
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isPal#(V) -> isNePal#(activate(V)) ->
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isPal#(V) -> isNePal#(activate(V)) ->
isNePal#(V) -> isQid#(activate(V))
isPal#(V) -> isNePal#(activate(V)) -> isNePal#(V) -> activate#(V)
isPal#(V) -> activate#(V) -> activate#(n__u()) -> u#()
isPal#(V) -> activate#(V) -> activate#(n__o()) -> o#()
isPal#(V) -> activate#(V) -> activate#(n__i()) -> i#()
isPal#(V) -> activate#(V) -> activate#(n__e()) -> e#()
isPal#(V) -> activate#(V) -> activate#(n__a()) -> a#()
isPal#(V) -> activate#(V) -> activate#(n__isPal(X)) -> isPal#(X)
isPal#(V) -> activate#(V) -> activate#(n__isNeList(X)) -> isNeList#(X)
isPal#(V) -> activate#(V) -> activate#(n__isList(X)) -> isList#(X)
isPal#(V) -> activate#(V) ->
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
isPal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(X1)
isPal#(V) -> activate#(V) -> activate#(n____(X1,X2)) -> activate#(X2)
isPal#(V) -> activate#(V) ->
activate#(n__nil()) -> nil#()
isNePal#(n____(I,n____(P,I))) -> activate#(P) ->
activate#(n__u()) -> u#()
isNePal#(n____(I,n____(P,I))) -> activate#(P) ->
activate#(n__o()) -> o#()
isNePal#(n____(I,n____(P,I))) -> activate#(P) ->
activate#(n__i()) -> i#()
isNePal#(n____(I,n____(P,I))) -> activate#(P) ->
activate#(n__e()) -> e#()
isNePal#(n____(I,n____(P,I))) -> activate#(P) ->
activate#(n__a()) -> a#()
isNePal#(n____(I,n____(P,I))) -> activate#(P) ->
activate#(n__isPal(X)) -> isPal#(X)
isNePal#(n____(I,n____(P,I))) -> activate#(P) ->
activate#(n__isNeList(X)) -> isNeList#(X)
isNePal#(n____(I,n____(P,I))) -> activate#(P) ->
activate#(n__isList(X)) -> isList#(X)
isNePal#(n____(I,n____(P,I))) -> activate#(P) ->
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
isNePal#(n____(I,n____(P,I))) -> activate#(P) ->
activate#(n____(X1,X2)) -> activate#(X1)
isNePal#(n____(I,n____(P,I))) -> activate#(P) ->
activate#(n____(X1,X2)) -> activate#(X2)
isNePal#(n____(I,n____(P,I))) -> activate#(P) ->
activate#(n__nil()) -> nil#()
isNePal#(n____(I,n____(P,I))) -> activate#(I) ->
activate#(n__u()) -> u#()
isNePal#(n____(I,n____(P,I))) -> activate#(I) ->
activate#(n__o()) -> o#()
isNePal#(n____(I,n____(P,I))) -> activate#(I) ->
activate#(n__i()) -> i#()
isNePal#(n____(I,n____(P,I))) -> activate#(I) ->
activate#(n__e()) -> e#()
isNePal#(n____(I,n____(P,I))) -> activate#(I) ->
activate#(n__a()) -> a#()
isNePal#(n____(I,n____(P,I))) -> activate#(I) ->
activate#(n__isPal(X)) -> isPal#(X)
isNePal#(n____(I,n____(P,I))) -> activate#(I) ->
activate#(n__isNeList(X)) -> isNeList#(X)
isNePal#(n____(I,n____(P,I))) -> activate#(I) ->
activate#(n__isList(X)) -> isList#(X)
isNePal#(n____(I,n____(P,I))) -> activate#(I) ->
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
isNePal#(n____(I,n____(P,I))) -> activate#(I) ->
activate#(n____(X1,X2)) -> activate#(X1)
isNePal#(n____(I,n____(P,I))) -> activate#(I) ->
activate#(n____(X1,X2)) -> activate#(X2)
isNePal#(n____(I,n____(P,I))) -> activate#(I) ->
activate#(n__nil()) -> nil#()
isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPal(activate(P))) ->
and#(tt(),X) -> activate#(X)
isNePal#(V) -> activate#(V) -> activate#(n__u()) -> u#()
isNePal#(V) -> activate#(V) -> activate#(n__o()) -> o#()
isNePal#(V) -> activate#(V) -> activate#(n__i()) -> i#()
isNePal#(V) -> activate#(V) -> activate#(n__e()) -> e#()
isNePal#(V) -> activate#(V) -> activate#(n__a()) -> a#()
isNePal#(V) -> activate#(V) -> activate#(n__isPal(X)) -> isPal#(X)
isNePal#(V) -> activate#(V) ->
activate#(n__isNeList(X)) -> isNeList#(X)
isNePal#(V) -> activate#(V) -> activate#(n__isList(X)) -> isList#(X)
isNePal#(V) -> activate#(V) ->
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
isNePal#(V) -> activate#(V) ->
activate#(n____(X1,X2)) -> activate#(X1)
isNePal#(V) -> activate#(V) ->
activate#(n____(X1,X2)) -> activate#(X2)
isNePal#(V) -> activate#(V) ->
activate#(n__nil()) -> nil#()
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) ->
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) ->
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1))
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) ->
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) ->
isNeList#(n____(V1,V2)) -> isList#(activate(V1))
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) ->
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) ->
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) ->
isNeList#(V) -> isQid#(activate(V))
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1)) ->
isNeList#(V) -> activate#(V)
isNeList#(n____(V1,V2)) -> isList#(activate(V1)) ->
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
isNeList#(n____(V1,V2)) -> isList#(activate(V1)) ->
isList#(n____(V1,V2)) -> isList#(activate(V1))
isNeList#(n____(V1,V2)) -> isList#(activate(V1)) ->
isList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> isList#(activate(V1)) ->
isList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> isList#(activate(V1)) ->
isList#(V) -> isNeList#(activate(V))
isNeList#(n____(V1,V2)) -> isList#(activate(V1)) ->
isList#(V) -> activate#(V)
isNeList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__u()) -> u#()
isNeList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__o()) -> o#()
isNeList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__i()) -> i#()
isNeList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__e()) -> e#()
isNeList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__a()) -> a#()
isNeList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__isPal(X)) -> isPal#(X)
isNeList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__isNeList(X)) -> isNeList#(X)
isNeList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__isList(X)) -> isList#(X)
isNeList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
isNeList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n____(X1,X2)) -> activate#(X1)
isNeList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n____(X1,X2)) -> activate#(X2)
isNeList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__nil()) -> nil#()
isNeList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__u()) -> u#()
isNeList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__o()) -> o#()
isNeList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__i()) -> i#()
isNeList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__e()) -> e#()
isNeList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__a()) -> a#()
isNeList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__isPal(X)) -> isPal#(X)
isNeList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__isNeList(X)) -> isNeList#(X)
isNeList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__isList(X)) -> isList#(X)
isNeList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
isNeList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n____(X1,X2)) -> activate#(X1)
isNeList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n____(X1,X2)) -> activate#(X2)
isNeList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__nil()) -> nil#()
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2))) ->
and#(tt(),X) -> activate#(X)
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2))) ->
and#(tt(),X) -> activate#(X)
isNeList#(V) -> activate#(V) -> activate#(n__u()) -> u#()
isNeList#(V) -> activate#(V) -> activate#(n__o()) -> o#()
isNeList#(V) -> activate#(V) -> activate#(n__i()) -> i#()
isNeList#(V) -> activate#(V) -> activate#(n__e()) -> e#()
isNeList#(V) -> activate#(V) -> activate#(n__a()) -> a#()
isNeList#(V) -> activate#(V) -> activate#(n__isPal(X)) -> isPal#(X)
isNeList#(V) -> activate#(V) ->
activate#(n__isNeList(X)) -> isNeList#(X)
isNeList#(V) -> activate#(V) ->
activate#(n__isList(X)) -> isList#(X)
isNeList#(V) -> activate#(V) ->
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
isNeList#(V) -> activate#(V) ->
activate#(n____(X1,X2)) -> activate#(X1)
isNeList#(V) -> activate#(V) ->
activate#(n____(X1,X2)) -> activate#(X2)
isNeList#(V) -> activate#(V) ->
activate#(n__nil()) -> nil#()
isList#(n____(V1,V2)) -> isList#(activate(V1)) ->
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
isList#(n____(V1,V2)) -> isList#(activate(V1)) ->
isList#(n____(V1,V2)) -> isList#(activate(V1))
isList#(n____(V1,V2)) -> isList#(activate(V1)) ->
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> isList#(activate(V1)) ->
isList#(n____(V1,V2)) -> activate#(V2)
isList#(n____(V1,V2)) -> isList#(activate(V1)) ->
isList#(V) -> isNeList#(activate(V))
isList#(n____(V1,V2)) -> isList#(activate(V1)) ->
isList#(V) -> activate#(V)
isList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__u()) -> u#()
isList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__o()) -> o#()
isList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__i()) -> i#()
isList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__e()) -> e#()
isList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__a()) -> a#()
isList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__isPal(X)) -> isPal#(X)
isList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__isNeList(X)) -> isNeList#(X)
isList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__isList(X)) -> isList#(X)
isList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
isList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n____(X1,X2)) -> activate#(X1)
isList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n____(X1,X2)) -> activate#(X2)
isList#(n____(V1,V2)) -> activate#(V2) ->
activate#(n__nil()) -> nil#()
isList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__u()) -> u#()
isList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__o()) -> o#()
isList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__i()) -> i#()
isList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__e()) -> e#()
isList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__a()) -> a#()
isList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__isPal(X)) -> isPal#(X)
isList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__isNeList(X)) -> isNeList#(X)
isList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__isList(X)) -> isList#(X)
isList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
isList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n____(X1,X2)) -> activate#(X1)
isList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n____(X1,X2)) -> activate#(X2)
isList#(n____(V1,V2)) -> activate#(V1) ->
activate#(n__nil()) -> nil#()
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2))) ->
and#(tt(),X) -> activate#(X)
isList#(V) -> isNeList#(activate(V)) ->
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
isList#(V) -> isNeList#(activate(V)) ->
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1))
isList#(V) -> isNeList#(activate(V)) ->
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2)))
isList#(V) -> isNeList#(activate(V)) ->
isNeList#(n____(V1,V2)) -> isList#(activate(V1))
isList#(V) -> isNeList#(activate(V)) ->
isNeList#(n____(V1,V2)) -> activate#(V1)
isList#(V) -> isNeList#(activate(V)) ->
isNeList#(n____(V1,V2)) -> activate#(V2)
isList#(V) -> isNeList#(activate(V)) ->
isNeList#(V) -> isQid#(activate(V))
isList#(V) -> isNeList#(activate(V)) -> isNeList#(V) -> activate#(V)
isList#(V) -> activate#(V) -> activate#(n__u()) -> u#()
isList#(V) -> activate#(V) -> activate#(n__o()) -> o#()
isList#(V) -> activate#(V) -> activate#(n__i()) -> i#()
isList#(V) -> activate#(V) -> activate#(n__e()) -> e#()
isList#(V) -> activate#(V) -> activate#(n__a()) -> a#()
isList#(V) -> activate#(V) -> activate#(n__isPal(X)) -> isPal#(X)
isList#(V) -> activate#(V) ->
activate#(n__isNeList(X)) -> isNeList#(X)
isList#(V) -> activate#(V) -> activate#(n__isList(X)) -> isList#(X)
isList#(V) -> activate#(V) ->
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
isList#(V) -> activate#(V) ->
activate#(n____(X1,X2)) -> activate#(X1)
isList#(V) -> activate#(V) ->
activate#(n____(X1,X2)) -> activate#(X2)
isList#(V) -> activate#(V) -> activate#(n__nil()) -> nil#()
activate#(n__isPal(X)) -> isPal#(X) ->
isPal#(V) -> isNePal#(activate(V))
activate#(n__isPal(X)) -> isPal#(X) ->
isPal#(V) -> activate#(V)
activate#(n__isNeList(X)) -> isNeList#(X) ->
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
activate#(n__isNeList(X)) -> isNeList#(X) ->
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1))
activate#(n__isNeList(X)) -> isNeList#(X) ->
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2)))
activate#(n__isNeList(X)) -> isNeList#(X) ->
isNeList#(n____(V1,V2)) -> isList#(activate(V1))
activate#(n__isNeList(X)) -> isNeList#(X) ->
isNeList#(n____(V1,V2)) -> activate#(V1)
activate#(n__isNeList(X)) -> isNeList#(X) ->
isNeList#(n____(V1,V2)) -> activate#(V2)
activate#(n__isNeList(X)) -> isNeList#(X) ->
isNeList#(V) -> isQid#(activate(V))
activate#(n__isNeList(X)) -> isNeList#(X) ->
isNeList#(V) -> activate#(V)
activate#(n__isList(X)) -> isList#(X) ->
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
activate#(n__isList(X)) -> isList#(X) ->
isList#(n____(V1,V2)) -> isList#(activate(V1))
activate#(n__isList(X)) -> isList#(X) ->
isList#(n____(V1,V2)) -> activate#(V1)
activate#(n__isList(X)) -> isList#(X) ->
isList#(n____(V1,V2)) -> activate#(V2)
activate#(n__isList(X)) -> isList#(X) ->
isList#(V) -> isNeList#(activate(V))
activate#(n__isList(X)) -> isList#(X) ->
isList#(V) -> activate#(V)
activate#(n____(X1,X2)) -> activate#(X2) ->
activate#(n__u()) -> u#()
activate#(n____(X1,X2)) -> activate#(X2) ->
activate#(n__o()) -> o#()
activate#(n____(X1,X2)) -> activate#(X2) ->
activate#(n__i()) -> i#()
activate#(n____(X1,X2)) -> activate#(X2) ->
activate#(n__e()) -> e#()
activate#(n____(X1,X2)) -> activate#(X2) ->
activate#(n__a()) -> a#()
activate#(n____(X1,X2)) -> activate#(X2) ->
activate#(n__isPal(X)) -> isPal#(X)
activate#(n____(X1,X2)) -> activate#(X2) ->
activate#(n__isNeList(X)) -> isNeList#(X)
activate#(n____(X1,X2)) -> activate#(X2) ->
activate#(n__isList(X)) -> isList#(X)
activate#(n____(X1,X2)) -> activate#(X2) ->
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
activate#(n____(X1,X2)) -> activate#(X2) ->
activate#(n____(X1,X2)) -> activate#(X1)
activate#(n____(X1,X2)) -> activate#(X2) ->
activate#(n____(X1,X2)) -> activate#(X2)
activate#(n____(X1,X2)) -> activate#(X2) ->
activate#(n__nil()) -> nil#()
activate#(n____(X1,X2)) -> activate#(X1) ->
activate#(n__u()) -> u#()
activate#(n____(X1,X2)) -> activate#(X1) ->
activate#(n__o()) -> o#()
activate#(n____(X1,X2)) -> activate#(X1) ->
activate#(n__i()) -> i#()
activate#(n____(X1,X2)) -> activate#(X1) ->
activate#(n__e()) -> e#()
activate#(n____(X1,X2)) -> activate#(X1) ->
activate#(n__a()) -> a#()
activate#(n____(X1,X2)) -> activate#(X1) ->
activate#(n__isPal(X)) -> isPal#(X)
activate#(n____(X1,X2)) -> activate#(X1) ->
activate#(n__isNeList(X)) -> isNeList#(X)
activate#(n____(X1,X2)) -> activate#(X1) ->
activate#(n__isList(X)) -> isList#(X)
activate#(n____(X1,X2)) -> activate#(X1) ->
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
activate#(n____(X1,X2)) -> activate#(X1) ->
activate#(n____(X1,X2)) -> activate#(X1)
activate#(n____(X1,X2)) -> activate#(X1) ->
activate#(n____(X1,X2)) -> activate#(X2)
activate#(n____(X1,X2)) -> activate#(X1) ->
activate#(n__nil()) -> nil#()
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) ->
__#(__(X,Y),Z) -> __#(X,__(Y,Z))
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2)) ->
__#(__(X,Y),Z) -> __#(Y,Z)
and#(tt(),X) -> activate#(X) -> activate#(n__u()) -> u#()
and#(tt(),X) -> activate#(X) -> activate#(n__o()) -> o#()
and#(tt(),X) -> activate#(X) -> activate#(n__i()) -> i#()
and#(tt(),X) -> activate#(X) -> activate#(n__e()) -> e#()
and#(tt(),X) -> activate#(X) -> activate#(n__a()) -> a#()
and#(tt(),X) -> activate#(X) -> activate#(n__isPal(X)) -> isPal#(X)
and#(tt(),X) -> activate#(X) ->
activate#(n__isNeList(X)) -> isNeList#(X)
and#(tt(),X) -> activate#(X) ->
activate#(n__isList(X)) -> isList#(X)
and#(tt(),X) -> activate#(X) ->
activate#(n____(X1,X2)) -> __#(activate(X1),activate(X2))
and#(tt(),X) -> activate#(X) ->
activate#(n____(X1,X2)) -> activate#(X1)
and#(tt(),X) -> activate#(X) ->
activate#(n____(X1,X2)) -> activate#(X2)
and#(tt(),X) -> activate#(X) -> activate#(n__nil()) -> nil#()
__#(__(X,Y),Z) -> __#(Y,Z) -> __#(__(X,Y),Z) -> __#(X,__(Y,Z))
__#(__(X,Y),Z) -> __#(Y,Z) -> __#(__(X,Y),Z) -> __#(Y,Z)
__#(__(X,Y),Z) -> __#(X,__(Y,Z)) ->
__#(__(X,Y),Z) -> __#(X,__(Y,Z))
__#(__(X,Y),Z) -> __#(X,__(Y,Z)) -> __#(__(X,Y),Z) -> __#(Y,Z)
SCC Processor:
#sccs: 2
#rules: 27
#arcs: 216/1369
DPs:
isPal#(V) -> isNePal#(activate(V))
isNePal#(V) -> activate#(V)
activate#(n____(X1,X2)) -> activate#(X2)
activate#(n____(X1,X2)) -> activate#(X1)
activate#(n__isList(X)) -> isList#(X)
isList#(V) -> activate#(V)
activate#(n__isNeList(X)) -> isNeList#(X)
isNeList#(V) -> activate#(V)
activate#(n__isPal(X)) -> isPal#(X)
isPal#(V) -> activate#(V)
isNeList#(n____(V1,V2)) -> activate#(V2)
isNeList#(n____(V1,V2)) -> activate#(V1)
isNeList#(n____(V1,V2)) -> isList#(activate(V1))
isList#(V) -> isNeList#(activate(V))
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2)))
and#(tt(),X) -> activate#(X)
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1))
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
isList#(n____(V1,V2)) -> activate#(V2)
isList#(n____(V1,V2)) -> activate#(V1)
isList#(n____(V1,V2)) -> isList#(activate(V1))
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
isNePal#(n____(I,n____(P,I))) -> activate#(P)
isNePal#(n____(I,n____(P,I))) -> activate#(I)
isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPal(activate(P)))
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
Arctic Interpretation Processor:
dimension: 1
interpretation:
[isPal#](x0) = 6x0 + 1,
[isNePal#](x0) = 6x0 + 0,
[isNeList#](x0) = 6x0 + 0,
[isList#](x0) = 6x0 + 0,
[activate#](x0) = 1x0 + 0,
[and#](x0, x1) = 1x0 + 1x1 + 0,
[u] = 0,
[o] = 0,
[i] = 0,
[e] = 1,
[a] = 0,
[n__u] = 0,
[n__o] = 0,
[n__i] = 0,
[n__e] = 1,
[n__a] = 0,
[isPal](x0) = 5x0 + 0,
[n__isPal](x0) = 5x0 + 0,
[isNePal](x0) = 5x0 + 0,
[n__isNeList](x0) = 5x0,
[isQid](x0) = x0,
[n__isList](x0) = 5x0,
[n____](x0, x1) = x0 + x1 + 1,
[n__nil] = 2,
[isNeList](x0) = 5x0,
[isList](x0) = 5x0,
[activate](x0) = x0,
[and](x0, x1) = x0 + x1,
[tt] = 0,
[nil] = 2,
[__](x0, x1) = x0 + x1 + 1
orientation:
isPal#(V) = 6V + 1 >= 6V + 0 = isNePal#(activate(V))
isNePal#(V) = 6V + 0 >= 1V + 0 = activate#(V)
activate#(n____(X1,X2)) = 1X1 + 1X2 + 2 >= 1X2 + 0 = activate#(X2)
activate#(n____(X1,X2)) = 1X1 + 1X2 + 2 >= 1X1 + 0 = activate#(X1)
activate#(n__isList(X)) = 6X + 0 >= 6X + 0 = isList#(X)
isList#(V) = 6V + 0 >= 1V + 0 = activate#(V)
activate#(n__isNeList(X)) = 6X + 0 >= 6X + 0 = isNeList#(X)
isNeList#(V) = 6V + 0 >= 1V + 0 = activate#(V)
activate#(n__isPal(X)) = 6X + 1 >= 6X + 1 = isPal#(X)
isPal#(V) = 6V + 1 >= 1V + 0 = activate#(V)
isNeList#(n____(V1,V2)) = 6V1 + 6V2 + 7 >= 1V2 + 0 = activate#(V2)
isNeList#(n____(V1,V2)) = 6V1 + 6V2 + 7 >= 1V1 + 0 = activate#(V1)
isNeList#(n____(V1,V2)) = 6V1 + 6V2 + 7 >= 6V1 + 0 = isList#(activate(V1))
isList#(V) = 6V + 0 >= 6V + 0 = isNeList#(activate(V))
isNeList#(n____(V1,V2)) = 6V1 + 6V2 + 7 >= 6V1 + 6V2 + 0 = and#(isList(activate(V1)),n__isNeList(activate(V2)))
and#(tt(),X) = 1X + 1 >= 1X + 0 = activate#(X)
isNeList#(n____(V1,V2)) = 6V1 + 6V2 + 7 >= 6V1 + 0 = isNeList#(activate(V1))
isNeList#(n____(V1,V2)) = 6V1 + 6V2 + 7 >= 6V1 + 6V2 + 0 = and#(isNeList(activate(V1)),n__isList(activate(V2)))
isList#(n____(V1,V2)) = 6V1 + 6V2 + 7 >= 1V2 + 0 = activate#(V2)
isList#(n____(V1,V2)) = 6V1 + 6V2 + 7 >= 1V1 + 0 = activate#(V1)
isList#(n____(V1,V2)) = 6V1 + 6V2 + 7 >= 6V1 + 0 = isList#(activate(V1))
isList#(n____(V1,V2)) = 6V1 + 6V2 + 7 >= 6V1 + 6V2 + 0 = and#(isList(activate(V1)),n__isList(activate(V2)))
isNePal#(n____(I,n____(P,I))) = 6I + 6P + 7 >= 1P + 0 = activate#(P)
isNePal#(n____(I,n____(P,I))) = 6I + 6P + 7 >= 1I + 0 = activate#(I)
isNePal#(n____(I,n____(P,I))) = 6I + 6P + 7 >= 1I + 6P + 1 = and#(isQid(activate(I)),n__isPal(activate(P)))
__(__(X,Y),Z) = X + Y + Z + 1 >= X + Y + Z + 1 = __(X,__(Y,Z))
__(X,nil()) = X + 2 >= X = X
__(nil(),X) = X + 2 >= X = X
and(tt(),X) = X + 0 >= X = activate(X)
isList(V) = 5V >= 5V = isNeList(activate(V))
isList(n__nil()) = 7 >= 0 = tt()
isList(n____(V1,V2)) = 5V1 + 5V2 + 6 >= 5V1 + 5V2 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) = 5V >= V = isQid(activate(V))
isNeList(n____(V1,V2)) = 5V1 + 5V2 + 6 >= 5V1 + 5V2 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) = 5V1 + 5V2 + 6 >= 5V1 + 5V2 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) = 5V + 0 >= V = isQid(activate(V))
isNePal(n____(I,n____(P,I))) = 5I + 5P + 6 >= I + 5P + 0 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) = 5V + 0 >= 5V + 0 = isNePal(activate(V))
isPal(n__nil()) = 7 >= 0 = tt()
isQid(n__a()) = 0 >= 0 = tt()
isQid(n__e()) = 1 >= 0 = tt()
isQid(n__i()) = 0 >= 0 = tt()
isQid(n__o()) = 0 >= 0 = tt()
isQid(n__u()) = 0 >= 0 = tt()
nil() = 2 >= 2 = n__nil()
__(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = n____(X1,X2)
isList(X) = 5X >= 5X = n__isList(X)
isNeList(X) = 5X >= 5X = n__isNeList(X)
isPal(X) = 5X + 0 >= 5X + 0 = n__isPal(X)
a() = 0 >= 0 = n__a()
e() = 1 >= 1 = n__e()
i() = 0 >= 0 = n__i()
o() = 0 >= 0 = n__o()
u() = 0 >= 0 = n__u()
activate(n__nil()) = 2 >= 2 = nil()
activate(n____(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(activate(X1),activate(X2))
activate(n__isList(X)) = 5X >= 5X = isList(X)
activate(n__isNeList(X)) = 5X >= 5X = isNeList(X)
activate(n__isPal(X)) = 5X + 0 >= 5X + 0 = isPal(X)
activate(n__a()) = 0 >= 0 = a()
activate(n__e()) = 1 >= 1 = e()
activate(n__i()) = 0 >= 0 = i()
activate(n__o()) = 0 >= 0 = o()
activate(n__u()) = 0 >= 0 = u()
activate(X) = X >= X = X
problem:
DPs:
isPal#(V) -> isNePal#(activate(V))
isNePal#(V) -> activate#(V)
activate#(n____(X1,X2)) -> activate#(X2)
activate#(n____(X1,X2)) -> activate#(X1)
activate#(n__isList(X)) -> isList#(X)
isList#(V) -> activate#(V)
activate#(n__isNeList(X)) -> isNeList#(X)
isNeList#(V) -> activate#(V)
activate#(n__isPal(X)) -> isPal#(X)
isNeList#(n____(V1,V2)) -> isList#(activate(V1))
isList#(V) -> isNeList#(activate(V))
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2)))
and#(tt(),X) -> activate#(X)
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1))
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
isList#(n____(V1,V2)) -> isList#(activate(V1))
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPal(activate(P)))
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
Arctic Interpretation Processor:
dimension: 1
interpretation:
[isPal#](x0) = 1x0,
[isNePal#](x0) = 1x0,
[isNeList#](x0) = x0,
[isList#](x0) = x0,
[activate#](x0) = x0,
[and#](x0, x1) = x1 + 0,
[u] = 4,
[o] = 0,
[i] = 1,
[e] = 4,
[a] = 2,
[n__u] = 4,
[n__o] = 0,
[n__i] = 1,
[n__e] = 4,
[n__a] = 2,
[isPal](x0) = 1x0 + 0,
[n__isPal](x0) = 1x0 + 0,
[isNePal](x0) = 1x0,
[n__isNeList](x0) = x0,
[isQid](x0) = x0,
[n__isList](x0) = x0 + 2,
[n____](x0, x1) = x0 + x1 + 2,
[n__nil] = 0,
[isNeList](x0) = x0,
[isList](x0) = x0 + 2,
[activate](x0) = x0,
[and](x0, x1) = x1,
[tt] = 0,
[nil] = 0,
[__](x0, x1) = x0 + x1 + 2
orientation:
isPal#(V) = 1V >= 1V = isNePal#(activate(V))
isNePal#(V) = 1V >= V = activate#(V)
activate#(n____(X1,X2)) = X1 + X2 + 2 >= X2 = activate#(X2)
activate#(n____(X1,X2)) = X1 + X2 + 2 >= X1 = activate#(X1)
activate#(n__isList(X)) = X + 2 >= X = isList#(X)
isList#(V) = V >= V = activate#(V)
activate#(n__isNeList(X)) = X >= X = isNeList#(X)
isNeList#(V) = V >= V = activate#(V)
activate#(n__isPal(X)) = 1X + 0 >= 1X = isPal#(X)
isNeList#(n____(V1,V2)) = V1 + V2 + 2 >= V1 = isList#(activate(V1))
isList#(V) = V >= V = isNeList#(activate(V))
isNeList#(n____(V1,V2)) = V1 + V2 + 2 >= V2 + 0 = and#(isList(activate(V1)),n__isNeList(activate(V2)))
and#(tt(),X) = X + 0 >= X = activate#(X)
isNeList#(n____(V1,V2)) = V1 + V2 + 2 >= V1 = isNeList#(activate(V1))
isNeList#(n____(V1,V2)) = V1 + V2 + 2 >= V2 + 2 = and#(isNeList(activate(V1)),n__isList(activate(V2)))
isList#(n____(V1,V2)) = V1 + V2 + 2 >= V1 = isList#(activate(V1))
isList#(n____(V1,V2)) = V1 + V2 + 2 >= V2 + 2 = and#(isList(activate(V1)),n__isList(activate(V2)))
isNePal#(n____(I,n____(P,I))) = 1I + 1P + 3 >= 1P + 0 = and#(isQid(activate(I)),n__isPal(activate(P)))
__(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = __(X,__(Y,Z))
__(X,nil()) = X + 2 >= X = X
__(nil(),X) = X + 2 >= X = X
and(tt(),X) = X >= X = activate(X)
isList(V) = V + 2 >= V = isNeList(activate(V))
isList(n__nil()) = 2 >= 0 = tt()
isList(n____(V1,V2)) = V1 + V2 + 2 >= V2 + 2 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) = V >= V = isQid(activate(V))
isNeList(n____(V1,V2)) = V1 + V2 + 2 >= V2 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) = V1 + V2 + 2 >= V2 + 2 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) = 1V >= V = isQid(activate(V))
isNePal(n____(I,n____(P,I))) = 1I + 1P + 3 >= 1P + 0 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) = 1V + 0 >= 1V = isNePal(activate(V))
isPal(n__nil()) = 1 >= 0 = tt()
isQid(n__a()) = 2 >= 0 = tt()
isQid(n__e()) = 4 >= 0 = tt()
isQid(n__i()) = 1 >= 0 = tt()
isQid(n__o()) = 0 >= 0 = tt()
isQid(n__u()) = 4 >= 0 = tt()
nil() = 0 >= 0 = n__nil()
__(X1,X2) = X1 + X2 + 2 >= X1 + X2 + 2 = n____(X1,X2)
isList(X) = X + 2 >= X + 2 = n__isList(X)
isNeList(X) = X >= X = n__isNeList(X)
isPal(X) = 1X + 0 >= 1X + 0 = n__isPal(X)
a() = 2 >= 2 = n__a()
e() = 4 >= 4 = n__e()
i() = 1 >= 1 = n__i()
o() = 0 >= 0 = n__o()
u() = 4 >= 4 = n__u()
activate(n__nil()) = 0 >= 0 = nil()
activate(n____(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = __(activate(X1),activate(X2))
activate(n__isList(X)) = X + 2 >= X + 2 = isList(X)
activate(n__isNeList(X)) = X >= X = isNeList(X)
activate(n__isPal(X)) = 1X + 0 >= 1X + 0 = isPal(X)
activate(n__a()) = 2 >= 2 = a()
activate(n__e()) = 4 >= 4 = e()
activate(n__i()) = 1 >= 1 = i()
activate(n__o()) = 0 >= 0 = o()
activate(n__u()) = 4 >= 4 = u()
activate(X) = X >= X = X
problem:
DPs:
isPal#(V) -> isNePal#(activate(V))
activate#(n____(X1,X2)) -> activate#(X2)
activate#(n____(X1,X2)) -> activate#(X1)
activate#(n__isList(X)) -> isList#(X)
isList#(V) -> activate#(V)
activate#(n__isNeList(X)) -> isNeList#(X)
isNeList#(V) -> activate#(V)
activate#(n__isPal(X)) -> isPal#(X)
isNeList#(n____(V1,V2)) -> isList#(activate(V1))
isList#(V) -> isNeList#(activate(V))
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2)))
and#(tt(),X) -> activate#(X)
isNeList#(n____(V1,V2)) -> isNeList#(activate(V1))
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
isList#(n____(V1,V2)) -> isList#(activate(V1))
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
isNePal#(n____(I,n____(P,I))) -> and#(isQid(activate(I)),n__isPal(activate(P)))
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
Arctic Interpretation Processor:
dimension: 1
interpretation:
[isPal#](x0) = 4x0 + 0,
[isNePal#](x0) = 4x0 + 0,
[isNeList#](x0) = 6x0 + 0,
[isList#](x0) = 6x0 + 0,
[activate#](x0) = x0 + 0,
[and#](x0, x1) = x0 + x1,
[u] = 0,
[o] = 0,
[i] = 1,
[e] = 0,
[a] = 3,
[n__u] = 0,
[n__o] = 0,
[n__i] = 1,
[n__e] = 0,
[n__a] = 3,
[isPal](x0) = 4x0,
[n__isPal](x0) = 4x0,
[isNePal](x0) = 3x0,
[n__isNeList](x0) = 6x0,
[isQid](x0) = 3x0,
[n__isList](x0) = 6x0 + 0,
[n____](x0, x1) = 1x0 + x1 + 0,
[n__nil] = 0,
[isNeList](x0) = 6x0,
[isList](x0) = 6x0 + 0,
[activate](x0) = x0,
[and](x0, x1) = 1x0 + x1,
[tt] = 2,
[nil] = 0,
[__](x0, x1) = 1x0 + x1 + 0
orientation:
isPal#(V) = 4V + 0 >= 4V + 0 = isNePal#(activate(V))
activate#(n____(X1,X2)) = 1X1 + X2 + 0 >= X2 + 0 = activate#(X2)
activate#(n____(X1,X2)) = 1X1 + X2 + 0 >= X1 + 0 = activate#(X1)
activate#(n__isList(X)) = 6X + 0 >= 6X + 0 = isList#(X)
isList#(V) = 6V + 0 >= V + 0 = activate#(V)
activate#(n__isNeList(X)) = 6X + 0 >= 6X + 0 = isNeList#(X)
isNeList#(V) = 6V + 0 >= V + 0 = activate#(V)
activate#(n__isPal(X)) = 4X + 0 >= 4X + 0 = isPal#(X)
isNeList#(n____(V1,V2)) = 7V1 + 6V2 + 6 >= 6V1 + 0 = isList#(activate(V1))
isList#(V) = 6V + 0 >= 6V + 0 = isNeList#(activate(V))
isNeList#(n____(V1,V2)) = 7V1 + 6V2 + 6 >= 6V1 + 6V2 + 0 = and#(isList(activate(V1)),n__isNeList(activate(V2)))
and#(tt(),X) = X + 2 >= X + 0 = activate#(X)
isNeList#(n____(V1,V2)) = 7V1 + 6V2 + 6 >= 6V1 + 0 = isNeList#(activate(V1))
isNeList#(n____(V1,V2)) = 7V1 + 6V2 + 6 >= 6V1 + 6V2 + 0 = and#(isNeList(activate(V1)),n__isList(activate(V2)))
isList#(n____(V1,V2)) = 7V1 + 6V2 + 6 >= 6V1 + 0 = isList#(activate(V1))
isList#(n____(V1,V2)) = 7V1 + 6V2 + 6 >= 6V1 + 6V2 + 0 = and#(isList(activate(V1)),n__isList(activate(V2)))
isNePal#(n____(I,n____(P,I))) = 5I + 5P + 4 >= 3I + 4P = and#(isQid(activate(I)),n__isPal(activate(P)))
__(__(X,Y),Z) = 2X + 1Y + Z + 1 >= 1X + 1Y + Z + 0 = __(X,__(Y,Z))
__(X,nil()) = 1X + 0 >= X = X
__(nil(),X) = X + 1 >= X = X
and(tt(),X) = X + 3 >= X = activate(X)
isList(V) = 6V + 0 >= 6V = isNeList(activate(V))
isList(n__nil()) = 6 >= 2 = tt()
isList(n____(V1,V2)) = 7V1 + 6V2 + 6 >= 7V1 + 6V2 + 1 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) = 6V >= 3V = isQid(activate(V))
isNeList(n____(V1,V2)) = 7V1 + 6V2 + 6 >= 7V1 + 6V2 + 1 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) = 7V1 + 6V2 + 6 >= 7V1 + 6V2 + 0 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) = 3V >= 3V = isQid(activate(V))
isNePal(n____(I,n____(P,I))) = 4I + 4P + 3 >= 4I + 4P = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) = 4V >= 3V = isNePal(activate(V))
isPal(n__nil()) = 4 >= 2 = tt()
isQid(n__a()) = 6 >= 2 = tt()
isQid(n__e()) = 3 >= 2 = tt()
isQid(n__i()) = 4 >= 2 = tt()
isQid(n__o()) = 3 >= 2 = tt()
isQid(n__u()) = 3 >= 2 = tt()
nil() = 0 >= 0 = n__nil()
__(X1,X2) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = n____(X1,X2)
isList(X) = 6X + 0 >= 6X + 0 = n__isList(X)
isNeList(X) = 6X >= 6X = n__isNeList(X)
isPal(X) = 4X >= 4X = n__isPal(X)
a() = 3 >= 3 = n__a()
e() = 0 >= 0 = n__e()
i() = 1 >= 1 = n__i()
o() = 0 >= 0 = n__o()
u() = 0 >= 0 = n__u()
activate(n__nil()) = 0 >= 0 = nil()
activate(n____(X1,X2)) = 1X1 + X2 + 0 >= 1X1 + X2 + 0 = __(activate(X1),activate(X2))
activate(n__isList(X)) = 6X + 0 >= 6X + 0 = isList(X)
activate(n__isNeList(X)) = 6X >= 6X = isNeList(X)
activate(n__isPal(X)) = 4X >= 4X = isPal(X)
activate(n__a()) = 3 >= 3 = a()
activate(n__e()) = 0 >= 0 = e()
activate(n__i()) = 1 >= 1 = i()
activate(n__o()) = 0 >= 0 = o()
activate(n__u()) = 0 >= 0 = u()
activate(X) = X >= X = X
problem:
DPs:
isPal#(V) -> isNePal#(activate(V))
activate#(n____(X1,X2)) -> activate#(X2)
activate#(n____(X1,X2)) -> activate#(X1)
activate#(n__isList(X)) -> isList#(X)
isList#(V) -> activate#(V)
activate#(n__isNeList(X)) -> isNeList#(X)
isNeList#(V) -> activate#(V)
activate#(n__isPal(X)) -> isPal#(X)
isList#(V) -> isNeList#(activate(V))
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2)))
and#(tt(),X) -> activate#(X)
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
SCC Processor:
#sccs: 1
#rules: 11
#arcs: 114/169
DPs:
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
and#(tt(),X) -> activate#(X)
activate#(n____(X1,X2)) -> activate#(X2)
activate#(n____(X1,X2)) -> activate#(X1)
activate#(n__isList(X)) -> isList#(X)
isList#(V) -> activate#(V)
activate#(n__isNeList(X)) -> isNeList#(X)
isNeList#(V) -> activate#(V)
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2)))
isList#(V) -> isNeList#(activate(V))
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
Arctic Interpretation Processor:
dimension: 1
interpretation:
[isNeList#](x0) = x0 + 0,
[isList#](x0) = x0 + 0,
[activate#](x0) = x0,
[and#](x0, x1) = x1 + 4,
[u] = 1,
[o] = 0,
[i] = 0,
[e] = 1,
[a] = 0,
[n__u] = 1,
[n__o] = 0,
[n__i] = 0,
[n__e] = 1,
[n__a] = 0,
[isPal](x0) = x0 + 7,
[n__isPal](x0) = x0 + 7,
[isNePal](x0) = x0 + 7,
[n__isNeList](x0) = x0 + 0,
[isQid](x0) = x0,
[n__isList](x0) = x0 + 0,
[n____](x0, x1) = 1x0 + x1 + 4,
[n__nil] = 0,
[isNeList](x0) = x0 + 0,
[isList](x0) = x0 + 0,
[activate](x0) = x0,
[and](x0, x1) = x0 + x1 + 1,
[tt] = 0,
[nil] = 0,
[__](x0, x1) = 1x0 + x1 + 4
orientation:
isNeList#(n____(V1,V2)) = 1V1 + V2 + 4 >= V2 + 4 = and#(isNeList(activate(V1)),n__isList(activate(V2)))
and#(tt(),X) = X + 4 >= X = activate#(X)
activate#(n____(X1,X2)) = 1X1 + X2 + 4 >= X2 = activate#(X2)
activate#(n____(X1,X2)) = 1X1 + X2 + 4 >= X1 = activate#(X1)
activate#(n__isList(X)) = X + 0 >= X + 0 = isList#(X)
isList#(V) = V + 0 >= V = activate#(V)
activate#(n__isNeList(X)) = X + 0 >= X + 0 = isNeList#(X)
isNeList#(V) = V + 0 >= V = activate#(V)
isNeList#(n____(V1,V2)) = 1V1 + V2 + 4 >= V2 + 4 = and#(isList(activate(V1)),n__isNeList(activate(V2)))
isList#(V) = V + 0 >= V + 0 = isNeList#(activate(V))
isList#(n____(V1,V2)) = 1V1 + V2 + 4 >= V2 + 4 = and#(isList(activate(V1)),n__isList(activate(V2)))
__(__(X,Y),Z) = 2X + 1Y + Z + 5 >= 1X + 1Y + Z + 4 = __(X,__(Y,Z))
__(X,nil()) = 1X + 4 >= X = X
__(nil(),X) = X + 4 >= X = X
and(tt(),X) = X + 1 >= X = activate(X)
isList(V) = V + 0 >= V + 0 = isNeList(activate(V))
isList(n__nil()) = 0 >= 0 = tt()
isList(n____(V1,V2)) = 1V1 + V2 + 4 >= V1 + V2 + 1 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) = V + 0 >= V = isQid(activate(V))
isNeList(n____(V1,V2)) = 1V1 + V2 + 4 >= V1 + V2 + 1 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) = 1V1 + V2 + 4 >= V1 + V2 + 1 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) = V + 7 >= V = isQid(activate(V))
isNePal(n____(I,n____(P,I))) = 1I + 1P + 7 >= I + P + 7 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) = V + 7 >= V + 7 = isNePal(activate(V))
isPal(n__nil()) = 7 >= 0 = tt()
isQid(n__a()) = 0 >= 0 = tt()
isQid(n__e()) = 1 >= 0 = tt()
isQid(n__i()) = 0 >= 0 = tt()
isQid(n__o()) = 0 >= 0 = tt()
isQid(n__u()) = 1 >= 0 = tt()
nil() = 0 >= 0 = n__nil()
__(X1,X2) = 1X1 + X2 + 4 >= 1X1 + X2 + 4 = n____(X1,X2)
isList(X) = X + 0 >= X + 0 = n__isList(X)
isNeList(X) = X + 0 >= X + 0 = n__isNeList(X)
isPal(X) = X + 7 >= X + 7 = n__isPal(X)
a() = 0 >= 0 = n__a()
e() = 1 >= 1 = n__e()
i() = 0 >= 0 = n__i()
o() = 0 >= 0 = n__o()
u() = 1 >= 1 = n__u()
activate(n__nil()) = 0 >= 0 = nil()
activate(n____(X1,X2)) = 1X1 + X2 + 4 >= 1X1 + X2 + 4 = __(activate(X1),activate(X2))
activate(n__isList(X)) = X + 0 >= X + 0 = isList(X)
activate(n__isNeList(X)) = X + 0 >= X + 0 = isNeList(X)
activate(n__isPal(X)) = X + 7 >= X + 7 = isPal(X)
activate(n__a()) = 0 >= 0 = a()
activate(n__e()) = 1 >= 1 = e()
activate(n__i()) = 0 >= 0 = i()
activate(n__o()) = 0 >= 0 = o()
activate(n__u()) = 1 >= 1 = u()
activate(X) = X >= X = X
problem:
DPs:
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
and#(tt(),X) -> activate#(X)
activate#(n____(X1,X2)) -> activate#(X2)
activate#(n__isList(X)) -> isList#(X)
isList#(V) -> activate#(V)
activate#(n__isNeList(X)) -> isNeList#(X)
isNeList#(V) -> activate#(V)
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2)))
isList#(V) -> isNeList#(activate(V))
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
Arctic Interpretation Processor:
dimension: 1
interpretation:
[isNeList#](x0) = 1x0,
[isList#](x0) = 1x0,
[activate#](x0) = x0,
[and#](x0, x1) = x0 + x1 + 1,
[u] = 6,
[o] = 3,
[i] = 0,
[e] = 0,
[a] = 7,
[n__u] = 6,
[n__o] = 3,
[n__i] = 0,
[n__e] = 0,
[n__a] = 7,
[isPal](x0) = x0 + 0,
[n__isPal](x0) = x0 + 0,
[isNePal](x0) = x0 + 0,
[n__isNeList](x0) = 1x0 + 0,
[isQid](x0) = 0,
[n__isList](x0) = 1x0 + 0,
[n____](x0, x1) = x0 + x1 + 0,
[n__nil] = 1,
[isNeList](x0) = 1x0 + 0,
[isList](x0) = 1x0 + 0,
[activate](x0) = x0,
[and](x0, x1) = x1,
[tt] = 0,
[nil] = 1,
[__](x0, x1) = x0 + x1 + 0
orientation:
isNeList#(n____(V1,V2)) = 1V1 + 1V2 + 1 >= 1V1 + 1V2 + 1 = and#(isNeList(activate(V1)),n__isList(activate(V2)))
and#(tt(),X) = X + 1 >= X = activate#(X)
activate#(n____(X1,X2)) = X1 + X2 + 0 >= X2 = activate#(X2)
activate#(n__isList(X)) = 1X + 0 >= 1X = isList#(X)
isList#(V) = 1V >= V = activate#(V)
activate#(n__isNeList(X)) = 1X + 0 >= 1X = isNeList#(X)
isNeList#(V) = 1V >= V = activate#(V)
isNeList#(n____(V1,V2)) = 1V1 + 1V2 + 1 >= 1V1 + 1V2 + 1 = and#(isList(activate(V1)),n__isNeList(activate(V2)))
isList#(V) = 1V >= 1V = isNeList#(activate(V))
isList#(n____(V1,V2)) = 1V1 + 1V2 + 1 >= 1V1 + 1V2 + 1 = and#(isList(activate(V1)),n__isList(activate(V2)))
__(__(X,Y),Z) = X + Y + Z + 0 >= X + Y + Z + 0 = __(X,__(Y,Z))
__(X,nil()) = X + 1 >= X = X
__(nil(),X) = X + 1 >= X = X
and(tt(),X) = X >= X = activate(X)
isList(V) = 1V + 0 >= 1V + 0 = isNeList(activate(V))
isList(n__nil()) = 2 >= 0 = tt()
isList(n____(V1,V2)) = 1V1 + 1V2 + 1 >= 1V2 + 0 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) = 1V + 0 >= 0 = isQid(activate(V))
isNeList(n____(V1,V2)) = 1V1 + 1V2 + 1 >= 1V2 + 0 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) = 1V1 + 1V2 + 1 >= 1V2 + 0 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) = V + 0 >= 0 = isQid(activate(V))
isNePal(n____(I,n____(P,I))) = I + P + 0 >= P + 0 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) = V + 0 >= V + 0 = isNePal(activate(V))
isPal(n__nil()) = 1 >= 0 = tt()
isQid(n__a()) = 0 >= 0 = tt()
isQid(n__e()) = 0 >= 0 = tt()
isQid(n__i()) = 0 >= 0 = tt()
isQid(n__o()) = 0 >= 0 = tt()
isQid(n__u()) = 0 >= 0 = tt()
nil() = 1 >= 1 = n__nil()
__(X1,X2) = X1 + X2 + 0 >= X1 + X2 + 0 = n____(X1,X2)
isList(X) = 1X + 0 >= 1X + 0 = n__isList(X)
isNeList(X) = 1X + 0 >= 1X + 0 = n__isNeList(X)
isPal(X) = X + 0 >= X + 0 = n__isPal(X)
a() = 7 >= 7 = n__a()
e() = 0 >= 0 = n__e()
i() = 0 >= 0 = n__i()
o() = 3 >= 3 = n__o()
u() = 6 >= 6 = n__u()
activate(n__nil()) = 1 >= 1 = nil()
activate(n____(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = __(activate(X1),activate(X2))
activate(n__isList(X)) = 1X + 0 >= 1X + 0 = isList(X)
activate(n__isNeList(X)) = 1X + 0 >= 1X + 0 = isNeList(X)
activate(n__isPal(X)) = X + 0 >= X + 0 = isPal(X)
activate(n__a()) = 7 >= 7 = a()
activate(n__e()) = 0 >= 0 = e()
activate(n__i()) = 0 >= 0 = i()
activate(n__o()) = 3 >= 3 = o()
activate(n__u()) = 6 >= 6 = u()
activate(X) = X >= X = X
problem:
DPs:
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
and#(tt(),X) -> activate#(X)
activate#(n____(X1,X2)) -> activate#(X2)
activate#(n__isList(X)) -> isList#(X)
activate#(n__isNeList(X)) -> isNeList#(X)
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2)))
isList#(V) -> isNeList#(activate(V))
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
Matrix Interpretation Processor: dim=1
interpretation:
[isNeList#](x0) = 1,
[isList#](x0) = 1,
[activate#](x0) = x0 + 1,
[and#](x0, x1) = x1 + 1,
[u] = 4,
[o] = 0,
[i] = 2,
[e] = 1,
[a] = 0,
[n__u] = 4,
[n__o] = 0,
[n__i] = 2,
[n__e] = 1,
[n__a] = 0,
[isPal](x0) = 0,
[n__isPal](x0) = 0,
[isNePal](x0) = 0,
[n__isNeList](x0) = 0,
[isQid](x0) = 0,
[n__isList](x0) = 0,
[n____](x0, x1) = 4x0 + x1 + 1,
[n__nil] = 0,
[isNeList](x0) = 0,
[isList](x0) = 0,
[activate](x0) = x0,
[and](x0, x1) = x1,
[tt] = 0,
[nil] = 0,
[__](x0, x1) = 4x0 + x1 + 1
orientation:
isNeList#(n____(V1,V2)) = 1 >= 1 = and#(isNeList(activate(V1)),n__isList(activate(V2)))
and#(tt(),X) = X + 1 >= X + 1 = activate#(X)
activate#(n____(X1,X2)) = 4X1 + X2 + 2 >= X2 + 1 = activate#(X2)
activate#(n__isList(X)) = 1 >= 1 = isList#(X)
activate#(n__isNeList(X)) = 1 >= 1 = isNeList#(X)
isNeList#(n____(V1,V2)) = 1 >= 1 = and#(isList(activate(V1)),n__isNeList(activate(V2)))
isList#(V) = 1 >= 1 = isNeList#(activate(V))
isList#(n____(V1,V2)) = 1 >= 1 = and#(isList(activate(V1)),n__isList(activate(V2)))
__(__(X,Y),Z) = 16X + 4Y + Z + 5 >= 4X + 4Y + Z + 2 = __(X,__(Y,Z))
__(X,nil()) = 4X + 1 >= X = X
__(nil(),X) = X + 1 >= X = X
and(tt(),X) = X >= X = activate(X)
isList(V) = 0 >= 0 = isNeList(activate(V))
isList(n__nil()) = 0 >= 0 = tt()
isList(n____(V1,V2)) = 0 >= 0 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) = 0 >= 0 = isQid(activate(V))
isNeList(n____(V1,V2)) = 0 >= 0 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) = 0 >= 0 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) = 0 >= 0 = isQid(activate(V))
isNePal(n____(I,n____(P,I))) = 0 >= 0 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) = 0 >= 0 = isNePal(activate(V))
isPal(n__nil()) = 0 >= 0 = tt()
isQid(n__a()) = 0 >= 0 = tt()
isQid(n__e()) = 0 >= 0 = tt()
isQid(n__i()) = 0 >= 0 = tt()
isQid(n__o()) = 0 >= 0 = tt()
isQid(n__u()) = 0 >= 0 = tt()
nil() = 0 >= 0 = n__nil()
__(X1,X2) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = n____(X1,X2)
isList(X) = 0 >= 0 = n__isList(X)
isNeList(X) = 0 >= 0 = n__isNeList(X)
isPal(X) = 0 >= 0 = n__isPal(X)
a() = 0 >= 0 = n__a()
e() = 1 >= 1 = n__e()
i() = 2 >= 2 = n__i()
o() = 0 >= 0 = n__o()
u() = 4 >= 4 = n__u()
activate(n__nil()) = 0 >= 0 = nil()
activate(n____(X1,X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = __(activate(X1),activate(X2))
activate(n__isList(X)) = 0 >= 0 = isList(X)
activate(n__isNeList(X)) = 0 >= 0 = isNeList(X)
activate(n__isPal(X)) = 0 >= 0 = isPal(X)
activate(n__a()) = 0 >= 0 = a()
activate(n__e()) = 1 >= 1 = e()
activate(n__i()) = 2 >= 2 = i()
activate(n__o()) = 0 >= 0 = o()
activate(n__u()) = 4 >= 4 = u()
activate(X) = X >= X = X
problem:
DPs:
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
and#(tt(),X) -> activate#(X)
activate#(n__isList(X)) -> isList#(X)
activate#(n__isNeList(X)) -> isNeList#(X)
isNeList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isNeList(activate(V2)))
isList#(V) -> isNeList#(activate(V))
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
Matrix Interpretation Processor: dim=1
interpretation:
[isNeList#](x0) = x0 + 2,
[isList#](x0) = x0 + 2,
[activate#](x0) = 2x0,
[and#](x0, x1) = 2x1,
[u] = 1,
[o] = 2,
[i] = 0,
[e] = 1,
[a] = 0,
[n__u] = 1,
[n__o] = 2,
[n__i] = 0,
[n__e] = 1,
[n__a] = 0,
[isPal](x0) = 0,
[n__isPal](x0) = 0,
[isNePal](x0) = 0,
[n__isNeList](x0) = 1/2x0 + 1,
[isQid](x0) = 0,
[n__isList](x0) = 1/2x0 + 2,
[n____](x0, x1) = 2x0 + x1 + 2,
[n__nil] = 0,
[isNeList](x0) = 1/2x0 + 1,
[isList](x0) = 1/2x0 + 2,
[activate](x0) = x0,
[and](x0, x1) = x1,
[tt] = 0,
[nil] = 0,
[__](x0, x1) = 2x0 + x1 + 2
orientation:
isNeList#(n____(V1,V2)) = 2V1 + V2 + 4 >= V2 + 4 = and#(isNeList(activate(V1)),n__isList(activate(V2)))
and#(tt(),X) = 2X >= 2X = activate#(X)
activate#(n__isList(X)) = X + 4 >= X + 2 = isList#(X)
activate#(n__isNeList(X)) = X + 2 >= X + 2 = isNeList#(X)
isNeList#(n____(V1,V2)) = 2V1 + V2 + 4 >= V2 + 2 = and#(isList(activate(V1)),n__isNeList(activate(V2)))
isList#(V) = V + 2 >= V + 2 = isNeList#(activate(V))
isList#(n____(V1,V2)) = 2V1 + V2 + 4 >= V2 + 4 = and#(isList(activate(V1)),n__isList(activate(V2)))
__(__(X,Y),Z) = 4X + 2Y + Z + 6 >= 2X + 2Y + Z + 4 = __(X,__(Y,Z))
__(X,nil()) = 2X + 2 >= X = X
__(nil(),X) = X + 2 >= X = X
and(tt(),X) = X >= X = activate(X)
isList(V) = 1/2V + 2 >= 1/2V + 1 = isNeList(activate(V))
isList(n__nil()) = 2 >= 0 = tt()
isList(n____(V1,V2)) = V1 + 1/2V2 + 3 >= 1/2V2 + 2 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) = 1/2V + 1 >= 0 = isQid(activate(V))
isNeList(n____(V1,V2)) = V1 + 1/2V2 + 2 >= 1/2V2 + 1 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) = V1 + 1/2V2 + 2 >= 1/2V2 + 2 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) = 0 >= 0 = isQid(activate(V))
isNePal(n____(I,n____(P,I))) = 0 >= 0 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) = 0 >= 0 = isNePal(activate(V))
isPal(n__nil()) = 0 >= 0 = tt()
isQid(n__a()) = 0 >= 0 = tt()
isQid(n__e()) = 0 >= 0 = tt()
isQid(n__i()) = 0 >= 0 = tt()
isQid(n__o()) = 0 >= 0 = tt()
isQid(n__u()) = 0 >= 0 = tt()
nil() = 0 >= 0 = n__nil()
__(X1,X2) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = n____(X1,X2)
isList(X) = 1/2X + 2 >= 1/2X + 2 = n__isList(X)
isNeList(X) = 1/2X + 1 >= 1/2X + 1 = n__isNeList(X)
isPal(X) = 0 >= 0 = n__isPal(X)
a() = 0 >= 0 = n__a()
e() = 1 >= 1 = n__e()
i() = 0 >= 0 = n__i()
o() = 2 >= 2 = n__o()
u() = 1 >= 1 = n__u()
activate(n__nil()) = 0 >= 0 = nil()
activate(n____(X1,X2)) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = __(activate(X1),activate(X2))
activate(n__isList(X)) = 1/2X + 2 >= 1/2X + 2 = isList(X)
activate(n__isNeList(X)) = 1/2X + 1 >= 1/2X + 1 = isNeList(X)
activate(n__isPal(X)) = 0 >= 0 = isPal(X)
activate(n__a()) = 0 >= 0 = a()
activate(n__e()) = 1 >= 1 = e()
activate(n__i()) = 0 >= 0 = i()
activate(n__o()) = 2 >= 2 = o()
activate(n__u()) = 1 >= 1 = u()
activate(X) = X >= X = X
problem:
DPs:
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
and#(tt(),X) -> activate#(X)
activate#(n__isNeList(X)) -> isNeList#(X)
isList#(V) -> isNeList#(activate(V))
isList#(n____(V1,V2)) -> and#(isList(activate(V1)),n__isList(activate(V2)))
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
SCC Processor:
#sccs: 1
#rules: 3
#arcs: 32/25
DPs:
isNeList#(n____(V1,V2)) -> and#(isNeList(activate(V1)),n__isList(activate(V2)))
and#(tt(),X) -> activate#(X)
activate#(n__isNeList(X)) -> isNeList#(X)
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
Arctic Interpretation Processor:
dimension: 1
interpretation:
[isNeList#](x0) = 3,
[activate#](x0) = x0 + 1,
[and#](x0, x1) = x1 + 1,
[u] = 6,
[o] = 5,
[i] = 2,
[e] = 4,
[a] = 5,
[n__u] = 5,
[n__o] = 4,
[n__i] = 2,
[n__e] = 3,
[n__a] = 5,
[isPal](x0) = 1x0 + 4,
[n__isPal](x0) = x0 + 3,
[isNePal](x0) = x0 + 0,
[n__isNeList](x0) = 3,
[isQid](x0) = 0,
[n__isList](x0) = 0,
[n____](x0, x1) = 2x0 + x1 + 5,
[n__nil] = 4,
[isNeList](x0) = 4,
[isList](x0) = 4,
[activate](x0) = 1x0 + 4,
[and](x0, x1) = x0 + 1x1 + 4,
[tt] = 0,
[nil] = 4,
[__](x0, x1) = 2x0 + x1 + 5
orientation:
isNeList#(n____(V1,V2)) = 3 >= 1 = and#(isNeList(activate(V1)),n__isList(activate(V2)))
and#(tt(),X) = X + 1 >= X + 1 = activate#(X)
activate#(n__isNeList(X)) = 3 >= 3 = isNeList#(X)
__(__(X,Y),Z) = 4X + 2Y + Z + 7 >= 2X + 2Y + Z + 5 = __(X,__(Y,Z))
__(X,nil()) = 2X + 5 >= X = X
__(nil(),X) = X + 6 >= X = X
and(tt(),X) = 1X + 4 >= 1X + 4 = activate(X)
isList(V) = 4 >= 4 = isNeList(activate(V))
isList(n__nil()) = 4 >= 0 = tt()
isList(n____(V1,V2)) = 4 >= 4 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) = 4 >= 0 = isQid(activate(V))
isNeList(n____(V1,V2)) = 4 >= 4 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) = 4 >= 4 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) = V + 0 >= 0 = isQid(activate(V))
isNePal(n____(I,n____(P,I))) = 2I + 2P + 5 >= 2P + 5 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) = 1V + 4 >= 1V + 4 = isNePal(activate(V))
isPal(n__nil()) = 5 >= 0 = tt()
isQid(n__a()) = 0 >= 0 = tt()
isQid(n__e()) = 0 >= 0 = tt()
isQid(n__i()) = 0 >= 0 = tt()
isQid(n__o()) = 0 >= 0 = tt()
isQid(n__u()) = 0 >= 0 = tt()
nil() = 4 >= 4 = n__nil()
__(X1,X2) = 2X1 + X2 + 5 >= 2X1 + X2 + 5 = n____(X1,X2)
isList(X) = 4 >= 0 = n__isList(X)
isNeList(X) = 4 >= 3 = n__isNeList(X)
isPal(X) = 1X + 4 >= X + 3 = n__isPal(X)
a() = 5 >= 5 = n__a()
e() = 4 >= 3 = n__e()
i() = 2 >= 2 = n__i()
o() = 5 >= 4 = n__o()
u() = 6 >= 5 = n__u()
activate(n__nil()) = 5 >= 4 = nil()
activate(n____(X1,X2)) = 3X1 + 1X2 + 6 >= 3X1 + 1X2 + 6 = __(activate(X1),activate(X2))
activate(n__isList(X)) = 4 >= 4 = isList(X)
activate(n__isNeList(X)) = 4 >= 4 = isNeList(X)
activate(n__isPal(X)) = 1X + 4 >= 1X + 4 = isPal(X)
activate(n__a()) = 6 >= 5 = a()
activate(n__e()) = 4 >= 4 = e()
activate(n__i()) = 4 >= 2 = i()
activate(n__o()) = 5 >= 5 = o()
activate(n__u()) = 6 >= 6 = u()
activate(X) = 1X + 4 >= X = X
problem:
DPs:
and#(tt(),X) -> activate#(X)
activate#(n__isNeList(X)) -> isNeList#(X)
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
SCC Processor:
#sccs: 0
#rules: 0
#arcs: 3/4
DPs:
__#(__(X,Y),Z) -> __#(Y,Z)
__#(__(X,Y),Z) -> __#(X,__(Y,Z))
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
Subterm Criterion Processor:
simple projection:
pi(__#) = 0
problem:
DPs:
TRS:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X,nil()) -> X
__(nil(),X) -> X
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) -> isQid(activate(V))
isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isNeList(X) -> n__isNeList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
o() -> n__o()
u() -> n__u()
activate(n__nil()) -> nil()
activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
activate(n__isList(X)) -> isList(X)
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
Qed