(VAR L X V1 V V2 N X1 X2)
(RULES 
a__zeros -> cons(0,zeros)
a__U11(tt,L) -> s(a__length(mark(L)))
a__and(tt,X) -> mark(X)
a__isNat(0) -> tt
a__isNat(length(V1)) -> a__isNatList(V1)
a__isNat(s(V1)) -> a__isNat(V1)
a__isNatIList(V) -> a__isNatList(V)
a__isNatIList(zeros) -> tt
a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2))
a__isNatList(nil) -> tt
a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2))
a__length(nil) -> 0
a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L)
mark(zeros) -> a__zeros
mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
mark(length(X)) -> a__length(mark(X))
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(isNat(X)) -> a__isNat(X)
mark(isNatList(X)) -> a__isNatList(X)
mark(isNatIList(X)) -> a__isNatIList(X)
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(0) -> 0
mark(tt) -> tt
mark(s(X)) -> s(mark(X))
mark(nil) -> nil
a__zeros -> zeros
a__U11(X1,X2) -> U11(X1,X2)
a__length(X) -> length(X)
a__and(X1,X2) -> and(X1,X2)
a__isNat(X) -> isNat(X)
a__isNatList(X) -> isNatList(X)
a__isNatIList(X) -> isNatIList(X)
)