Problem:
dbl(0()) -> 0()
dbl(s(X)) -> s(s(dbl(X)))
dbls(nil()) -> nil()
dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
sel(0(),cons(X,Y)) -> X
sel(s(X),cons(Y,Z)) -> sel(X,Z)
indx(nil(),X) -> nil()
indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
from(X) -> cons(X,from(s(X)))
dbl1(0()) -> 01()
dbl1(s(X)) -> s1(s1(dbl1(X)))
sel1(0(),cons(X,Y)) -> X
sel1(s(X),cons(Y,Z)) -> sel1(X,Z)
quote(0()) -> 01()
quote(s(X)) -> s1(quote(X))
quote(dbl(X)) -> dbl1(X)
quote(sel(X,Y)) -> sel1(X,Y)
Proof:
Containment Processor: loop length: 1
terms:
from(X)
context: cons(X,[])
substitution:
X -> s(X)
Qed