Problem:
sel(s(X),cons(Y,Z)) -> sel(X,Z)
sel(0(),cons(X,Z)) -> X
first(0(),Z) -> nil()
first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
from(X) -> cons(X,from(s(X)))
sel1(s(X),cons(Y,Z)) -> sel1(X,Z)
sel1(0(),cons(X,Z)) -> quote(X)
first1(0(),Z) -> nil1()
first1(s(X),cons(Y,Z)) -> cons1(quote(Y),first1(X,Z))
quote(0()) -> 01()
quote1(cons(X,Z)) -> cons1(quote(X),quote1(Z))
quote1(nil()) -> nil1()
quote(s(X)) -> s1(quote(X))
quote(sel(X,Z)) -> sel1(X,Z)
quote1(first(X,Z)) -> first1(X,Z)
unquote(01()) -> 0()
unquote(s1(X)) -> s(unquote(X))
unquote1(nil1()) -> nil()
unquote1(cons1(X,Z)) -> fcons(unquote(X),unquote1(Z))
fcons(X,Z) -> cons(X,Z)
Proof:
Containment Processor: loop length: 1
terms:
from(X)
context: cons(X,[])
substitution:
X -> s(X)
Qed