(0) Obligation:

Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:

sel(s(X), cons(Y)) → sel(X, Z)
sel1(s(X), cons(Y)) → sel1(X, Z)
first1(s(X), cons(Y)) → cons1(quote, first1(X, Z))
quotesel1(X, Z)
quote1first1(X, Z)
sel(0, cons(X)) → X
first(0, Z) → nil
first(s(X), cons(Y)) → cons(Y)
from(X) → cons(X)
sel1(0, cons(X)) → quote
first1(0, Z) → nil1
quote01
quote1cons1(quote, quote1)
quote1nil1
quotes1(quote)
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)

(1) CritRuleProof (EQUIVALENT transformation)

The rule sel(s(X), cons(Y)) → sel(X, Z) contains free variables in its right-hand side. Hence the TRS is not-terminating.

(2) NO