(0) Obligation:

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

tail(cons(X)) → L
incr(nil) → nil
incr(cons(X)) → cons(s(X))
adx(nil) → nil
adx(cons(X)) → incr(cons(X))
natsadx(zeros)
zeroscons(0)
head(cons(X)) → X

(1) CritRuleProof (EQUIVALENT transformation)

The rule tail(cons(X)) → L contains free variables in its right-hand side. Hence the TRS is not-terminating.

(2) NO