(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))
nats → adx(zeros)
zeros → cons(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) FALSE