Termination of the given GTRS could be disproven:

(0) Obligation:

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

hd(cons) → X
tl(cons) → Y
nats → adx(zeros)
zeros → cons
incr(cons) → cons
adx(cons) → incr(cons)

(1) CritRuleProof (EQUIVALENT transformation)

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

(2) FALSE