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:

tail(cons(X)) → XS
nats → cons(0)
pairs → cons(0)
odds → incr(pairs)
incr(cons(X)) → cons(s(X))
head(cons(X)) → X

(1) CritRuleProof (EQUIVALENT transformation)

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

(2) NO