Termination of the following Term Rewriting System could be disproven:
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
↳ GTRS
↳ CritRuleProof
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
The rule tail(cons(X)) → XS contains free variables in its right-hand side. Hence the TRS is not-terminating.