(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)) → Y
if(true) → X
if(false) → Y
primes → sieve(from(s(s(0))))
from(X) → cons(X)
head(cons(X)) → X
filter(s(s(X)), cons(Y)) → if(divides(s(s(X)), Y))
sieve(cons(X)) → cons(X)
(1) CritRuleProof (EQUIVALENT transformation)
The rule tail(cons(X)) → Y contains free variables in its right-hand side. Hence the TRS is not-terminating.
(2) NO