(0) Obligation:
Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:
if(true) → X
if(false) → Y
minus → 0
minus → minus
geq → true
geq → false
geq → geq
div(0) → 0
div(s(X)) → if(geq)
(1) CritRuleProof (EQUIVALENT transformation)
The rule if(true) → X contains free variables in its right-hand side. Hence the TRS is not-terminating.
(2) NO