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:

if(false, X) → Y
f(X) → if(X, c)
if(true, X) → X

(1) CritRuleProof (EQUIVALENT transformation)

The rule if(false, X) → Y contains free variables in its right-hand side. Hence the TRS is not-terminating.

(2) NO