Termination proof of /tmp/tmpPzr_UW/Ex15_Luc98

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:

and(true) → X
if(true) → X
if(false) → Y
add(0) → X
and(false) → false
add(s) → s
first(0, X) → nil
first(s, cons) → cons
from → cons

↳ GTRS

  ↳ CritRuleProof

Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:

and(true) → X
if(true) → X
if(false) → Y
add(0) → X
and(false) → false
add(s) → s
first(0, X) → nil
first(s, cons) → cons
from → cons

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