Termination proof of /tmp/tmp92aTKz/ExIntrod_Zan97

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:

if(true) → X
if(false) → Y
fact(X) → if(zero(X))
add(0, X) → X
add(s(X), Y) → s(add(X, Y))
prod(0, X) → 0
prod(s(X), Y) → add(Y, prod(X, Y))
zero(0) → true
zero(s(X)) → false
p(s(X)) → X

↳ GTRS

  ↳ CritRuleProof

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
fact(X) → if(zero(X))
add(0, X) → X
add(s(X), Y) → s(add(X, Y))
prod(0, X) → 0
prod(s(X), Y) → add(Y, prod(X, Y))
zero(0) → true
zero(s(X)) → false
p(s(X)) → X

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