Termination proof of /tmp/tmphi0nSV/Ex1_GM03

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
p(0) → 0
p(s(X)) → X
leq(0, Y) → true
leq(s(X), 0) → false
leq(s(X), s(Y)) → leq(X, Y)
diff(X, Y) → if(leq(X, Y))

↳ 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
p(0) → 0
p(s(X)) → X
leq(0, Y) → true
leq(s(X), 0) → false
leq(s(X), s(Y)) → leq(X, Y)
diff(X, Y) → if(leq(X, Y))

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