(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(X) → if(X, c, n__f(true))
if(true, X, Y) → X
if(false, X, Y) → activate(Y)
f(X) → n__f(X)
activate(n__f(X)) → f(X)
activate(X) → X
Q is empty.
(1) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(2) Obligation:
Q DP problem:
The TRS P consists of the following rules:
F(X) → IF(X, c, n__f(true))
IF(false, X, Y) → ACTIVATE(Y)
ACTIVATE(n__f(X)) → F(X)
The TRS R consists of the following rules:
f(X) → if(X, c, n__f(true))
if(true, X, Y) → X
if(false, X, Y) → activate(Y)
f(X) → n__f(X)
activate(n__f(X)) → f(X)
activate(X) → X
Q is empty.
We have to consider all minimal (P,Q,R)-chains.