(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(n__a, X, X) → f(activate(X), b, n__b)
b → a
a → n__a
b → n__b
activate(n__a) → a
activate(n__b) → b
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(n__a, X, X) → F(activate(X), b, n__b)
F(n__a, X, X) → ACTIVATE(X)
F(n__a, X, X) → B
B → A
ACTIVATE(n__a) → A
ACTIVATE(n__b) → B
The TRS R consists of the following rules:
f(n__a, X, X) → f(activate(X), b, n__b)
b → a
a → n__a
b → n__b
activate(n__a) → a
activate(n__b) → b
activate(X) → X
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
(3) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
F(n__a, X, X) → F(activate(X), b, n__b)
The TRS R consists of the following rules:
f(n__a, X, X) → f(activate(X), b, n__b)
b → a
a → n__a
b → n__b
activate(n__a) → a
activate(n__b) → b
activate(X) → X
Q is empty.
We have to consider all minimal (P,Q,R)-chains.