(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(n__f(n__a)) → f(n__g(f(n__a)))
f(X) → n__f(X)
a → n__a
g(X) → n__g(X)
activate(n__f(X)) → f(X)
activate(n__a) → a
activate(n__g(X)) → g(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(n__f(n__a)) → F(n__g(f(n__a)))
F(n__f(n__a)) → F(n__a)
ACTIVATE(n__f(X)) → F(X)
ACTIVATE(n__a) → A
ACTIVATE(n__g(X)) → G(X)
The TRS R consists of the following rules:
f(n__f(n__a)) → f(n__g(f(n__a)))
f(X) → n__f(X)
a → n__a
g(X) → n__g(X)
activate(n__f(X)) → f(X)
activate(n__a) → a
activate(n__g(X)) → g(X)
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 0 SCCs with 5 less nodes.
(4) TRUE