(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
g(a) → g(b)
b → f(a, a)
f(a, a) → g(d)
Q is empty.
(1) Overlay + Local Confluence (EQUIVALENT transformation)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
g(a) → g(b)
b → f(a, a)
f(a, a) → g(d)
The set Q consists of the following terms:
g(a)
b
f(a, a)
(3) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
G(a) → G(b)
G(a) → B
B → F(a, a)
F(a, a) → G(d)
The TRS R consists of the following rules:
g(a) → g(b)
b → f(a, a)
f(a, a) → g(d)
The set Q consists of the following terms:
g(a)
b
f(a, a)
We have to consider all minimal (P,Q,R)-chains.
(5) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 4 less nodes.
(6) TRUE