(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(g(X), Y) → f(X, f(g(X), Y))
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(g(X), Y) → F(X, f(g(X), Y))
F(g(X), Y) → F(g(X), Y)
The TRS R consists of the following rules:
f(g(X), Y) → f(X, f(g(X), Y))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
(3) NonLoopProof (EQUIVALENT transformation)
By Theorem 8 [NONLOOP] we deduce infiniteness of the QDP.
We apply the theorem with m = 1, b = 0,
σ' = [ ], and μ' = [ ] on the rule
F(g(x1), x0)[ ]n[ ] → F(g(x1), x0)[ ]n[ ]
This rule is correct for the QDP as the following derivation shows:
intermediate steps: Instantiation
F(g(X), Y)[ ]n[ ] → F(g(X), Y)[ ]n[ ]
by OriginalRule from TRS P
(4) NO