(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)
a → b
a → c
Q is empty.
(1) AAECC Innermost (EQUIVALENT transformation)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none
The TRS R 2 is
f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)
a → b
a → c
The signature Sigma is {
c,
a,
f,
g,
b}
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)
a → b
a → c
The set Q consists of the following terms:
f(x0, x1, x2)
g(0, 1, x0)
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:
F(x, y, z) → G(x, y, z)
G(0, 1, x) → F(x, x, x)
The TRS R consists of the following rules:
f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)
a → b
a → c
The set Q consists of the following terms:
f(x0, x1, x2)
g(0, 1, x0)
a
We have to consider all minimal (P,Q,R)-chains.