(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, y) → x
g(a) → h(a, b, a)
i(x) → f(x, x)
h(x, x, y) → g(x)
Q is empty.
(1) AAECC Innermost (EQUIVALENT transformation)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is
f(x, y) → x
i(x) → f(x, x)
The TRS R 2 is
g(a) → h(a, b, a)
h(x, x, y) → g(x)
The signature Sigma is {
g,
h}
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, y) → x
g(a) → h(a, b, a)
i(x) → f(x, x)
h(x, x, y) → g(x)
The set Q consists of the following terms:
f(x0, x1)
g(a)
i(x0)
h(x0, x0, x1)
(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) → H(a, b, a)
I(x) → F(x, x)
H(x, x, y) → G(x)
The TRS R consists of the following rules:
f(x, y) → x
g(a) → h(a, b, a)
i(x) → f(x, x)
h(x, x, y) → g(x)
The set Q consists of the following terms:
f(x0, x1)
g(a)
i(x0)
h(x0, x0, x1)
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 3 less nodes.
(6) TRUE