(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(s(x), y) → f(x, s(x))
f(x, s(y)) → f(y, x)
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(s(x), y) → f(x, s(x))
f(x, s(y)) → f(y, x)
The signature Sigma is {
f}
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(s(x), y) → f(x, s(x))
f(x, s(y)) → f(y, x)
The set Q consists of the following terms:
f(s(x0), x1)
f(x0, s(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:
F(s(x), y) → F(x, s(x))
F(x, s(y)) → F(y, x)
The TRS R consists of the following rules:
f(s(x), y) → f(x, s(x))
f(x, s(y)) → f(y, x)
The set Q consists of the following terms:
f(s(x0), x1)
f(x0, s(x1))
We have to consider all minimal (P,Q,R)-chains.