Certification Problem

Input (COPS 503)

We consider the TRS containing the following rules:

f(a,a,b,b) f(c,c,c,c) (1)
a b (2)
a c (3)
b a (4)
b c (5)

The underlying signature is as follows:

{f/4, a/0, b/0, c/0}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by csi @ CoCo 2023)

1 Redundant Rules Transformation

To prove that the TRS is (non-)confluent, we show (non-)confluence of the following modified system:

b c (5)
b a (4)
a c (3)
a b (2)
f(a,a,b,b) f(c,c,c,c) (1)
b b (6)
a a (7)

All redundant rules that were added or removed can be simulated in 2 steps .

1.1 Parallel Closed

Confluence is proven since the TRS is (almost) parallel closed. The joins can be performed using 1 parallel step(s).