Certification Problem

Input (COPS 705)

We consider the TRS containing the following rules:

a → c (1)
c → a (2)
c → h(a,c) (3)

The underlying signature is as follows:

{a/0, c/0, h/2}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by csi @ CoCo 2022)

1 Redundant Rules Transformation

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

c → h(a,c) (3)
c → a (2)
a → c (1)
a → h(a,c) (4)

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).