Certification Problem

Input (COPS 761)

We consider the TRS containing the following rules:

a b (1)
a d (2)
b a (3)
c a (4)
c b (5)

The underlying signature is as follows:

{a/0, b/0, d/0, c/0}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by csi @ CoCo 2020)

1 Redundant Rules Transformation

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

c b (5)
c a (4)
b a (3)
a d (2)
a b (1)
c d (6)
b d (7)
b b (8)
a a (9)

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).