Certificate for #928 ⟨a, b, c | aa=b, bcb=a⟩

Completion settings:

[1] b=aa

Axiom: aa=b.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2].

[2] aacaa=a

Axiom: bcb=a.

Reduce LHS:

[1](b)cb
[1]⇒ aac(b)
⇒ aacaa

Referenced by [3], [4].

[3] acaa=aaca

Overlap of [2] aacaa=a with [2] aacaa=a:

aac aa aacaa

Critical pair: aaca=acaa.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4].

[4] aaaca=a

Overlap of [2] aacaa=a with [3] acaa=aaca:

a acaa acaa

Critical pair: aaaca=a.

Defines rule #2.