Certificate for #19817 ⟨a, b | aaa=a, abba=abb⟩

Back:⟨a, b | aaa=a, abba=abb⟩

Completion settings:

[1] aaa=a

Axiom: aaa=a.

Defines rule #2.

Referenced by [6].

[2] abba=abb

Axiom: abba=abb.

Referenced by [4].

[3] ab=c

Axiom: ab=c.

Defines rule #1.

Referenced by [4], [5], [6], [7].

[4] abba=cb

Simplify [2] abba=abb.

Reduce RHS:

[3](ab)b
⇒ cb

Referenced by [5].

[5] cba=cb

Overlap of [4] abba=cb with [3] ab=c:

abba ab

Critical pair: cba=cb.

Defines rule #4.

Referenced by [7].

[6] aac=c

Overlap of [1] aaa=a with [3] ab=c:

aa a ab

Critical pair: aac=ab.

Reduce RHS:

[3](ab)
⇒ c

Defines rule #3.

[7] cbb=cbc

Overlap of [5] cba=cb with [3] ab=c:

cb a ab

Critical pair: cbc=cbb.

Flip LHS and RHS.

Defines rule #5.