Certificate for #231 ⟨a, b | abbba=ab⟩

Back:⟨a, b | abbba=ab⟩

Completion settings:

[1] abbba=ab

Axiom: abbba=ab.

Referenced by [3].

[2] abbb=c

Axiom: abbb=c.

Referenced by [3], [4].

[3] ab=ca

Overlap of [1] abbba=ab with [2] abbb=c:

abbba abbb

Critical pair: ca=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5].

[4] ccca=c

Overlap of [2] abbb=c with [3] ab=ca:

abbb ab

Critical pair: cabb=c.

Reduce LHS:

[3]c(ab)b
[3]⇒ cc(ab)
⇒ ccca

Defines rule #3.

Referenced by [5].

[5] cb=cc

Overlap of [4] ccca=c with [3] ab=ca:

ccc a ab

Critical pair: cccca=cb.

Reduce LHS:

[4]c(ccca)
⇒ cc

Flip LHS and RHS.

Defines rule #1.