Certificate for #483 ⟨a, b | abbbba=ab⟩

Back:⟨a, b | abbbba=ab⟩

Completion settings:

[1] abbbba=ab

Axiom: abbbba=ab.

Referenced by [3].

[2] abbbb=c

Axiom: abbbb=c.

Referenced by [3], [4].

[3] ab=ca

Overlap of [1] abbbba=ab with [2] abbbb=c:

abbbba abbbb

Critical pair: ca=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5].

[4] cccca=c

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

abbbb ab

Critical pair: cabbb=c.

Reduce LHS:

[3]c(ab)bb
[3]⇒ cc(ab)b
[3]⇒ ccc(ab)
⇒ cccca

Defines rule #3.

Referenced by [5].

[5] cb=cc

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

cccc a ab

Critical pair: ccccca=cb.

Reduce LHS:

[4]c(cccca)
⇒ cc

Flip LHS and RHS.

Defines rule #1.