Certificate for #2089 ⟨a, b | abbbbbba=ab⟩

Back:⟨a, b | abbbbbba=ab⟩

Completion settings:

[1] abbbbbba=ab

Axiom: abbbbbba=ab.

Referenced by [3].

[2] abbbbbb=c

Axiom: abbbbbb=c.

Referenced by [3], [4].

[3] ab=ca

Overlap of [1] abbbbbba=ab with [2] abbbbbb=c:

abbbbbba abbbbbb

Critical pair: ca=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5].

[4] cccccca=c

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

abbbbbb ab

Critical pair: cabbbbb=c.

Reduce LHS:

[3]c(ab)bbbb
[3]⇒ cc(ab)bbb
[3]⇒ ccc(ab)bb
[3]⇒ cccc(ab)b
[3]⇒ ccccc(ab)
⇒ cccccca

Defines rule #3.

Referenced by [5].

[5] cb=cc

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

cccccc a ab

Critical pair: ccccccca=cb.

Reduce LHS:

[4]c(cccccca)
⇒ cc

Flip LHS and RHS.

Defines rule #1.