Certificate for #9757 ⟨a, b | aa=1, abbbbba=b⟩

Back:⟨a, b | aa=1, abbbbba=b⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #3.

Referenced by [3], [4], [6].

[2] abbbbba=b

Axiom: abbbbba=b.

Referenced by [3], [4].

[3] bbbbba=ab

Overlap of [1] aa=1 with [2] abbbbba=b:

a a abbbbba

Critical pair: ab=bbbbba.

Flip LHS and RHS.

Referenced by [5].

[4] ba=abbbbb

Overlap of [2] abbbbba=b with [1] aa=1:

abbbbb a aa

Critical pair: abbbbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] abbbbbbbbbbbbbbbbbbbbbbbbb=ab

Simplify [3] bbbbba=ab.

Reduce LHS:

[4]bbbb(ba)
[4]⇒ bbb(ba)bbbbb
[4]⇒ bb(ba)bbbbbbbbbb
[4]⇒ b(ba)bbbbbbbbbbbbbbb
[4]⇒ (ba)bbbbbbbbbbbbbbbbbbbb
⇒ abbbbbbbbbbbbbbbbbbbbbbbbb

Referenced by [6].

[6] bbbbbbbbbbbbbbbbbbbbbbbbb=b

Overlap of [1] aa=1 with [5] abbbbbbbbbbbbbbbbbbbbbbbbb=ab:

a a abbbbbbbbbbbbbbbbbbbbbbbbb

Critical pair: aab=bbbbbbbbbbbbbbbbbbbbbbbbb.

Reduce LHS:

[1](aa)b
⇒ b

Flip LHS and RHS.

Defines rule #1.