Certificate for #26637 ⟨a, b | aa=1, abbbbbba=b⟩

Back:⟨a, b | aa=1, abbbbbba=b⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #3.

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

[2] abbbbbba=b

Axiom: abbbbbba=b.

Referenced by [3], [4].

[3] bbbbbba=ab

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

a a abbbbbba

Critical pair: ab=bbbbbba.

Flip LHS and RHS.

Referenced by [5].

[4] ba=abbbbbb

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

abbbbbb a aa

Critical pair: abbbbbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=ab

Simplify [3] bbbbbba=ab.

Reduce LHS:

[4]bbbbb(ba)
[4]⇒ bbbb(ba)bbbbbb
[4]⇒ bbb(ba)bbbbbbbbbbbb
[4]⇒ bb(ba)bbbbbbbbbbbbbbbbbb
[4]⇒ b(ba)bbbbbbbbbbbbbbbbbbbbbbbb
[4]⇒ (ba)bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
⇒ abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Referenced by [6].

[6] bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=b

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

a a abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Critical pair: aab=bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Reduce LHS:

[1](aa)b
⇒ b

Flip LHS and RHS.

Defines rule #1.