Certificate for #3385 ⟨a, b | aa=1, abbbba=b⟩

Back:⟨a, b | aa=1, abbbba=b⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #3.

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

[2] abbbba=b

Axiom: abbbba=b.

Referenced by [3], [4].

[3] bbbba=ab

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

a a abbbba

Critical pair: ab=bbbba.

Flip LHS and RHS.

Referenced by [5].

[4] ba=abbbb

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

abbbb a aa

Critical pair: abbbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] abbbbbbbbbbbbbbbb=ab

Simplify [3] bbbba=ab.

Reduce LHS:

[4]bbb(ba)
[4]⇒ bb(ba)bbbb
[4]⇒ b(ba)bbbbbbbb
[4]⇒ (ba)bbbbbbbbbbbb
⇒ abbbbbbbbbbbbbbbb

Referenced by [6].

[6] bbbbbbbbbbbbbbbb=b

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

a a abbbbbbbbbbbbbbbb

Critical pair: aab=bbbbbbbbbbbbbbbb.

Reduce LHS:

[1](aa)b
⇒ b

Flip LHS and RHS.

Defines rule #1.