Certificate for #26635 ⟨a, b | aa=1, abbbbbab=b⟩

Back:⟨a, b | aa=1, abbbbbab=b⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #1.

Referenced by [3], [5].

[2] abbbbbab=b

Axiom: abbbbbab=b.

Referenced by [3], [4].

[3] bbbbbab=ab

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

a a abbbbbab

Critical pair: ab=bbbbbab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] abbbbbb=ab

Overlap of [2] abbbbbab=b with [2] abbbbbab=b:

abbbbb ab abbbbbab

Critical pair: abbbbbb=bbbbbab.

Reduce RHS:

[3](bbbbbab)
⇒ ab

Referenced by [5].

[5] bbbbbb=b

Overlap of [1] aa=1 with [4] abbbbbb=ab:

a a abbbbbb

Critical pair: aab=bbbbbb.

Reduce LHS:

[1](aa)b
⇒ b

Flip LHS and RHS.

Defines rule #2.