Certificate for #9755 ⟨a, b | aa=1, abbbbab=b⟩

Back:⟨a, b | aa=1, abbbbab=b⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #1.

Referenced by [3], [5].

[2] abbbbab=b

Axiom: abbbbab=b.

Referenced by [3], [4].

[3] bbbbab=ab

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

a a abbbbab

Critical pair: ab=bbbbab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] abbbbb=ab

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

abbbb ab abbbbab

Critical pair: abbbbb=bbbbab.

Reduce RHS:

[3](bbbbab)
⇒ ab

Referenced by [5].

[5] bbbbb=b

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

a a abbbbb

Critical pair: aab=bbbbb.

Reduce LHS:

[1](aa)b
⇒ b

Flip LHS and RHS.

Defines rule #2.