Certificate for #19602 ⟨a, b | aab=b, bbaaa=ba⟩

Back:⟨a, b | aab=b, bbaaa=ba⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #1.

Referenced by [3].

[2] bbaaa=ba

Axiom: bbaaa=ba.

Referenced by [3], [4], [5].

[3] bbb=bb

Overlap of [2] bbaaa=ba with [1] aab=b:

bbaa a aab

Critical pair: bbaab=baab.

Reduce LHS:

[1]bb(aab)
⇒ bbb

Reduce RHS:

[1]b(aab)
⇒ bb

Defines rule #3.

Referenced by [4].

[4] bba=ba

Overlap of [3] bbb=bb with [2] bbaaa=ba:

b bb bbaaa

Critical pair: bba=bbaaa.

Reduce RHS:

[2](bbaaa)
⇒ ba

Defines rule #2.

Referenced by [5].

[5] baaa=ba

Overlap of [2] bbaaa=ba with [4] bba=ba:

bbaaa bba

Critical pair: baaa=ba.

Defines rule #4.