Certificate for #12263 ⟨a, b | aaab=ab, bbaa=b⟩

Back:⟨a, b | aaab=ab, bbaa=b⟩

Completion settings:

[1] aaab=ab

Axiom: aaab=ab.

Defines rule #3.

Referenced by [3].

[2] bbaa=b

Axiom: bbaa=b.

Referenced by [3], [4], [5], [6].

[3] baab=bb

Overlap of [2] bbaa=b with [1] aaab=ab:

bba a aaab

Critical pair: bbaab=baab.

Reduce LHS:

[2](bbaa)b
⇒ bb

Flip LHS and RHS.

Referenced by [4], [5].

[4] bbb=bb

Overlap of [2] bbaa=b with [3] baab=bb:

b baa baab

Critical pair: bbb=bb.

Referenced by [5].

[5] bb=b

Overlap of [3] baab=bb with [2] bbaa=b:

baa b bbaa

Critical pair: baab=bbbaa.

Reduce LHS:

[3](baab)
⇒ bb

Reduce RHS:

[4](bbb)aa
[2]⇒ (bbaa)
⇒ b

Defines rule #1.

Referenced by [6].

[6] baa=b

Overlap of [2] bbaa=b with [5] bb=b:

bbaa bb

Critical pair: baa=b.

Defines rule #2.