Certificate for #7143 ⟨a, b | bb=aa, aaab=ba⟩

Back:⟨a, b | bb=aa, aaab=ba⟩

Completion settings:

[1] aa=bb

Axiom: bb=aa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3], [5].

[2] bbab=ba

Axiom: aaab=ba.

Reduce LHS:

[1](aa)ab
⇒ bbab

Referenced by [4].

[3] bba=abb

Overlap of [1] aa=bb with [1] aa=bb:

a a aa

Critical pair: abb=bba.

Flip LHS and RHS.

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

[4] ba=abbb

Simplify [2] bbab=ba.

Reduce LHS:

[3](bba)b
⇒ abbb

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [6].

[5] bbbbbbb=bbb

Overlap of [4] ba=abbb with [1] aa=bb:

b a aa

Critical pair: bbb=abbba.

Reduce RHS:

[3]ab(bba)
[4]⇒ a(ba)bb
[1]⇒ (aa)bbbbb
⇒ bbbbbbb

Flip LHS and RHS.

Defines rule #1.

[6] abbbbbb=abb

Overlap of [3] bba=abb with [4] ba=abbb:

b ba ba

Critical pair: babbb=abb.

Reduce LHS:

[4](ba)bbb
⇒ abbbbbb

Defines rule #2.