Certificate for #7116 ⟨a, b | ab=aa, bbbb=ba⟩

Back:⟨a, b | ab=aa, bbbb=ba⟩

Completion settings:

[1] aa=ab

Axiom: ab=aa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4].

[2] ba=bbbb

Axiom: bbbb=ba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] abbbb=abb

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

a a aa

Critical pair: aab=aba.

Reduce LHS:

[1](aa)b
⇒ abb

Reduce RHS:

[2]a(ba)
⇒ abbbb

Flip LHS and RHS.

Defines rule #2.

[4] bbbbbbb=bbbbb

Overlap of [2] ba=bbbb with [1] aa=ab:

b a aa

Critical pair: bab=bbbba.

Reduce LHS:

[2](ba)b
⇒ bbbbb

Reduce RHS:

[2]bbb(ba)
⇒ bbbbbbb

Flip LHS and RHS.

Defines rule #1.