Certificate for #2258 ⟨a, b | ab=aa, bbb=ba⟩

Back:⟨a, b | ab=aa, bbb=ba⟩

Completion settings:

[1] aa=ab

Axiom: ab=aa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4].

[2] ba=bbb

Axiom: bbb=ba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] abbb=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)
⇒ abbb

Flip LHS and RHS.

Defines rule #2.

[4] bbbbb=bbbb

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

b a aa

Critical pair: bab=bbba.

Reduce LHS:

[2](ba)b
⇒ bbbb

Reduce RHS:

[2]bb(ba)
⇒ bbbbb

Flip LHS and RHS.

Defines rule #1.