Certificate for #2255 ⟨a, b | ab=aa, bba=bb⟩

Back:⟨a, b | ab=aa, bba=bb⟩

Completion settings:

[1] aa=ab

Axiom: ab=aa.

Flip LHS and RHS.

Defines rule #1.

Referenced by [3], [4].

[2] bba=bb

Axiom: bba=bb.

Defines rule #3.

Referenced by [4].

[3] aba=abb

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

a a aa

Critical pair: aab=aba.

Reduce LHS:

[1](aa)b
⇒ abb

Flip LHS and RHS.

Defines rule #4.

[4] bbb=bb

Overlap of [2] bba=bb with [1] aa=ab:

bb a aa

Critical pair: bbab=bba.

Reduce LHS:

[2](bba)b
⇒ bbb

Reduce RHS:

[2](bba)
⇒ bb

Defines rule #2.