Certificate for #5405 ⟨a, b | aab=bb, aba=ab⟩

Back:⟨a, b | aab=bb, aba=ab⟩

Completion settings:

[1] aab=bb

Axiom: aab=bb.

Defines rule #1.

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

[2] aba=ab

Axiom: aba=ab.

Defines rule #2.

Referenced by [3], [4].

[3] bba=bb

Overlap of [1] aab=bb with [2] aba=ab:

a ab aba

Critical pair: aab=bba.

Reduce LHS:

[1](aab)
⇒ bb

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[4] abbb=abb

Overlap of [2] aba=ab with [1] aab=bb:

ab a aab

Critical pair: abbb=abab.

Reduce RHS:

[2](aba)b
⇒ abb

Defines rule #4.

[5] bbbb=bbb

Overlap of [3] bba=bb with [1] aab=bb:

bb a aab

Critical pair: bbbb=bbab.

Reduce RHS:

[3](bba)b
⇒ bbb

Defines rule #5.