Certificate for #16431 ⟨a, b | aba=ab, bbba=ba⟩

Back:⟨a, b | aba=ab, bbba=ba⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #1.

Referenced by [3], [4].

[2] bbba=ba

Axiom: bbba=ba.

Defines rule #4.

Referenced by [4].

[3] abba=abb

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

ab a aba

Critical pair: abab=abba.

Reduce LHS:

[1](aba)b
⇒ abb

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

[4] abbb=ab

Overlap of [1] aba=ab with [3] abba=abb:

ab a abba

Critical pair: ababb=abbba.

Reduce LHS:

[1](aba)bb
⇒ abbb

Reduce RHS:

[2]a(bbba)
[1]⇒ (aba)
⇒ ab

Defines rule #3.