Certificate for #16419 ⟨a, b | aba=ab, babb=ba⟩

Back:⟨a, b | aba=ab, babb=ba⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #1.

Referenced by [3], [4].

[2] babb=ba

Axiom: babb=ba.

Defines rule #5.

Referenced by [4], [5].

[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 #3.

Referenced by [5].

[4] abbb=ab

Overlap of [1] aba=ab with [2] babb=ba:

a ba babb

Critical pair: aba=abbb.

Reduce LHS:

[1](aba)
⇒ ab

Flip LHS and RHS.

Defines rule #4.

[5] baa=ba

Overlap of [2] babb=ba with [3] abba=abb:

b abb abba

Critical pair: babb=baa.

Reduce LHS:

[2](babb)
⇒ ba

Flip LHS and RHS.

Defines rule #2.