Certificate for #24180 ⟨a, b | aa=a, bbababb=a⟩

Back:⟨a, b | aa=a, bbababb=a⟩

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #1.

Referenced by [3].

[2] bbababb=a

Axiom: bbababb=a.

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

[3] bbaba=ababb

Overlap of [2] bbababb=a with [2] bbababb=a:

bbaba bb bbababb

Critical pair: bbabaa=aababb.

Reduce LHS:

[1]bbab(aa)
⇒ bbaba

Reduce RHS:

[1](aa)babb
⇒ ababb

Referenced by [4].

[4] ababbbb=a

Overlap of [2] bbababb=a with [3] bbaba=ababb:

bbababb bbaba

Critical pair: ababbbb=a.

Defines rule #3.

Referenced by [5].

[5] bba=abb

Overlap of [2] bbababb=a with [4] ababbbb=a:

bb ababb ababbbb

Critical pair: bba=abb.

Defines rule #2.