Certificate for #18926 ⟨a, b | aab=a, babbbb=a⟩

Back:⟨a, b | aab=a, babbbb=a⟩

Completion settings:

[1] aab=a

Axiom: aab=a.

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

[2] babbbb=a

Axiom: babbbb=a.

Referenced by [3], [6].

[3] aaa=abbb

Overlap of [1] aab=a with [2] babbbb=a:

aa b babbbb

Critical pair: aaa=aabbbb.

Reduce RHS:

[1](aab)bbb
⇒ abbb

Referenced by [4].

[4] aa=abbbb

Overlap of [3] aaa=abbb with [1] aab=a:

a aa aab

Critical pair: aa=abbbb.

Defines rule #3.

Referenced by [5].

[5] abbbbb=a

Overlap of [1] aab=a with [4] aa=abbbb:

aab aa

Critical pair: abbbbb=a.

Defines rule #1.

Referenced by [6].

[6] ba=ab

Overlap of [2] babbbb=a with [5] abbbbb=a:

b abbbb abbbbb

Critical pair: ba=ab.

Defines rule #2.