Certificate for #6544 ⟨a, b | aaa=a, abab=bb⟩

Back:⟨a, b | aaa=a, abab=bb⟩

Completion settings:

[1] aaa=a

Axiom: aaa=a.

Defines rule #1.

Referenced by [3].

[2] abab=bb

Axiom: abab=bb.

Defines rule #3.

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

[3] aabb=bb

Overlap of [1] aaa=a with [2] abab=bb:

aa a abab

Critical pair: aabb=abab.

Reduce RHS:

[2](abab)
⇒ bb

Defines rule #2.

Referenced by [5].

[4] bbab=abbb

Overlap of [2] abab=bb with [2] abab=bb:

ab ab abab

Critical pair: abbb=bbab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [5].

[5] babbb=abbbb

Overlap of [2] abab=bb with [4] bbab=abbb:

aba b bbab

Critical pair: abaabbb=bbbab.

Reduce LHS:

[3]ab(aabb)b
⇒ abbbb

Reduce RHS:

[4]b(bbab)
⇒ babbb

Flip LHS and RHS.

Defines rule #5.