Certificate for #22823 ⟨a, b | aaa=1, abbbb=bbb⟩

Back:⟨a, b | aaa=1, abbbb=bbb⟩

Completion settings:

[1] aaa=1

Axiom: aaa=1.

Defines rule #3.

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

[2] abbbb=bbb

Axiom: abbbb=bbb.

Referenced by [3].

[3] aabbb=bbbb

Overlap of [1] aaa=1 with [2] abbbb=bbb:

aa a abbbb

Critical pair: aabbb=bbbb.

Referenced by [4], [5].

[4] abbb=bbbbb

Overlap of [1] aaa=1 with [3] aabbb=bbbb:

aa a aabbb

Critical pair: aabbbb=abbb.

Reduce LHS:

[3](aabbb)b
⇒ bbbbb

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] bbbbbb=bbb

Overlap of [1] aaa=1 with [4] abbb=bbbbb:

aa a abbb

Critical pair: aabbbbb=bbb.

Reduce LHS:

[3](aabbb)bb
⇒ bbbbbb

Defines rule #1.