Certificate for #19022 ⟨a, b | aab=b, abbbbb=a⟩

Back:⟨a, b | aab=b, abbbbb=a⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #2.

Referenced by [3], [4].

[2] abbbbb=a

Axiom: abbbbb=a.

Referenced by [3], [5].

[3] bbbbb=aa

Overlap of [1] aab=b with [2] abbbbb=a:

a ab abbbbb

Critical pair: aa=bbbbb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4].

[4] baa=b

Overlap of [3] bbbbb=aa with [3] bbbbb=aa:

b bbbb bbbbb

Critical pair: baa=aab.

Reduce RHS:

[1](aab)
⇒ b

Defines rule #3.

Referenced by [5].

[5] aaa=a

Overlap of [2] abbbbb=a with [4] baa=b:

abbbb b baa

Critical pair: abbbbb=aaa.

Reduce LHS:

[2](abbbbb)
⇒ a

Flip LHS and RHS.

Defines rule #1.