Certificate for #2066 ⟨a, b | aab=b, abbb=a⟩

Back:⟨a, b | aab=b, abbb=a⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #2.

Referenced by [3], [4].

[2] abbb=a

Axiom: abbb=a.

Referenced by [3], [5].

[3] bbb=aa

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

a ab abbb

Critical pair: aa=bbb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4].

[4] baa=b

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

b bb bbb

Critical pair: baa=aab.

Reduce RHS:

[1](aab)
⇒ b

Defines rule #3.

Referenced by [5].

[5] aaa=a

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

abb b baa

Critical pair: abbb=aaa.

Reduce LHS:

[2](abbb)
⇒ a

Flip LHS and RHS.

Defines rule #1.