Certificate for #2271 ⟨a, b | bb=aa, aaa=ab⟩

Back:⟨a, b | bb=aa, aaa=ab⟩

Completion settings:

[1] aa=bb

Axiom: bb=aa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3], [4].

[2] ab=bba

Axiom: aaa=ab.

Reduce LHS:

[1](aa)a
⇒ bba

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] bbbba=bba

Overlap of [1] aa=bb with [1] aa=bb:

a a aa

Critical pair: abb=bba.

Reduce LHS:

[2](ab)b
[2]⇒ bb(ab)
⇒ bbbba

Referenced by [4], [5].

[4] bbbb=bbb

Overlap of [1] aa=bb with [2] ab=bba:

a a ab

Critical pair: abba=bbb.

Reduce LHS:

[2](ab)ba
[2]⇒ bb(ab)a
[3]⇒ (bbbba)a
[1]⇒ bb(aa)
⇒ bbbb

Defines rule #1.

Referenced by [5].

[5] bbba=bba

Simplify [3] bbbba=bba.

Reduce LHS:

[4](bbbb)a
⇒ bbba

Defines rule #2.