Certificate for #21084 ⟨a, b | bb=aa, aaaa=aaa⟩

Back:⟨a, b | bb=aa, aaaa=aaa⟩

Completion settings:

[1] aa=bb

Axiom: bb=aa.

Flip LHS and RHS.

Defines rule #4.

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

[2] bba=bbbb

Axiom: aaaa=aaa.

Reduce LHS:

[1](aa)aa
[1]⇒ bb(aa)
⇒ bbbb

Reduce RHS:

[1](aa)a
⇒ bba

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[3] abb=bbbb

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

a a aa

Critical pair: abb=bba.

Reduce RHS:

[2](bba)
⇒ bbbb

Defines rule #2.

Referenced by [4].

[4] bbbbbb=bbbb

Overlap of [1] aa=bb with [3] abb=bbbb:

a a abb

Critical pair: abbbb=bbbb.

Reduce LHS:

[3](abb)bb
⇒ bbbbbb

Defines rule #1.