Certificate for #15978 ⟨a, b | aaa=aa, bbbb=aa⟩

Back:⟨a, b | aaa=aa, bbbb=aa⟩

Completion settings:

[1] aaa=aa

Axiom: aaa=aa.

Referenced by [3].

[2] aa=bbbb

Axiom: bbbb=aa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4], [5], [6].

[3] aaa=bbbb

Simplify [1] aaa=aa.

Reduce RHS:

[2](aa)
⇒ bbbb

Referenced by [4].

[4] bbbba=bbbb

Overlap of [3] aaa=bbbb with [2] aa=bbbb:

aaa aa

Critical pair: bbbba=bbbb.

Defines rule #3.

Referenced by [5].

[5] abbbb=bbbb

Overlap of [2] aa=bbbb with [2] aa=bbbb:

a a aa

Critical pair: abbbb=bbbba.

Reduce RHS:

[4](bbbba)
⇒ bbbb

Defines rule #2.

Referenced by [6].

[6] bbbbbbbb=bbbb

Overlap of [2] aa=bbbb with [5] abbbb=bbbb:

a a abbbb

Critical pair: abbbb=bbbbbbbb.

Reduce LHS:

[5](abbbb)
⇒ bbbb

Flip LHS and RHS.

Defines rule #1.