Certificate for #20927 ⟨a, b | ab=aa, aaaa=bbb⟩

Back:⟨a, b | ab=aa, aaaa=bbb⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] aaaa=bbb

Axiom: aaaa=bbb.

Defines rule #2.

Referenced by [3], [4].

[3] bbbb=bbba

Overlap of [2] aaaa=bbb with [1] ab=aa:

aaa a ab

Critical pair: aaaaa=bbbb.

Reduce LHS:

[2](aaaa)a
⇒ bbba

Flip LHS and RHS.

Referenced by [5].

[4] bbba=bbb

Overlap of [2] aaaa=bbb with [2] aaaa=bbb:

a aaa aaaa

Critical pair: abbb=bbba.

Reduce LHS:

[1](ab)bb
[1]⇒ a(ab)b
[1]⇒ aa(ab)
[2]⇒ (aaaa)
⇒ bbb

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] bbbb=bbb

Simplify [3] bbbb=bbba.

Reduce RHS:

[4](bbba)
⇒ bbb

Defines rule #4.