Certificate for #21023 ⟨a, b | ab=aa, bbaa=bbb⟩

Back:⟨a, b | ab=aa, bbaa=bbb⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] bbaa=bbb

Axiom: bbaa=bbb.

Defines rule #2.

Referenced by [3], [4].

[3] aaaaa=aaaa

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

a b bbaa

Critical pair: abbb=aabaa.

Reduce LHS:

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

Reduce RHS:

[1]a(ab)aa
⇒ aaaaa

Flip LHS and RHS.

Defines rule #4.

[4] bbbb=bbba

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

bba a ab

Critical pair: bbaaa=bbbb.

Reduce LHS:

[2](bbaa)a
⇒ bbba

Flip LHS and RHS.

Defines rule #3.