Certificate for #20991 ⟨a, b | ab=aa, baaa=bbb⟩

Back:⟨a, b | ab=aa, baaa=bbb⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #2.

Referenced by [3], [4].

[2] bbb=baaa

Axiom: baaa=bbb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4].

[3] aaaaa=aaaa

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

a b bbb

Critical pair: abaaa=aabb.

Reduce LHS:

[1](ab)aaa
⇒ aaaaa

Reduce RHS:

[1]a(ab)b
[1]⇒ aa(ab)
⇒ aaaa

Defines rule #1.

[4] bbaaa=baaaa

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

b bb bbb

Critical pair: bbaaa=baaab.

Reduce RHS:

[1]baa(ab)
⇒ baaaa

Defines rule #3.