Certificate for #7105 ⟨a, b | ab=aa, bbaa=bb⟩

Back:⟨a, b | ab=aa, bbaa=bb⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] bbaa=bb

Axiom: bbaa=bb.

Defines rule #3.

Referenced by [3], [4].

[3] aaaaa=aaa

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

a b bbaa

Critical pair: abb=aabaa.

Reduce LHS:

[1](ab)b
[1]⇒ a(ab)
⇒ aaa

Reduce RHS:

[1]a(ab)aa
⇒ aaaaa

Flip LHS and RHS.

Defines rule #4.

[4] bbb=bba

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

bba a ab

Critical pair: bbaaa=bbb.

Reduce LHS:

[2](bbaa)a
⇒ bba

Flip LHS and RHS.

Defines rule #2.