Certificate for #20819 ⟨a, b | ab=aa, bbaaa=bb⟩

Back:⟨a, b | ab=aa, bbaaa=bb⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] bbaaa=bb

Axiom: bbaaa=bb.

Defines rule #3.

Referenced by [3], [4].

[3] aaaaaa=aaa

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

a b bbaaa

Critical pair: abb=aabaaa.

Reduce LHS:

[1](ab)b
[1]⇒ a(ab)
⇒ aaa

Reduce RHS:

[1]a(ab)aaa
⇒ aaaaaa

Flip LHS and RHS.

Defines rule #4.

[4] bbb=bba

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

bbaa a ab

Critical pair: bbaaaa=bbb.

Reduce LHS:

[2](bbaaa)a
⇒ bba

Flip LHS and RHS.

Defines rule #2.