Certificate for #25055 ⟨a, b | ab=a, bbaaaa=bb⟩

Back:⟨a, b | ab=a, bbaaaa=bb⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bbaaaa=bb

Axiom: bbaaaa=bb.

Defines rule #4.

Referenced by [3], [4].

[3] aaaaa=a

Overlap of [1] ab=a with [2] bbaaaa=bb:

a b bbaaaa

Critical pair: abb=abaaaa.

Reduce LHS:

[1](ab)b
[1]⇒ (ab)
⇒ a

Reduce RHS:

[1](ab)aaaa
⇒ aaaaa

Flip LHS and RHS.

Defines rule #3.

[4] bbb=bb

Overlap of [2] bbaaaa=bb with [1] ab=a:

bbaaa a ab

Critical pair: bbaaaa=bbb.

Reduce LHS:

[2](bbaaaa)
⇒ bb

Flip LHS and RHS.

Defines rule #2.