Certificate for #25634 ⟨a, b | ab=a, bbbaa=bba⟩

Back:⟨a, b | ab=a, bbbaa=bba⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3].

[2] bbbaa=bba

Axiom: bbbaa=bba.

Referenced by [3], [4], [5].

[3] aaa=aa

Overlap of [1] ab=a with [2] bbbaa=bba:

a b bbbaa

Critical pair: abba=abbaa.

Reduce LHS:

[1](ab)ba
[1]⇒ (ab)a
⇒ aa

Reduce RHS:

[1](ab)baa
[1]⇒ (ab)aa
⇒ aaa

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

[4] bbaa=bba

Overlap of [2] bbbaa=bba with [3] aaa=aa:

bbb aa aaa

Critical pair: bbbaa=bbaa.

Reduce LHS:

[2](bbbaa)
⇒ bba

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] bbba=bba

Overlap of [2] bbbaa=bba with [4] bbaa=bba:

b bbaa bbaa

Critical pair: bbba=bba.

Defines rule #4.