Certificate for #20640 ⟨a, b | ab=aa, bbbbaa=a⟩

Back:⟨a, b | ab=aa, bbbbaa=a⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3].

[2] bbbbaa=a

Axiom: bbbbaa=a.

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

[3] aaaaaaa=aa

Overlap of [1] ab=aa with [2] bbbbaa=a:

a b bbbbaa

Critical pair: aa=aabbbaa.

Reduce RHS:

[1]a(ab)bbaa
[1]⇒ aa(ab)baa
[1]⇒ aaa(ab)aa
⇒ aaaaaaa

Flip LHS and RHS.

Referenced by [4].

[4] aaaaaa=a

Overlap of [2] bbbbaa=a with [3] aaaaaaa=aa:

bbbb aa aaaaaaa

Critical pair: bbbbaa=aaaaaa.

Reduce LHS:

[2](bbbbaa)
⇒ a

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] bbbba=aaaaa

Overlap of [2] bbbbaa=a with [4] aaaaaa=a:

bbbb aa aaaaaa

Critical pair: bbbba=aaaaa.

Defines rule #2.