Certificate for #15499 ⟨a, b | aaa=ab, bbbab=a⟩

Back:⟨a, b | aaa=ab, bbbab=a⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [2], [3].

[2] bbbaaa=a

Axiom: bbbab=a.

Reduce LHS:

[1]bbb(ab)
⇒ bbbaaa

Referenced by [3], [4], [5], [6].

[3] aaaaaaaaaa=aa

Overlap of [1] ab=aaa with [2] bbbaaa=a:

a b bbbaaa

Critical pair: aa=aaabbaaa.

Reduce RHS:

[1]aa(ab)baaa
[1]⇒ aaaa(ab)aaa
⇒ aaaaaaaaaa

Flip LHS and RHS.

Referenced by [4].

[4] bbbaa=aaaaaaaa

Overlap of [2] bbbaaa=a with [3] aaaaaaaaaa=aa:

bbb aaa aaaaaaaaaa

Critical pair: bbbaa=aaaaaaaa.

Referenced by [5].

[5] aaaaaaaaa=a

Overlap of [2] bbbaaa=a with [4] bbbaa=aaaaaaaa:

bbbaaa bbbaa

Critical pair: aaaaaaaaa=a.

Defines rule #1.

Referenced by [6].

[6] bbba=aaaaaaa

Overlap of [2] bbbaaa=a with [5] aaaaaaaaa=a:

bbb aaa aaaaaaaaa

Critical pair: bbba=aaaaaaa.

Defines rule #3.