Certificate for #15491 ⟨a, b | aaa=ab, bbaab=a⟩

Back:⟨a, b | aaa=ab, bbaab=a⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [2], [3].

[2] bbaaaa=a

Axiom: bbaab=a.

Reduce LHS:

[1]bba(ab)
⇒ bbaaaa

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

[3] aaaaaaaaa=aa

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

a b bbaaaa

Critical pair: aa=aaabaaaa.

Reduce RHS:

[1]aa(ab)aaaa
⇒ aaaaaaaaa

Flip LHS and RHS.

Referenced by [4].

[4] bbaa=aaaaaa

Overlap of [2] bbaaaa=a with [3] aaaaaaaaa=aa:

bb aaaa aaaaaaaaa

Critical pair: bbaa=aaaaaa.

Referenced by [5].

[5] aaaaaaaa=a

Overlap of [2] bbaaaa=a with [4] bbaa=aaaaaa:

bbaaaa bbaa

Critical pair: aaaaaaaa=a.

Defines rule #1.

Referenced by [6].

[6] bba=aaaaa

Overlap of [2] bbaaaa=a with [5] aaaaaaaa=a:

bb aaaa aaaaaaaa

Critical pair: bba=aaaaa.

Defines rule #3.