Certificate for #15495 ⟨a, b | aaa=ab, bbabb=a⟩

Back:⟨a, b | aaa=ab, bbabb=a⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [2], [3].

[2] bbaaaaa=a

Axiom: bbabb=a.

Reduce LHS:

[1]bb(ab)b
[1]⇒ bbaa(ab)
⇒ bbaaaaa

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

[3] aaaaaaaaaa=aa

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

a b bbaaaaa

Critical pair: aa=aaabaaaaa.

Reduce RHS:

[1]aa(ab)aaaaa
⇒ aaaaaaaaaa

Flip LHS and RHS.

Referenced by [4].

[4] bbaa=aaaaaa

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

bb aaaaa aaaaaaaaaa

Critical pair: bbaa=aaaaaa.

Referenced by [5].

[5] aaaaaaaaa=a

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

bbaaaaa bbaa

Critical pair: aaaaaaaaa=a.

Defines rule #1.

Referenced by [6].

[6] bba=aaaaa

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

bb aaaaa aaaaaaaaa

Critical pair: bba=aaaaa.

Defines rule #3.