Certificate for #15487 ⟨a, b | aaa=ab, babbb=a⟩

Back:⟨a, b | aaa=ab, babbb=a⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [3].

[2] baaaaaaa=a

Axiom: babbb=a.

Reduce LHS:

[1]b(ab)bb
[1]⇒ baa(ab)b
[1]⇒ baaaa(ab)
⇒ baaaaaaa

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

[3] aaaaaaaaaa=aa

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

a b baaaaaaa

Critical pair: aa=aaaaaaaaaa.

Flip LHS and RHS.

Referenced by [4].

[4] baa=aaaa

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

b aaaaaaa aaaaaaaaaa

Critical pair: baa=aaaa.

Referenced by [5].

[5] aaaaaaaaa=a

Overlap of [2] baaaaaaa=a with [4] baa=aaaa:

baaaaaaa baa

Critical pair: aaaaaaaaa=a.

Defines rule #1.

Referenced by [6].

[6] ba=aaa

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

b aaaaaaa aaaaaaaaa

Critical pair: ba=aaa.

Defines rule #2.