Certificate for #5064 ⟨a, b | aaa=ab, babb=a⟩

Back:⟨a, b | aaa=ab, babb=a⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [3].

[2] baaaaa=a

Axiom: babb=a.

Reduce LHS:

[1]b(ab)b
[1]⇒ baa(ab)
⇒ baaaaa

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

[3] aaaaaaaa=aa

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

a b baaaaa

Critical pair: aa=aaaaaaaa.

Flip LHS and RHS.

Referenced by [4].

[4] baa=aaaa

Overlap of [2] baaaaa=a with [3] aaaaaaaa=aa:

b aaaaa aaaaaaaa

Critical pair: baa=aaaa.

Referenced by [5].

[5] aaaaaaa=a

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

baaaaa baa

Critical pair: aaaaaaa=a.

Defines rule #1.

Referenced by [6].

[6] ba=aaa

Overlap of [2] baaaaa=a with [5] aaaaaaa=a:

b aaaaa aaaaaaa

Critical pair: ba=aaa.

Defines rule #2.