Certificate for #5060 ⟨a, b | aaa=ab, baab=a⟩

Back:⟨a, b | aaa=ab, baab=a⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [3].

[2] baaaa=a

Axiom: baab=a.

Reduce LHS:

[1]ba(ab)
⇒ baaaa

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

[3] aaaaaaa=aa

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

a b baaaa

Critical pair: aa=aaaaaaa.

Flip LHS and RHS.

Referenced by [4].

[4] baa=aaaa

Overlap of [2] baaaa=a with [3] aaaaaaa=aa:

b aaaa aaaaaaa

Critical pair: baa=aaaa.

Referenced by [5].

[5] aaaaaa=a

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

baaaa baa

Critical pair: aaaaaa=a.

Defines rule #1.

Referenced by [6].

[6] ba=aaa

Overlap of [2] baaaa=a with [5] aaaaaa=a:

b aaaa aaaaaa

Critical pair: ba=aaa.

Defines rule #2.