Certificate for #12182 ⟨a, b | aaaa=ab, baab=a⟩

Back:⟨a, b | aaaa=ab, baab=a⟩

Completion settings:

[1] ab=aaaa

Axiom: aaaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [3].

[2] baaaaa=a

Axiom: baab=a.

Reduce LHS:

[1]ba(ab)
⇒ baaaaa

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

[3] aaaaaaaaa=aa

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

a b baaaaa

Critical pair: aa=aaaaaaaaa.

Flip LHS and RHS.

Referenced by [4].

[4] baa=aaaaa

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

b aaaaa aaaaaaaaa

Critical pair: baa=aaaaa.

Referenced by [5].

[5] aaaaaaaa=a

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

baaaaa baa

Critical pair: aaaaaaaa=a.

Defines rule #1.

Referenced by [6].

[6] ba=aaaa

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

b aaaaa aaaaaaaa

Critical pair: ba=aaaa.

Defines rule #2.