Certificate for #1594 ⟨a, b | aaa=ab, bab=a⟩

Back:⟨a, b | aaa=ab, bab=a⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [3].

[2] baaa=a

Axiom: bab=a.

Reduce LHS:

[1]b(ab)
⇒ baaa

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

[3] aaaaaa=aa

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

a b baaa

Critical pair: aa=aaaaaa.

Flip LHS and RHS.

Referenced by [4].

[4] baa=aaaa

Overlap of [2] baaa=a with [3] aaaaaa=aa:

b aaa aaaaaa

Critical pair: baa=aaaa.

Referenced by [5].

[5] aaaaa=a

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

baaa baa

Critical pair: aaaaa=a.

Defines rule #1.

Referenced by [6].

[6] ba=aaa

Overlap of [2] baaa=a with [5] aaaaa=a:

b aaa aaaaa

Critical pair: ba=aaa.

Defines rule #2.