Certificate for #590 ⟨a, b | aab=a, bba=a⟩

Back:⟨a, b | aab=a, bba=a⟩

Completion settings:

[1] aab=a

Axiom: aab=a.

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

[2] bba=a

Axiom: bba=a.

Defines rule #3.

Referenced by [3].

[3] aba=aaa

Overlap of [1] aab=a with [2] bba=a:

aa b bba

Critical pair: aaa=aba.

Flip LHS and RHS.

Referenced by [4], [5].

[4] aaaa=aa

Overlap of [1] aab=a with [3] aba=aaa:

a ab aba

Critical pair: aaaa=aa.

Referenced by [5].

[5] aaa=a

Overlap of [3] aba=aaa with [1] aab=a:

ab a aab

Critical pair: aba=aaaab.

Reduce LHS:

[3](aba)
⇒ aaa

Reduce RHS:

[4](aaaa)b
[1]⇒ (aab)
⇒ a

Defines rule #2.

Referenced by [6].

[6] ab=aa

Overlap of [5] aaa=a with [1] aab=a:

a aa aab

Critical pair: aa=ab.

Flip LHS and RHS.

Defines rule #1.