Certificate for #2048 ⟨a, b | aab=a, bbba=a⟩

Back:⟨a, b | aab=a, bbba=a⟩

Completion settings:

[1] aab=a

Axiom: aab=a.

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

[2] bbba=a

Axiom: bbba=a.

Defines rule #3.

Referenced by [3].

[3] abba=aaa

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

aa b bbba

Critical pair: aaa=abba.

Flip LHS and RHS.

Referenced by [4].

[4] aaaaa=aa

Overlap of [3] abba=aaa with [3] abba=aaa:

abb a abba

Critical pair: abbaaa=aaabba.

Reduce LHS:

[3](abba)aa
⇒ aaaaa

Reduce RHS:

[1]a(aab)ba
[1]⇒ (aab)a
⇒ aa

Referenced by [5].

[5] aaaa=a

Overlap of [4] aaaaa=aa with [1] aab=a:

aaa aa aab

Critical pair: aaaa=aab.

Reduce RHS:

[1](aab)
⇒ a

Defines rule #1.

Referenced by [6].

[6] ab=aaa

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

aa aa aab

Critical pair: aaa=ab.

Flip LHS and RHS.

Defines rule #2.