Certificate for #19498 ⟨a, b | aab=a, bbbba=ba⟩

Back:⟨a, b | aab=a, bbbba=ba⟩

Completion settings:

[1] aab=a

Axiom: aab=a.

Referenced by [3], [4], [5], [6], [7].

[2] bbbba=ba

Axiom: bbbba=ba.

Defines rule #3.

Referenced by [3].

[3] abbba=aa

Overlap of [1] aab=a with [2] bbbba=ba:

aa b bbbba

Critical pair: aaba=abbba.

Reduce LHS:

[1](aab)a
⇒ aa

Flip LHS and RHS.

Referenced by [4].

[4] abba=aaa

Overlap of [1] aab=a with [3] abbba=aa:

a ab abbba

Critical pair: aaa=abba.

Flip LHS and RHS.

Referenced by [5].

[5] aaaaa=aa

Overlap of [4] abba=aaa with [4] abba=aaa:

abb a abba

Critical pair: abbaaa=aaabba.

Reduce LHS:

[4](abba)aa
⇒ aaaaa

Reduce RHS:

[1]a(aab)ba
[1]⇒ (aab)a
⇒ aa

Referenced by [6].

[6] aaaa=a

Overlap of [5] aaaaa=aa with [1] aab=a:

aaa aa aab

Critical pair: aaaa=aab.

Reduce RHS:

[1](aab)
⇒ a

Defines rule #1.

Referenced by [7].

[7] ab=aaa

Overlap of [6] aaaa=a with [1] aab=a:

aa aa aab

Critical pair: aaa=ab.

Flip LHS and RHS.

Defines rule #2.