Certificate for #19794 ⟨a, b | aaa=a, aaba=baa⟩

Completion settings:

Auxiliary generators:
1. c = ba
Reduction order:
- Left-to-right shortlex with a < c < b

[1] aaa=a

Axiom: aaa=a.

Defines rule #4.

Referenced by [6], [7].

[2] aaba=baa

Axiom: aaba=baa.

Referenced by [4].

[3] ba=c

Axiom: ba=c.

Defines rule #2.

Referenced by [4], [5], [6], [8].

[4] aaba=ca

Simplify [2] aaba=baa.

Reduce RHS:

[3]	(ba)a
	⇒ ca

Referenced by [5].

[5] aac=ca

Overlap of [4] aaba=ca with [3] ba=c:

aa ba ba

Critical pair: aac=ca.

Referenced by [7], [8], [9].

[6] caa=c

Overlap of [3] ba=c with [1] aaa=a:

b a aaa

Critical pair: ba=caa.

Reduce LHS:

[3]	(ba)
	⇒ c

Flip LHS and RHS.

Referenced by [7].

[7] ca=c

Overlap of [1] aaa=a with [5] aac=ca:

aa a aac

Critical pair: aaca=aac.

Reduce LHS:

[5]	(aac)a
[6]	⇒ (caa)
	⇒ c

Reduce RHS:

[5]	(aac)
	⇒ ca

Flip LHS and RHS.

Defines rule #1.

Referenced by [8], [9].

[8] bc=cc

Overlap of [3] ba=c with [5] aac=ca:

b a aac

Critical pair: bca=cac.

Reduce LHS:

[7]	b(ca)
	⇒ bc

Reduce RHS:

[7]	(ca)c
	⇒ cc

Defines rule #3.

[9] aac=c

Simplify [5] aac=ca.

Reduce RHS:

[7]	(ca)
	⇒ c

Defines rule #5.