Certificate for #6248 ⟨a, b | aaa=a, aabab=a⟩

Completion settings:

Auxiliary generators:
1. c = ab
Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1

[1] aaa=a

Axiom: aaa=a.

Defines rule #2.

Referenced by [5].

[2] aabab=a

Axiom: aabab=a.

Referenced by [4].

[3] ab=c

Axiom: ab=c.

Defines rule #5.

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

[4] acc=a

Overlap of [2] aabab=a with [3] ab=c:

a abab ab

Critical pair: acab=a.

Reduce LHS:

[3]	ac(ab)
	⇒ acc

Referenced by [6].

[5] aac=c

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

aa a ab

Critical pair: aac=ab.

Reduce RHS:

[3]	(ab)
	⇒ c

Defines rule #3.

Referenced by [6], [7].

[6] cc=aa

Overlap of [5] aac=c with [4] acc=a:

a ac acc

Critical pair: aa=cc.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7].

[7] caa=c

Overlap of [6] cc=aa with [6] cc=aa:

c c cc

Critical pair: caa=aac.

Reduce RHS:

[5]	(aac)
	⇒ c

Defines rule #4.

Referenced by [8].

[8] cb=cac

Overlap of [7] caa=c with [3] ab=c:

ca a ab

Critical pair: cac=cb.

Flip LHS and RHS.

Defines rule #6.