Certificate for #4653 ⟨a, b | aaab=a, abaa=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] aaab=a

Axiom: aaab=a.

Referenced by [4].

[2] abaa=a

Axiom: abaa=a.

Referenced by [5].

[3] ab=c

Axiom: ab=c.

Defines rule #4.

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

[4] aac=a

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

aa ab ab

Critical pair: aac=a.

Defines rule #2.

Referenced by [7].

[5] caa=a

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

abaa ab

Critical pair: caa=a.

Referenced by [6], [7].

[6] cac=c

Overlap of [5] caa=a with [3] ab=c:

ca a ab

Critical pair: cac=ab.

Reduce RHS:

[3]	(ab)
	⇒ c

Referenced by [9].

[7] ca=ac

Overlap of [5] caa=a with [4] aac=a:

c aa aac

Critical pair: ca=ac.

Defines rule #1.

Referenced by [8], [9], [10].

[8] acb=cc

Overlap of [7] ca=ac with [3] ab=c:

c a ab

Critical pair: cc=acb.

Flip LHS and RHS.

Referenced by [10].

[9] acc=c

Simplify [6] cac=c.

Reduce LHS:

[7]	(ca)c
	⇒ acc

Defines rule #3.

Referenced by [10].

[10] cb=ccc

Overlap of [7] ca=ac with [8] acb=cc:

c a acb

Critical pair: ccc=accb.

Reduce RHS:

[9]	(acc)b
	⇒ cb

Flip LHS and RHS.

Defines rule #5.