Certificate for #14339 ⟨a, b | aaaa=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] aaaa=a

Axiom: aaaa=a.

Referenced by [5], [7].

[2] aabab=a

Axiom: aabab=a.

Referenced by [4].

[3] ab=c

Axiom: ab=c.

Defines rule #5.

Referenced by [4], [5], [9].

[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

Defines rule #2.

Referenced by [6].

[5] aaac=c

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

aaa a ab

Critical pair: aaac=ab.

Reduce RHS:

[3]	(ab)
	⇒ c

Referenced by [6], [8].

[6] aaa=cc

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

aa ac acc

Critical pair: aaa=cc.

Defines rule #1.

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

[7] cca=a

Overlap of [1] aaaa=a with [6] aaa=cc:

aaaa aaa

Critical pair: cca=a.

Defines rule #3.

[8] ccc=c

Overlap of [5] aaac=c with [6] aaa=cc:

aaac aaa

Critical pair: ccc=c.

Defines rule #4.

Referenced by [10].

[9] ccb=aac

Overlap of [6] aaa=cc with [3] ab=c:

aa a ab

Critical pair: aac=ccb.

Flip LHS and RHS.

Referenced by [10].

[10] cb=caac

Overlap of [8] ccc=c with [9] ccb=aac:

c cc ccb

Critical pair: caac=cb.

Flip LHS and RHS.

Defines rule #6.