Certificate for #2293 ⟨a, b | abaaaab=aba⟩

Completion settings:

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

[1] abaaaab=aba

Axiom: abaaaab=aba.

Referenced by [3].

[2] abaaa=c

Axiom: abaaa=c.

Referenced by [3], [4].

[3] aba=cab

Overlap of [1] abaaaab=aba with [2] abaaa=c:

abaaaab abaaa

Critical pair: cab=aba.

Flip LHS and RHS.

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

[4] cccab=c

Overlap of [2] abaaa=c with [3] aba=cab:

abaaa aba

Critical pair: cabaa=c.

Reduce LHS:

[3]	c(aba)a
[3]	⇒ cc(aba)
	⇒ cccab

Referenced by [6], [9].

[5] cabba=abcab

Overlap of [3] aba=cab with [3] aba=cab:

ab a aba

Critical pair: abcab=cabba.

Flip LHS and RHS.

Referenced by [7].

[6] ca=cc

Overlap of [4] cccab=c with [3] aba=cab:

ccc ab aba

Critical pair: ccccab=ca.

Reduce LHS:

[4]	c(cccab)
	⇒ cc

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [8], [9], [10].

[7] ccbba=abccb

Simplify [5] cabba=abcab.

Reduce LHS:

[6]	(ca)bba
	⇒ ccbba

Reduce RHS:

[6]	ab(ca)b
	⇒ abccb

Defines rule #4.

Referenced by [10].

[8] aba=ccb

Simplify [3] aba=cab.

Reduce RHS:

[6]	(ca)b
	⇒ ccb

Defines rule #5.

[9] ccccb=c

Overlap of [4] cccab=c with [6] ca=cc:

cc cab ca

Critical pair: ccccb=c.

Defines rule #1.

Referenced by [10].

[10] cba=cccbccb

Overlap of [9] ccccb=c with [7] ccbba=abccb:

cc ccb ccbba

Critical pair: ccabccb=cba.

Reduce LHS:

[6]	c(ca)bccb
	⇒ cccbccb

Flip LHS and RHS.

Defines rule #3.