Certificate for #7591 ⟨a, b, c | ab=1, cacc=ac⟩

Completion settings:

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

[1] ab=1

Axiom: ab=1.

Defines rule #3.

Referenced by [5].

[2] cacc=ac

Axiom: cacc=ac.

Referenced by [4].

[3] ca=d

Axiom: ca=d.

Referenced by [4], [5], [6], [9].

[4] dcc=ac

Overlap of [2] cacc=ac with [3] ca=d:

cacc ca

Critical pair: dcc=ac.

Referenced by [7].

[5] c=db

Overlap of [3] ca=d with [1] ab=1:

c a ab

Critical pair: c=db.

Defines rule #6.

Referenced by [6], [7], [9].

[6] dba=d

Overlap of [3] ca=d with [5] c=db:

ca c

Critical pair: dba=d.

Defines rule #5.

Referenced by [8].

[7] adb=ddbdb

Simplify [4] dcc=ac.

Reduce LHS:

[5]	d(c)c
[5]	⇒ ddb(c)
	⇒ ddbdb

Reduce RHS:

[5]	a(c)
	⇒ adb

Flip LHS and RHS.

Referenced by [8].

[8] ad=ddbd

Overlap of [7] adb=ddbdb with [6] dba=d:

a db dba

Critical pair: ad=ddbdba.

Reduce RHS:

[6]	ddb(dba)
	⇒ ddbd

Defines rule #4.

Referenced by [9].

[9] dbddbd=dd

Overlap of [3] ca=d with [8] ad=ddbd:

c a ad

Critical pair: cddbd=dd.

Reduce LHS:

[5]	(c)ddbd
	⇒ dbddbd

Defines rule #2.

Referenced by [10].

[10] dddbd=dbddd

Overlap of [9] dbddbd=dd with [9] dbddbd=dd:

dbd dbd dbddbd

Critical pair: dbddd=dddbd.

Flip LHS and RHS.

Defines rule #1.