Certificate for #5747 ⟨a, b, c | aa=b, bcb=bc⟩

Completion settings:

Auxiliary generators:
1. d = bc
Reduction order:
- Left-to-right shortlex with a < b < d < c

[1] aa=b

Axiom: aa=b.

Defines rule #1.

Referenced by [6].

[2] bcb=bc

Axiom: bcb=bc.

Referenced by [4].

[3] bc=d

Axiom: bc=d.

Defines rule #3.

Referenced by [4], [5], [7], [9].

[4] bcb=d

Simplify [2] bcb=bc.

Reduce RHS:

[3]	(bc)
	⇒ d

Referenced by [5].

[5] db=d

Overlap of [4] bcb=d with [3] bc=d:

bcb bc

Critical pair: db=d.

Defines rule #4.

Referenced by [7], [8].

[6] ba=ab

Overlap of [1] aa=b with [1] aa=b:

a a aa

Critical pair: ab=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

[7] dc=dd

Overlap of [5] db=d with [3] bc=d:

d b bc

Critical pair: dd=dc.

Flip LHS and RHS.

Defines rule #5.

[8] dab=da

Overlap of [5] db=d with [6] ba=ab:

d b ba

Critical pair: dab=da.

Defines rule #6.

Referenced by [9].

[9] dac=dad

Overlap of [8] dab=da with [3] bc=d:

da b bc

Critical pair: dad=dac.

Flip LHS and RHS.

Defines rule #7.