Certificate for #460 ⟨a, b, c | ba=ab, abc=1⟩

Completion settings:

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

Axiom: ba=ab.

Flip LHS and RHS.

Referenced by [2], [4].

Axiom: abc=1.

Reduce LHS:

[1]	(ab)c
	⇒ bac

Referenced by [5].

Axiom: ba=d.

Defines rule #3.

Referenced by [4], [5], [6], [7].

Simplify [1] ab=ba.

Reduce RHS:

[3]	(ba)
	⇒ d

Defines rule #4.

Referenced by [6], [7].

bac ba

Critical pair: dc=1.

Defines rule #2.

Overlap of [4] ab=d with [3] ba=d:

a b ba

Critical pair: ad=da.

Flip LHS and RHS.

Defines rule #1.

Overlap of [3] ba=d with [4] ab=d:

b a ab

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #5.