#5867 ⟨a, b | ababab=aabba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b(ab)² = a²b²a and a ⋅ ab²a = a²b²a, however b(ab)² ≠ ab²a
Enveloping group: ⟨a, b | aaabb⟩

Rewriting system

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Auxiliary generators:
1. c = ab
2. d = cccb
Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = 0, c < d; deg(a) = deg(b) = 1, a < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	d²c ⇒ cd²	[11]
2.	c(dc)² ⇒ d³	[13]
3.	cda ⇒ dc²	[7]
4.	d²a ⇒ cdc³	[10]
5.	c³b ⇒ d	[3]
6.	dc²b ⇒ cdc	[9]
7.	c²d²b ⇒ (dc)²	[12]
8.	dcd²b ⇒ (cdc)²	[14]
9.	cd⁴b ⇒ d(cdc)²	[15]
10.	d⁵b ⇒ (cdc)³	[16]
11.	ab ⇒ c	[2]
12.	acbc ⇒ d	[6]
13.	acbd ⇒ cdc	[8]
14.	acba ⇒ c³	[5]

# ab:ababab=aabba cd/ab ab=c,cccb=d morph:2/0,4/0
ddc=cdd
cdcdc=ddd
cda=dcc
dda=cdccc
cccb=d
dccb=cdc
ccddb=dcdc
dcddb=cdccdc
cddddb=dcdccdc
dddddb=cdccdccdc
ab=c
acbc=d
acbd=cdc
acba=ccc