#1991 ⟨a, b | aabbaabb=ba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite cancellative non-commutative monoid
Submonoid of enveloping group: ⟨a, b | aabbaabba^-1b^-1⟩

Embedding: φ(a) = a, φ(b) = b

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

#	Rule	Proof
1.	bd ⇒ d²c	[5]
2.	bcd ⇒ d⁴cdc	[10]
3.	d²b² ⇒ bc	[7]
4.	ba ⇒ d²	[4]
5.	ac ⇒ d	[3]
6.	ad²cd ⇒ ca	[6]
7.	bc² ⇒ d⁴cdb²	[12]
8.	bca ⇒ d⁴cd	[9]
9.	b²c ⇒ d²cdb²	[8]
10.	ab² ⇒ c	[2]
11.	(bc)² ⇒ d⁴(cd)²b²	[13]
12.	ad²cbc ⇒ cadb²	[11]

# ab:aabbaabb=ba d/cba abb=c,ac=d morph:3/0,2/0
bd=ddc
bcd=ddddcdc
ddbb=bc
ba=dd
ac=d
addcd=ca
bcc=ddddcdbb
bca=ddddcd
bbc=ddcdbb
abb=c
bcbc=ddddcdcdbb
addcbc=cadbb