#14293 ⟨a, b | abba=b, aaaaaa=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

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

#	Rule	Proof
1.	cd ⇒ dc	[11]
2.	d⁴c² ⇒ d	[52]
3.	d³c³ ⇒ c	[25]
4.	bd³c² ⇒ b	[21]
5.	cb ⇒ bc	[5]
6.	d³b ⇒ bd³	[53]
7.	(db)² ⇒ b²d²c	[42]
8.	d²b² ⇒ bdbd⁴c	[60]
9.	b³ ⇒ c	[3]
10.	da ⇒ a(bdb)²d⁴c	[61]
11.	ca ⇒ ac	[6]
12.	ba ⇒ abdb²	[46]
13.	a²d ⇒ b²db²d⁴c	[58]
14.	a²c ⇒ b²db²	[23]
15.	a²b ⇒ b²d	[17]
16.	a⁶ ⇒ 1	[2]

# ab:abba=b,aaaaaa=1 dc/b/a bbb=c,abababa=d morph:3/1,7/0
cd=dc
ddddcc=d
dddccc=c
bdddcc=b
cb=bc
dddb=bddd
dbdb=bbddc
ddbb=bdbddddc
bbb=c
da=abdbbdbddddc
ca=ac
ba=abdbb
aad=bbdbbddddc
aac=bbdbb
aab=bbd
aaaaaa=1