#3671 ⟨a, b | aabbbabaab=a⟩

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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

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

#	Rule	Proof
1.	db ⇒ c²	[5]
2.	cdc² ⇒ cbd²	[25]
3.	d²c² ⇒ c²d²	[22]
4.	dcb²d ⇒ c²bdc	[10]
5.	c²bdc² ⇒ d	[18]
6.	cbdc²b ⇒ c	[27]
7.	dcb²c² ⇒ c²bdcb	[23]
8.	dcbdc² ⇒ c²bdcd	[13]
9.	cbdc³b²d ⇒ cbdc	[26]
10.	cd(cb)²dc² ⇒ cbd²cb²cd	[30]
11.	d²(cb)²dc² ⇒ c²d²cb²cd	[31]
12.	cbdc³b²c² ⇒ cbdcb	[28]
13.	cbd(cb)²dc² ⇒ cbdc³b²cd	[29]
14.	a ⇒ cbdc²	[32]

# ab:aabbbabaab=a cbd/a ab=c,ca=d morph:2/0,2/1
db=cc
cdcc=cbdd
ddcc=ccdd
dcbbd=ccbdc
ccbdcc=d
cbdccb=c
dcbbcc=ccbdcb
dcbdcc=ccbdcd
cbdcccbbd=cbdc
cdcbcbdcc=cbddcbbcd
ddcbcbdcc=ccddcbbcd
cbdcccbbcc=cbdcb
cbdcbcbdcc=cbdcccbbcd
a=cbdcc