#4334 ⟨a, b | abbaabaab=ba⟩

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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(d) = 0, c < d; deg(b) = 1; deg(a) = 2
Auxiliary generators:
1. baa=c
2. ab=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	dc²bd ⇒ cb	[9]
2.	dc³b ⇒ cd	[10]
3.	(dc²)²b ⇒ c	[5]
4.	d²c²dcbd² ⇒ cdb	[19]
5.	dc(cd)²c²bc ⇒ c³dc²b	[16]
6.	cbc³b ⇒ dc²bcd	[14]
7.	cbc²dc²b ⇒ dc²bc	[11]
8.	cdbc³b ⇒ d²c²dcbdcd	[24]
9.	cdbc²dc²b ⇒ d²c²dcbdc	[21]
10.	c³b² ⇒ dc²dcbd²	[15]
11.	dc²b² ⇒ bd	[7]
12.	dc(cb)² ⇒ cbc²bd	[13]
13.	dc²bcdb ⇒ cbdc²dcbd²	[20]
14.	dc²bc⁴b ⇒ cbc(cd)²c²bcd	[18]
15.	dc²bc³dc²b ⇒ cbc(cd)²c²bc	[17]
16.	c³d(c²b)² ⇒ dc(cd)³c²bcd	[29]
17.	c²(cdc²b)² ⇒ dc(cd)³c²bc	[27]
18.	d²c²dcbcdb ⇒ cdbc²dcbd²	[25]
19.	d²c²(dcb)² ⇒ cdbc²bd	[23]
20.	d²c²dcbdcdb ⇒ cdbdc²dcbd²	[26]
21.	d²c²dcbdc⁴b ⇒ cdbc(cd)²c²bcd	[31]
22.	d²c²dcbdc³dc²b ⇒ cdbc(cd)²c²bc	[30]
23.	cbc²b² ⇒ bd²	[12]
24.	cdbc²b² ⇒ d²c²dc(bd)²	[22]
25.	c⁴bc²bdb ⇒ dc²(dc)²bd²	[28]
26.	ab ⇒ d	[3]
27.	ca ⇒ dc³	[8]
28.	da ⇒ adc²b	[6]
29.	ba ⇒ dc²b	[4]

# ab:abbaabaab=ba cd/b/a baa=c,ab=d morph:3/1,2/5
dccbd=cb
dcccb=cd
dccdccb=c
ddccdcbdd=cdb
dccdcdccbc=cccdccb
cbcccb=dccbcd
cbccdccb=dccbc
cdbcccb=ddccdcbdcd
cdbccdccb=ddccdcbdc
cccbb=dccdcbdd
dccbb=bd
dccbcb=cbccbd
dccbcdb=cbdccdcbdd
dccbccccb=cbccdcdccbcd
dccbcccdccb=cbccdcdccbc
cccdccbccb=dccdcdcdccbcd
cccdccbcdccb=dccdcdcdccbc
ddccdcbcdb=cdbccdcbdd
ddccdcbdcb=cdbccbd
ddccdcbdcdb=cdbdccdcbdd
ddccdcbdccccb=cdbccdcdccbcd
ddccdcbdcccdccb=cdbccdcdccbc
cbccbb=bdd
cdbccbb=ddccdcbdbd
ccccbccbdb=dccdcdcbdd
ab=d
ca=dccc
da=adccb
ba=dccb