#4327 ⟨a, b | abbaaaaab=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. baaaaa=c
2. ab=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	dc²b ⇒ cd	[10]
2.	(dc)⁴bd ⇒ cb	[9]
3.	(dc)⁵b ⇒ c	[5]
4.	d²(cd)⁴(dc)³bd² ⇒ cdb	[19]
5.	d(cd)⁴(dc)⁴bc ⇒ c²(dc)⁴b	[16]
6.	cbc²b ⇒ (dc)⁴bcd	[14]
7.	cbc(dc)⁴b ⇒ (dc)⁴bc	[11]
8.	c²b² ⇒ d(cd)⁴(dc)³bd²	[15]
9.	cdbc²b ⇒ d²(cd)⁴(dc)³bdcd	[24]
10.	cdbc(dc)⁴b ⇒ d²(cd)⁴(dc)³bdc	[21]
11.	dcb² ⇒ bd	[7]
12.	c³bc(dc)³b ⇒ dc(d(cd)³)³cbc	[29]
13.	c²(dc)³bdb ⇒ (dc)⁴(d(dc)³)²bd²	[28]
14.	(dc)⁴bcb ⇒ cbc(dc)³bd	[13]
15.	(dc)⁴bcdb ⇒ cbd(cd)⁴(dc)³bd²	[20]
16.	(dc)⁴bc³b ⇒ cb(cd)⁴(dc)⁴bcd	[18]
17.	(dc)⁴bc²(dc)⁴b ⇒ cb(cd)⁴(dc)⁴bc	[17]
18.	d²(cd)⁴(dc)³bcdb ⇒ cdb(cd)⁴(dc)³bd²	[25]
19.	d²(cd)⁴(dc)³bdcb ⇒ cdbc(dc)³bd	[23]
20.	d²(cd)⁴(dc)³bdcdb ⇒ cdbd(cd)⁴(dc)³bd²	[26]
21.	d²(cd)⁴(dc)³bdc³b ⇒ cdb(cd)⁴(dc)⁴bcd	[32]
22.	d²(cd)⁴(dc)³bdc²(dc)⁴b ⇒ cdb(cd)⁴(dc)⁴bc	[31]
23.	cbcb² ⇒ (dc)³bd²	[12]
24.	cbc(dc)³bdb ⇒ d(cd)³(dc)³bd²	[27]
25.	cdbcb² ⇒ d²(cd)⁴(dc)³(bd)²	[22]
26.	cdbc(dc)³bdb ⇒ d²(cd)⁴(dc)²bd²	[33]
27.	c³bc(dc)²bdb ⇒ (dc)⁴(d(dc)³)³bd²	[30]
28.	ab ⇒ d	[3]
29.	ca ⇒ dc²	[8]
30.	da ⇒ adcb	[6]
31.	ba ⇒ dcb	[4]

# ab:abbaaaaab=ba cd/b/a baaaaa=c,ab=d morph:6/1,2/0
dccb=cd
dcdcdcdcbd=cb
dcdcdcdcdcb=c
ddcdcdcdcddcdcdcbdd=cdb
dcdcdcdcddcdcdcdcbc=ccdcdcdcdcb
cbccb=dcdcdcdcbcd
cbcdcdcdcdcb=dcdcdcdcbc
ccbb=dcdcdcdcddcdcdcbdd
cdbccb=ddcdcdcdcddcdcdcbdcd
cdbcdcdcdcdcb=ddcdcdcdcddcdcdcbdc
dcbb=bd
cccbcdcdcdcb=dcdcdcdcddcdcdcddcdcdcdcbc
ccdcdcdcbdb=dcdcdcdcddcdcdcddcdcdcbdd
dcdcdcdcbcb=cbcdcdcdcbd
dcdcdcdcbcdb=cbdcdcdcdcddcdcdcbdd
dcdcdcdcbcccb=cbcdcdcdcddcdcdcdcbcd
dcdcdcdcbccdcdcdcdcb=cbcdcdcdcddcdcdcdcbc
ddcdcdcdcddcdcdcbcdb=cdbcdcdcdcddcdcdcbdd
ddcdcdcdcddcdcdcbdcb=cdbcdcdcdcbd
ddcdcdcdcddcdcdcbdcdb=cdbdcdcdcdcddcdcdcbdd
ddcdcdcdcddcdcdcbdcccb=cdbcdcdcdcddcdcdcdcbcd
ddcdcdcdcddcdcdcbdccdcdcdcdcb=cdbcdcdcdcddcdcdcdcbc
cbcbb=dcdcdcbdd
cbcdcdcdcbdb=dcdcdcddcdcdcbdd
cdbcbb=ddcdcdcdcddcdcdcbdbd
cdbcdcdcdcbdb=ddcdcdcdcddcdcbdd
cccbcdcdcbdb=dcdcdcdcddcdcdcddcdcdcddcdcdcbdd
ab=d
ca=dcc
da=adcb
ba=dcb