#4876 ⟨a, b | abbabbba=bab⟩

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

#	Rule	Proof
1.	ab ⇒ c	[2]
2.	acbda ⇒ c²	[6]
3.	bc ⇒ cbda	[5]
4.	acbd² ⇒ cdb	[14]
5.	acbdc ⇒ c²b	[9]
6.	ac²bd³ ⇒ cd²cb	[22]
7.	ac³bd³ ⇒ cdcbdc	[26]
8.	ac⁴bd³ ⇒ cd²c	[35]
9.	ac⁵bd³ ⇒ cdcbda	[37]
10.	c⁶bd³ ⇒ bd²a	[42]
11.	c²bdcda ⇒ dc	[7]
12.	bd²c ⇒ c⁴bd³	[32]
13.	c²bdcd² ⇒ d²b	[15]
14.	c²b(dc)² ⇒ dcb	[19]
15.	cb² ⇒ d	[3]
16.	bdb ⇒ cbd²	[11]
17.	cbdcb ⇒ bd	[8]
18.	c²bd³b ⇒ bd³	[24]
19.	b²d ⇒ cb(dc)²b	[10]
20.	bd²bd ⇒ c²bd⁴cb	[25]
21.	c²bdcdbd ⇒ d³cb	[21]
22.	bdcbda ⇒ c⁵bd³	[41]
23.	cbdc²bda ⇒ bdc	[12]
24.	c²bd³cbda ⇒ bd³c	[27]
25.	bdcbd² ⇒ cbd³b	[18]
26.	cbdc²bd² ⇒ bd²b	[16]
27.	c²bd³cbd² ⇒ bd⁴b	[28]
28.	(bdc)² ⇒ c³bd³	[31]
29.	(cbdc)² ⇒ bdcb	[20]
30.	c²bd³cbdc ⇒ bd³cb	[39]
31.	bdc²bd³ ⇒ cbd⁴cb	[23]
32.	bdc³bd³ ⇒ cbd³cbdc	[34]
33.	(c²bd³)² ⇒ bd⁵cb	[29]
34.	bdc⁴bd³ ⇒ cbd⁴c	[36]
35.	c²bd³c³bd³ ⇒ bd⁴cbdc	[43]
36.	bdc⁵bd³ ⇒ cbd³cbda	[40]
37.	c²bd³c⁴bd³ ⇒ bd⁵c	[38]
38.	c²bd³c⁵bd³ ⇒ bd⁴cbda	[44]

# ab:abbabbba=bab reversed:a/dc/b ab=c,cbb=d morph:2/1,3/1
ab=c
acbda=cc
bc=cbda
acbdd=cdb
acbdc=ccb
accbddd=cddcb
acccbddd=cdcbdc
accccbddd=cddc
acccccbddd=cdcbda
ccccccbddd=bdda
ccbdcda=dc
bddc=ccccbddd
ccbdcdd=ddb
ccbdcdc=dcb
cbb=d
bdb=cbdd
cbdcb=bd
ccbdddb=bddd
bbd=cbdcdcb
bddbd=ccbddddcb
ccbdcdbd=dddcb
bdcbda=cccccbddd
cbdccbda=bdc
ccbdddcbda=bdddc
bdcbdd=cbdddb
cbdccbdd=bddb
ccbdddcbdd=bddddb
bdcbdc=cccbddd
cbdccbdc=bdcb
ccbdddcbdc=bdddcb
bdccbddd=cbddddcb
bdcccbddd=cbdddcbdc
ccbdddccbddd=bdddddcb
bdccccbddd=cbddddc
ccbdddcccbddd=bddddcbdc
bdcccccbddd=cbdddcbda
ccbdddccccbddd=bdddddc
ccbdddcccccbddd=bddddcbda