#5401 ⟨a, b | abbabba=abab⟩

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

#	Rule	Proof
1.	dc ⇒ d⁷	[31]
2.	d⁵a ⇒ dad	[32]
3.	cac ⇒ cad⁶	[33]
4.	c²a ⇒ ad³	[20]
5.	d³b ⇒ bc	[16]
6.	cad⁴a ⇒ ca²d	[34]
7.	abc ⇒ abd⁶	[23]
8.	adb ⇒ abd²	[11]
9.	ad²b ⇒ abd⁴	[28]
10.	d³ab ⇒ dabd	[17]
11.	cab ⇒ abd³	[21]
12.	bad ⇒ dab	[7]
13.	bca ⇒ d²ab	[19]
14.	d²ba ⇒ dab	[10]
15.	cad²ab ⇒ ca²bd	[27]
16.	abdad ⇒ ca²b	[24]
17.	abd²ad ⇒ ad²ab	[15]
18.	abd³ad ⇒ cadab	[22]
19.	abd⁴a ⇒ adab	[30]
20.	abd²b ⇒ c	[13]
21.	dab² ⇒ d³	[14]
22.	dabdb ⇒ d⁵	[25]
23.	bab ⇒ d	[3]
24.	ca²b² ⇒ cad²	[26]
25.	ca²bdb ⇒ cad⁴	[29]
26.	abdab ⇒ ca	[18]
27.	abd²ab ⇒ ad²	[12]
28.	abdba ⇒ ad	[5]

# ab:abbabba=abab d/c/ab ababbb=c,bab=d morph:6/1,3/1
dc=ddddddd
ddddda=dad
cac=cadddddd
cca=addd
dddb=bc
cadddda=caad
abc=abdddddd
adb=abdd
addb=abdddd
dddab=dabd
cab=abddd
bad=dab
bca=ddab
ddba=dab
caddab=caabd
abdad=caab
abddad=addab
abdddad=cadab
abdddda=adab
abddb=c
dabb=ddd
dabdb=ddddd
bab=d
caabb=cadd
caabdb=cadddd
abdab=ca
abddab=add
abdba=ad