#4356 ⟨a, b | abbbabbba=ab⟩

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

#	Rule	Proof
1.	ca² ⇒ ab	[27]
2.	cba² ⇒ ab²	[30]
3.	cab ⇒ cba	[20]
4.	c²a ⇒ cb	[49]
5.	cac ⇒ cb	[28]
6.	cb²a² ⇒ ab³	[39]
7.	cbab ⇒ cb²a	[38]
8.	cbca ⇒ cb²	[50]
9.	cbac ⇒ cb²	[29]
10.	c²b ⇒ cbc	[23]
11.	ab³ab ⇒ ab⁴a	[3]
12.	ab³ca ⇒ ab⁴	[35]
13.	cb³a ⇒ ab³c	[47]
14.	cb²ab ⇒ ab³c	[48]
15.	cb²ca ⇒ cb³	[51]
16.	cb²ac ⇒ cb³	[41]
17.	(cb)² ⇒ cb²c	[40]
18.	ab⁴ab ⇒ ab⁵a	[10]
19.	ab⁴ca ⇒ ab⁵	[53]
20.	ab³cb ⇒ ab⁴c	[9]
21.	cb⁴ ⇒ ab³c²	[37]
22.	cb³ca ⇒ ab³c²	[52]
23.	cb²cb ⇒ cb³c	[43]
24.	ab⁶ ⇒ c	[2]
25.	ab⁵ab ⇒ ca	[15]
26.	ab⁵ca ⇒ c	[45]
27.	ab⁴cb ⇒ ab⁵c	[32]
28.	cb³cb ⇒ ab³c³	[46]
29.	ab⁵cb ⇒ c²	[19]

# ab:abbbabbba=ab a/bc abbbbbb=c morph:7/0
caa=ab
cbaa=abb
cab=cba
cca=cb
cac=cb
cbbaa=abbb
cbab=cbba
cbca=cbb
cbac=cbb
ccb=cbc
abbbab=abbbba
abbbca=abbbb
cbbba=abbbc
cbbab=abbbc
cbbca=cbbb
cbbac=cbbb
cbcb=cbbc
abbbbab=abbbbba
abbbbca=abbbbb
abbbcb=abbbbc
cbbbb=abbbcc
cbbbca=abbbcc
cbbcb=cbbbc
abbbbbb=c
abbbbbab=ca
abbbbbca=c
abbbbcb=abbbbbc
cbbbcb=abbbccc
abbbbbcb=cc