#4292 ⟨a, b | ababaabba=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:
- Right-to-left recursive path with deg(c) = deg(a) = 0, c < a; deg(b) = 1
Auxiliary generators:
1. baabba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c²a ⇒ c	[9]
2.	c²ba ⇒ cabc	[29]
3.	cbc² ⇒ c³b	[25]
4.	cabc² ⇒ c²b	[17]
5.	cbac ⇒ cb	[5]
6.	abac ⇒ ab	[3]
7.	cbca ⇒ cb	[12]
8.	abca ⇒ ab	[11]
9.	cb²a ⇒ cba²bc	[20]
10.	cab²a ⇒ ba²bc	[4]
11.	(cb)²a ⇒ cbabc	[31]
12.	abcba ⇒ (ab)²c	[30]
13.	cb²c² ⇒ c³b²	[27]
14.	ab²c² ⇒ abc²b	[26]
15.	cbabc² ⇒ (cb)²	[23]
16.	(ab)²c² ⇒ abcb	[22]
17.	ba²bc² ⇒ cab²	[10]
18.	ab²ac ⇒ ab²	[6]
19.	cb²ca ⇒ cb²	[14]
20.	ab²ca ⇒ ab²	[13]
21.	cb³ ⇒ c⁵	[38]
22.	cab³ ⇒ c⁴	[34]
23.	ba²b² ⇒ c²	[8]
24.	ab³a ⇒ ab²a²bc	[21]
25.	cbab²a ⇒ cbaba²bc	[18]
26.	abab²a ⇒ (ab)²a²bc	[16]
27.	cb²cba ⇒ cba²(bc)²	[33]
28.	ab²cba ⇒ ab²abc	[32]
29.	ab³c² ⇒ abc²b²	[28]
30.	ab²abc² ⇒ ab²cb	[24]
31.	ab³ca ⇒ ab³	[15]
32.	ab⁴ ⇒ abc⁴	[39]
33.	cbab³ ⇒ c³bc	[36]
34.	abab³ ⇒ abc³	[35]
35.	a(b²a)² ⇒ ab²aba²bc	[19]
36.	ab³cba ⇒ ab²a²(bc)²	[40]
37.	ab²ab³ ⇒ abc²bc	[37]

# ab:ababaabba=ab reversed:ca/b baabba=c morph:6/0
cca=c
ccba=cabc
cbcc=cccb
cabcc=ccb
cbac=cb
abac=ab
cbca=cb
abca=ab
cbba=cbaabc
cabba=baabc
cbcba=cbabc
abcba=ababc
cbbcc=cccbb
abbcc=abccb
cbabcc=cbcb
ababcc=abcb
baabcc=cabb
abbac=abb
cbbca=cbb
abbca=abb
cbbb=ccccc
cabbb=cccc
baabb=cc
abbba=abbaabc
cbabba=cbabaabc
ababba=ababaabc
cbbcba=cbaabcbc
abbcba=abbabc
abbbcc=abccbb
abbabcc=abbcb
abbbca=abbb
abbbb=abcccc
cbabbb=cccbc
ababbb=abccc
abbabba=abbabaabc
abbbcba=abbaabcbc
abbabbb=abccbc