#4148 ⟨a, b | aababbbba=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(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. bbbba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a²bac ⇒ ab	[3]
2.	cabac ⇒ cb	[4]
3.	acbaca ⇒ abc	[13]
4.	c²baca ⇒ cbc	[17]
5.	ab²c ⇒ a(cba)²	[14]
6.	cb²c ⇒ c(cba)²	[29]
7.	a(ba)²c ⇒ ab²	[5]
8.	c(ba)²c ⇒ cb²	[6]
9.	abcbac ⇒ (acb)²	[24]
10.	(cb)²ac ⇒ c²bacb	[28]
11.	ab²aca ⇒ a(ab)²c	[18]
12.	cb²aca ⇒ c(ab)²c	[19]
13.	ab³c ⇒ (acb)²ba	[15]
14.	cb³c ⇒ c²bacb²a	[30]
15.	ab(ba)²c ⇒ ab³	[7]
16.	cb(ba)²c ⇒ cb³	[8]
17.	ab³aca ⇒ (ab)³c	[20]
18.	cb³aca ⇒ cb(ab)²c	[21]
19.	b⁴a ⇒ c	[2]
20.	ab⁴c ⇒ (acb)²b²a	[16]
21.	cb⁴c ⇒ c²bacb³a	[31]
22.	ab²(ab)²c ⇒ ac²a	[22]
23.	cb²(ab)²c ⇒ c³a	[23]
24.	ab³abac ⇒ ab⁴	[9]
25.	cb³abac ⇒ cb⁴	[10]
26.	ab⁵ ⇒ acbac	[11]
27.	cb⁵ ⇒ c²bac	[12]
28.	ab³(ab)²c ⇒ abc²a	[32]
29.	cb³(ab)²c ⇒ cbc²a	[33]

# ab:aababbbba=ab reversed:ac/b bbbba=c morph:5/0
aabac=ab
cabac=cb
acbaca=abc
ccbaca=cbc
abbc=acbacba
cbbc=ccbacba
ababac=abb
cbabac=cbb
abcbac=acbacb
cbcbac=ccbacb
abbaca=aababc
cbbaca=cababc
abbbc=acbacbba
cbbbc=ccbacbba
abbabac=abbb
cbbabac=cbbb
abbbaca=abababc
cbbbaca=cbababc
bbbba=c
abbbbc=acbacbbba
cbbbbc=ccbacbbba
abbababc=acca
cbbababc=ccca
abbbabac=abbbb
cbbbabac=cbbbb
abbbbb=acbac
cbbbbb=ccbac
abbbababc=abcca
cbbbababc=cbcca