#4007 ⟨a, b | aaababbba=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. bbba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a³bac ⇒ ab	[3]
2.	ca²bac ⇒ cb	[4]
3.	acabaca ⇒ abc	[11]
4.	c²abaca ⇒ cbc	[14]
5.	ab²c ⇒ acabacba	[12]
6.	cb²c ⇒ c²abacba	[23]
7.	(aba)²c ⇒ ab²	[5]
8.	cba²bac ⇒ cb²	[6]
9.	abcabac ⇒ acabacb	[19]
10.	cbcabac ⇒ c²abacb	[21]
11.	a(ba)²ca ⇒ a³babc	[15]
12.	c(ba)²ca ⇒ ca(ab)²c	[16]
13.	abcbaca ⇒ ac(ab)²c	[20]
14.	(cb)²aca ⇒ c²(ab)²c	[22]
15.	b³a ⇒ c	[2]
16.	ab³c ⇒ acabacb²a	[13]
17.	cb³c ⇒ c²abacb²a	[24]
18.	ab²a²bac ⇒ ab³	[7]
19.	cb²a²bac ⇒ cb³	[8]
20.	ab(ba)²ca ⇒ (aba)²bc	[17]
21.	cb(ba)²ca ⇒ cba(ab)²c	[18]
22.	ab⁴ ⇒ acabac	[9]
23.	cb⁴ ⇒ c²abac	[10]
24.	ab²a(ab)²c ⇒ acbaca	[25]
25.	cb²a(ab)²c ⇒ c²baca	[26]

# ab:aaababbba=ab reversed:ac/b bbba=c morph:4/0
aaabac=ab
caabac=cb
acabaca=abc
ccabaca=cbc
abbc=acabacba
cbbc=ccabacba
abaabac=abb
cbaabac=cbb
abcabac=acabacb
cbcabac=ccabacb
ababaca=aaababc
cbabaca=caababc
abcbaca=acababc
cbcbaca=ccababc
bbba=c
abbbc=acabacbba
cbbbc=ccabacbba
abbaabac=abbb
cbbaabac=cbbb
abbabaca=abaababc
cbbabaca=cbaababc
abbbb=acabac
cbbbb=ccabac
abbaababc=acbaca
cbbaababc=ccbaca