#4105 ⟨a, b | aabaabbba=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(c) = 0; deg(a) = deg(b) = 1, a < b
Auxiliary generators:
1. abbb=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a²bac² ⇒ cb	[4]
2.	cabaca ⇒ cb	[9]
3.	ab³ ⇒ c	[2]
4.	c(ba)²c² ⇒ cabac²b	[15]
5.	cb²aca ⇒ cabacb	[17]
6.	cb⁴ ⇒ cabac²	[10]
7.	a²baca ⇒ ab	[3]
8.	a(ba)²c² ⇒ cb²	[6]
9.	ab²aca ⇒ a²bacb	[11]
10.	c(ba)²ca ⇒ cb²	[12]
11.	cb(ba)²c² ⇒ cabac²b²	[16]
12.	cb³aca ⇒ c(ba)²cb	[21]
13.	a(ba)²ca ⇒ ab²	[5]
14.	a(ba)²cb ⇒ (ca)²	[13]
15.	ab(ba)²c² ⇒ cb³	[7]
16.	cb(ba)²ca ⇒ cb³	[14]
17.	cb(ba)²cb ⇒ cabac(ca)²	[22]
18.	cb³abac² ⇒ cabac²b³	[20]
19.	ab(ba)²ca ⇒ c	[8]
20.	ab(ba)²cb ⇒ cbaca	[18]
21.	cb³abaca ⇒ cabac²	[19]
22.	cb³abacb ⇒ cabac²baca	[23]

# ab:aabaabbba=ab c/ab abbb=c morph:4/0
aabacc=cb
cabaca=cb
abbb=c
cbabacc=cabaccb
cbbaca=cabacb
cbbbb=cabacc
aabaca=ab
ababacc=cbb
abbaca=aabacb
cbabaca=cbb
cbbabacc=cabaccbb
cbbbaca=cbabacb
ababaca=abb
ababacb=caca
abbabacc=cbbb
cbbabaca=cbbb
cbbabacb=cabaccaca
cbbbabacc=cabaccbbb
abbabaca=c
abbabacb=cbaca
cbbbabaca=cabacc
cbbbabacb=cabaccbaca