#5670 ⟨a, b | aabaab=bbaab⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by b is not injective:
- a²ba² ⋅ b = b²a²b and b²a² ⋅ b = b²a²b, however a²ba² ≠ b²a²
Enveloping group is isomorphic to ℤ

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

Auxiliary generators:
1. c = bbaab
Reduction order:
- Right-to-left recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	b²c² ⇒ cb²c	[10]
2.	b⁴c ⇒ c²	[8]
3.	(b²c)² ⇒ c³	[11]
4.	ca²b ⇒ b²c	[7]
5.	b²a²b ⇒ c	[2]
6.	ca²c ⇒ b²cba²b	[9]
7.	b²a²c ⇒ cba²b	[4]
8.	a²bc ⇒ b²c	[12]
9.	a²b³c ⇒ c²	[13]
10.	(a²b)² ⇒ c	[3]
11.	a²ba²c ⇒ cba²b	[6]

# ab:aabaab=bbaab reversed:bc/a bbaab=c magic:0
bbcc=cbbc
bbbbc=cc
bbcbbc=ccc
caab=bbc
bbaab=c
caac=bbcbaab
bbaac=cbaab
aabc=bbc
aabbbc=cc
aabaab=c
aabaac=cbaab

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