#4192 ⟨a, b | aabbbaaab=ba⟩

Contents

Properties
Rewriting system

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabbbaab^-1a^-1b⟩
- Anti-isomorphic embedding: φ(a) = a, φ(b) = b

Rewriting system

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

Auxiliary generators:
1. c = abbba
2. d = aab
Reduction order:
- Right-to-left recursive path with deg(d) = 0; deg(c) = deg(a) = 1, c < a; deg(b) = 2
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	da(cd)² ⇒ ac	[12]
2.	a³cd ⇒ da	[7]
3.	a²(cd)³ ⇒ c	[11]
4.	dacdcac ⇒ aca(cd)²	[13]
5.	a³cac ⇒ da²(cd)²	[10]
6.	a²c(dc)²ac ⇒ ca(cd)²	[14]
7.	a²b ⇒ d	[3]
8.	bd ⇒ acdab	[9]
9.	bc ⇒ acac²d	[8]
10.	ba ⇒ acd	[6]

# ab:aabbbaaab=ba reversed:d/ca/b abbba=c,aab=d morph:5/0,3/0
dacdcd=ac
aaacd=da
aacdcdcd=c
dacdcac=acacdcd
aaacac=daacdcd
aacdcdcac=cacdcd
aab=d
bd=acdab
bc=acaccd
ba=acd