#4925 ⟨a, b | aaaaaba=baba⟩

Properties
Rewriting system

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by a is not injective:
- a⁵b ⋅ a = (ba)² and bab ⋅ a = (ba)², however a⁵b ≠ bab

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 = baba
Reduction order:
- Right-to-left shortlex with a < b < c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	bac ⇒ cba	[4]
2.	(ba)² ⇒ c	[2]
3.	a⁵c ⇒ cba	[6]
4.	ca⁴c ⇒ babcba	[8]
5.	a⁵ba ⇒ c	[3]
6.	ca⁴ba ⇒ babc	[7]
7.	a⁵bc ⇒ babc	[10]
8.	(bab)²c ⇒ ca⁴bc	[9]
9.	a⁵b²abc ⇒ ca⁴bc	[11]
10.	ca⁴b²abc ⇒ babca⁴bc	[12]

# ab:aaaaaba=baba reversed:abc baba=c magic:0
bac=cba
baba=c
aaaaac=cba
caaaac=babcba
aaaaaba=c
caaaaba=babc
aaaaabc=babc
babbabc=caaaabc
aaaaabbabc=caaaabc
caaaabbabc=babcaaaabc

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#4925 ⟨a, b | aaaaaba=baba⟩

Contents

Properties

Rewriting system