#1175 ⟨a, b | aaaba=baba⟩

Properties
Rewriting system

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by a is not injective:
- a³b ⋅ a = (ba)² and bab ⋅ a = (ba)², however a³b ≠ 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 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.	bac ⇒ cba	[4]
2.	(ba)² ⇒ c	[2]
3.	ca²c ⇒ babcba	[8]
4.	(bab)²c ⇒ ca²bc	[9]
5.	ca²ba ⇒ babc	[7]
6.	a³c ⇒ cba	[6]
7.	a³bc ⇒ babc	[10]
8.	ca²b²abc ⇒ babca²bc	[12]
9.	a³ba ⇒ c	[3]
10.	a³b²abc ⇒ ca²bc	[11]

# ab:aaaba=baba reversed:bc/a baba=c magic:0
bac=cba
baba=c
caac=babcba
babbabc=caabc
caaba=babc
aaac=cba
aaabc=babc
caabbabc=babcaabc
aaaba=c
aaabbabc=caabc

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#1175 ⟨a, b | aaaba=baba⟩

Contents

Properties

Rewriting system