#2002 ⟨a, b | aabbbaab=ba⟩

Properties
Rewriting system

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabbab^-1a^-1bb⟩
- Embedding: φ(a) = b, φ(b) = a

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

#	Rule	Proof
1.	(a²c²a²(ac²)³a³c²a)²c² ⇒ ca	[11]
2.	ba ⇒ a²c²ab	[7]
3.	bc ⇒ c²ab	[6]
4.	(a²c²a²(ac²)³a³c²a)²b³ ⇒ c	[12]

# ab:aabbbaab=ba reversed:ac/b bbaab=c morph:5/0
aaccaaaccaccaccaaaccaaaccaaaccaccaccaaaccacc=ca
ba=aaccab
bc=ccab
aaccaaaccaccaccaaaccaaaccaaaccaccaccaaaccabbb=c

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#2002 ⟨a, b | aabbbaab=ba⟩

Contents

Properties

Rewriting system