#7705 ⟨a, b, c | aa=1, cbc=bcb⟩

Contents

Properties
Rewriting system

Properties

Sum of relation sides is 8
Infinite non-commutative monoid
Element ba has infinite order

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. d = cb
Reduction order:
- Left-to-right shortlex with a < b < c < d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a² ⇒ 1	[1]
2.	cb ⇒ d	[3]
3.	dc ⇒ bd	[5]
4.	bdb ⇒ d²	[6]
5.	d²b ⇒ cd²	[7]

# abc:aa=1,cbc=bcb abcd cb=d morph:2/1
aa=1
cb=d
dc=bd
bdb=dd
ddb=cdd