⟨a, b, c | aa=1, bbbccb=1⟩

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

#	Rule	Proof
1.	a² ⇒ 1	[1]
2.	b⁴d ⇒ db⁴	[27]
3.	cb ⇒ d	[3]
4.	b⁴c ⇒ db³	[25]
5.	db³d ⇒ b	[28]
6.	db³c ⇒ 1	[26]
7.	cdb³ ⇒ 1	[18]
8.	bcd ⇒ cdb	[13]
9.	bc² ⇒ cd	[14]
10.	dcdb² ⇒ c	[19]
11.	cd² ⇒ bdc²	[17]
12.	cdbd ⇒ b²dc²	[20]
13.	cdb²d ⇒ b³dc²	[21]
14.	c²d ⇒ dc²	[15]
15.	d(cd)²b ⇒ c³	[16]
16.	d(cd)³ ⇒ c⁵	[22]

# abc:aa=1,bbbccb=1 ab/dc cb=d morph:2/1 aa=1 bbbbd=dbbbb cb=d bbbbc=dbbb dbbbd=b dbbbc=1 cdbbb=1 bcd=cdb bcc=cd dcdbb=c cdd=bdcc cdbd=bbdcc cdbbd=bbbdcc ccd=dcc dcdcdb=ccc dcdcdcd=ccccc

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

Σ	#	Presentation	Mapping
8	6272	⟨a, b, c \| aa=1, bccccb=1⟩	φ(a) = a, φ(b) = c, φ(c) = b

Presentation

Mapping

6272

⟨a, b, c | aa=1, bccccb=1⟩

φ(a) = a, φ(b) = c, φ(c) = b

Up:	Monoid enumeration
Prev:	#6250 ⟨a, b, c \| aa=1, bbbcbc=1⟩
Next:	#6252 ⟨a, b, c \| aa=1, bbbccc=1⟩

#6251 ⟨a, b, c | aa=1, bbbccb=1⟩

Contents

Properties

Rewriting system

Isomorphic instances