⟨a, b | abaaabababa=1⟩

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Monoids with two generators and one relation

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Reduction order:
- Right-to-left recursive path with deg(d) = deg(c) = 0, d < c; deg(a) = 1; deg(b) = 2
Auxiliary generators:
1. ba=c
2. acaa=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	dc ⇒ cd	[14]
2.	c³d ⇒ 1	[20]
3.	acad ⇒ cda²	[16]
4.	ac³ac ⇒ c³aca	[24]
5.	(ac)²d ⇒ cda²c	[15]
6.	a²c² ⇒ c²dac³a	[22]
7.	acac²d ⇒ dac³a	[21]
8.	aca² ⇒ d	[3]
9.	a(cac)² ⇒ dac⁶aca	[25]
10.	b ⇒ c⁴aca	[26]

# ab:abaaabababa=1 reversed:dc/a/b ba=c,acaa=d morph:2/0,4/0 dc=cd cccd=1 acad=cdaa acccac=cccaca acacd=cdaac aacc=ccdaccca acaccd=daccca acaa=d acaccac=daccccccaca b=ccccaca

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

Σ	#	Presentation	Mapping
11	3201	⟨a, b \| abaabaaabab=1⟩	φ(a) = a, φ(b) = ccccaca
11	3233	⟨a, b \| ababaabaaab=1⟩	φ(a) = a, φ(b) = cccacac

Presentation

Mapping

3201

⟨a, b | abaabaaabab=1⟩

φ(a) = a, φ(b) = ccccaca

3233

⟨a, b | ababaabaaab=1⟩

φ(a) = a, φ(b) = cccacac

Up:	Monoids with two generators and one relation
Prev:	#3188 ⟨a, b \| abaaabaabba=1⟩
Next:	#3191 ⟨a, b \| abaaababbab=1⟩

#3190 ⟨a, b | abaaabababa=1⟩

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Properties

Rewriting system

Isomorphic instances