⟨a, b | aababbbaaba=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:
- Left-to-right recursive path with deg(c) = deg(b) = 0, c < b; deg(d) = 1; deg(a) = 2
Auxiliary generators:
1. bbb=c
2. aabaaaba=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	bc ⇒ cb	[5]
2.	b³ ⇒ c	[2]
3.	dc ⇒ 1	[14]
4.	cd ⇒ 1	[10]
5.	bd ⇒ db	[15]
6.	ca²ba ⇒ a²bac	[9]
7.	cba²ba ⇒ ba²bac	[12]
8.	cb²a²ba ⇒ b²a²bac	[21]
9.	da²ba ⇒ a²bad	[6]
10.	dba²ba ⇒ ba²bad	[16]
11.	db²a²ba ⇒ b²a²bad	[22]
12.	ba³ba ⇒ abaca²db	[27]
13.	b(ba)²ca² ⇒ ca³bab²	[23]
14.	b²a²ba³ ⇒ a³bacadb²	[25]
15.	b²a²baca² ⇒ ca³bacadb²	[28]
16.	b²a²bac²a² ⇒ c²a³bacadb²	[30]
17.	c³a³baca ⇒ b²a²bac³a²b	[33]
18.	da³baca ⇒ b²a²bada²b	[31]
19.	a³baca² ⇒ db²	[18]

# ab:aababbbaaba=1 cb/d/a bbb=c,aabaaaba=d magic:1 bc=cb bbb=c dc=1 cd=1 bd=db caaba=aabac cbaaba=baabac cbbaaba=bbaabac daaba=aabad dbaaba=baabad dbbaaba=bbaabad baaaba=abacaadb bbabacaa=caaababb bbaabaaa=aaabacadbb bbaabacaa=caaabacadbb bbaabaccaa=ccaaabacadbb cccaaabaca=bbaabacccaab daaabaca=bbaabadaab aaabacaa=dbb

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

Σ	#	Presentation	Mapping
11	3130	⟨a, b \| aabbabbbaba=1⟩	φ(a) = b, φ(b) = a
11	3192	⟨a, b \| abaaababbba=1⟩	φ(a) = a, φ(b) = b
11	3297	⟨a, b \| abbbaabaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3130

⟨a, b | aabbabbbaba=1⟩

φ(a) = b, φ(b) = a

3192

⟨a, b | abaaababbba=1⟩

φ(a) = a, φ(b) = b

3297

⟨a, b | abbbaabaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#3083 ⟨a, b \| aababbabbba=1⟩
Next:	#3086 ⟨a, b \| aababbbaabb=1⟩

#3085 ⟨a, b | aababbbaaba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances