⟨a, b | aaabbabbbba=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(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aaaa=c
2. bbabbbb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[11]
2.	cd ⇒ 1	[8]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[10]
5.	a⁴ ⇒ c	[2]
6.	bcb²a ⇒ cb²ab	[21]
7.	b²aba³ ⇒ dbcb²c	[24]
8.	b⁴c ⇒ a²(ab²)²	[16]
9.	b²ab²d ⇒ adb⁴	[12]
10.	b⁴ac ⇒ a³(b²a)²	[18]
11.	(b²a)²d ⇒ adb⁴a	[14]
12.	b⁴a²c ⇒ a³(b²a)²a	[28]
13.	(b²a)²ad ⇒ adb⁴a²	[26]
14.	b⁴a³ ⇒ a³db²cb²	[31]
15.	b²ab²a³ ⇒ d(b²c)²	[29]
16.	b²ab³d ⇒ dbab⁴	[13]
17.	b²ab³ad ⇒ dbab⁴a	[27]
18.	b²ab³a²d ⇒ dbab⁴a²	[32]
19.	b²ab³a³ ⇒ db(b²c)²	[33]
20.	b²ab⁴ ⇒ d	[3]

# ab:aaabbabbbba=1 reversed:cda/b aaaa=c,bbabbbb=d magic:0 dc=1 cd=1 ca=ac da=ad aaaa=c bcbba=cbbab bbabaaa=dbcbbc bbbbc=aaabbabb bbabbd=adbbbb bbbbac=aaabbabba bbabbad=adbbbba bbbbaac=aaabbabbaa bbabbaad=adbbbbaa bbbbaaa=aaadbbcbb bbabbaaa=dbbcbbc bbabbbd=dbabbbb bbabbbad=dbabbbba bbabbbaad=dbabbbbaa bbabbbaaa=dbbbcbbc bbabbbb=d

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

Σ	#	Presentation	Mapping
11	2993	⟨a, b \| aaabbbbaaba=1⟩	φ(a) = b, φ(b) = a
11	3131	⟨a, b \| aabbabbbbaa=1⟩	φ(a) = a, φ(b) = b
11	3184	⟨a, b \| abaaaabbbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

2993

⟨a, b | aaabbbbaaba=1⟩

φ(a) = b, φ(b) = a

3131

⟨a, b | aabbabbbbaa=1⟩

φ(a) = a, φ(b) = b

3184

⟨a, b | abaaaabbbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#2978 ⟨a, b \| aaabbabbbab=1⟩
Next:	#2981 ⟨a, b \| aaabbbaaaba=1⟩

#2979 ⟨a, b | aaabbabbbba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances