⟨a, b | aaaababbbba=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. aaaaa=c
2. babbbb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[13]
2.	cd ⇒ 1	[8]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[12]
5.	a⁵ ⇒ c	[2]
6.	bcba ⇒ cbab	[21]
7.	baba⁴ ⇒ d(bc)²	[23]
8.	bab²a⁴ ⇒ db(bc)²	[25]
9.	b⁴c ⇒ a⁴bab³	[17]
10.	bab³d ⇒ adb⁴	[14]
11.	b⁴ac ⇒ a⁴bab³a	[19]
12.	bab³ad ⇒ adb⁴a	[15]
13.	b⁴a²c ⇒ a⁴bab³a²	[28]
14.	bab³a²d ⇒ adb⁴a²	[27]
15.	b⁴a³c ⇒ a⁴bab³a³	[31]
16.	bab³a³d ⇒ adb⁴a³	[29]
17.	b⁴a⁴ ⇒ a⁴db³cb	[33]
18.	bab³a⁴ ⇒ db³cbc	[30]
19.	bab⁴ ⇒ d	[3]

# ab:aaaababbbba=1 reversed:cda/b aaaaa=c,babbbb=d magic:0 dc=1 cd=1 ca=ac da=ad aaaaa=c bcba=cbab babaaaa=dbcbc babbaaaa=dbbcbc bbbbc=aaaababbb babbbd=adbbbb bbbbac=aaaababbba babbbad=adbbbba bbbbaac=aaaababbbaa babbbaad=adbbbbaa bbbbaaac=aaaababbbaaa babbbaaad=adbbbbaaa bbbbaaaa=aaaadbbbcb babbbaaaa=dbbbcbc babbbb=d

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

Σ	#	Presentation	Mapping
11	2951	⟨a, b \| aaababbbbaa=1⟩	φ(a) = a, φ(b) = b
11	3302	⟨a, b \| abbbbaaaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

2951

⟨a, b | aaababbbbaa=1⟩

φ(a) = a, φ(b) = b

3302

⟨a, b | abbbbaaaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2868 ⟨a, b \| aaaababbbab=1⟩
Next:	#2870 ⟨a, b \| aaaabbaaaab=1⟩

#2869 ⟨a, b | aaaababbbba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances