⟨a, b | aaababbbbba=1⟩

Up:

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. babbbbb=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.	bcba ⇒ cbab	[21]
7.	baba³ ⇒ d(bc)²	[23]
8.	bab²a³ ⇒ db(bc)²	[25]
9.	bab³a³ ⇒ db³cbc	[27]
10.	b⁵c ⇒ a³bab⁴	[15]
11.	bab⁴d ⇒ adb⁵	[12]
12.	b⁵ac ⇒ a³bab⁴a	[17]
13.	bab⁴ad ⇒ adb⁵a	[13]
14.	b⁵a²c ⇒ a³bab⁴a²	[30]
15.	bab⁴a²d ⇒ adb⁵a²	[29]
16.	b⁵a³ ⇒ a³db⁴cb	[33]
17.	bab⁴a³ ⇒ db⁴cbc	[31]
18.	bab⁵ ⇒ d	[3]

# ab:aaababbbbba=1 reversed:cda/b aaaa=c,babbbbb=d magic:0 dc=1 cd=1 ca=ac da=ad aaaa=c bcba=cbab babaaa=dbcbc babbaaa=dbbcbc babbbaaa=dbbbcbc bbbbbc=aaababbbb babbbbd=adbbbbb bbbbbac=aaababbbba babbbbad=adbbbbba bbbbbaac=aaababbbbaa babbbbaad=adbbbbbaa bbbbbaaa=aaadbbbbcb babbbbaaa=dbbbbcbc babbbbb=d

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

Σ	#	Presentation	Mapping
11	3092	⟨a, b \| aababbbbbaa=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3092

⟨a, b | aababbbbbaa=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2952 ⟨a, b \| aaababbbbab=1⟩
Next:	#2956 ⟨a, b \| aaabbaaaabb=1⟩

#2953 ⟨a, b | aaababbbbba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances