⟨a, b | aaaabbabbba=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. bbabbb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[14]
2.	cd ⇒ 1	[8]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[13]
5.	a⁵ ⇒ c	[2]
6.	b³c ⇒ a⁴b²ab	[18]
7.	b²abd ⇒ adb³	[15]
8.	bcb²a ⇒ cb²ab	[25]
9.	b³ac ⇒ a⁴b(ba)²	[20]
10.	b(ba)²d ⇒ adb³a	[16]
11.	b³a²c ⇒ a⁴b²aba²	[27]
12.	b²aba²d ⇒ adb³a²	[21]
13.	b³a³c ⇒ a⁴b²aba³	[31]
14.	b²aba³d ⇒ adb³a³	[28]
15.	b³a⁴ ⇒ a⁴dbcb²	[33]
16.	b²aba⁴ ⇒ dbcb²c	[26]
17.	b²ab²d ⇒ dbab³	[10]
18.	(b²a)²d ⇒ dbab³a	[22]
19.	(b²a)²ad ⇒ dbab³a²	[30]
20.	b²ab²a³d ⇒ dbab³a³	[34]
21.	b²ab²a⁴ ⇒ d(b²c)²	[35]
22.	b²ab³ ⇒ d	[3]

# ab:aaaabbabbba=1 reversed:cda/b aaaaa=c,bbabbb=d magic:0 dc=1 cd=1 ca=ac da=ad aaaaa=c bbbc=aaaabbab bbabd=adbbb bcbba=cbbab bbbac=aaaabbaba bbabad=adbbba bbbaac=aaaabbabaa bbabaad=adbbbaa bbbaaac=aaaabbabaaa bbabaaad=adbbbaaa bbbaaaa=aaaadbcbb bbabaaaa=dbcbbc bbabbd=dbabbb bbabbad=dbabbba bbabbaad=dbabbbaa bbabbaaad=dbabbbaaa bbabbaaaa=dbbcbbc bbabbb=d

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

Σ	#	Presentation	Mapping
11	2977	⟨a, b \| aaabbabbbaa=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

2977

⟨a, b | aaabbabbbaa=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2882 ⟨a, b \| aaaabbabbab=1⟩
Next:	#2885 ⟨a, b \| aaaabbbaaab=1⟩

#2883 ⟨a, b | aaaabbabbba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances