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

#	Rule	Proof
1.	cd ⇒ 1	[12]
2.	dc ⇒ 1	[19]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[18]
5.	a⁵ ⇒ c	[2]
6.	abcb ⇒ babc	[28]
7.	a⁴bab ⇒ (cb)²d	[30]
8.	cb³ ⇒ b²aba⁴	[24]
9.	db²ab ⇒ b³da	[20]
10.	cab³ ⇒ ab²aba⁴	[25]
11.	dab²ab ⇒ ab³da	[23]
12.	ca²b³ ⇒ a²b²aba⁴	[32]
13.	da²b²ab ⇒ a²b³da	[22]
14.	ca³b³ ⇒ a³b²aba⁴	[35]
15.	da³b²ab ⇒ a³b³da	[33]
16.	a⁴b³ ⇒ bcb²da⁴	[37]
17.	a⁴b²ab ⇒ cbcb²d	[34]
18.	b³ab ⇒ d	[3]

# ab:aaaabbbaba=1 cda/b aaaaa=c,bbbab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaaa=c abcb=babc aaaabab=cbcbd cbbb=bbabaaaa dbbab=bbbda cabbb=abbabaaaa dabbab=abbbda caabbb=aabbabaaaa daabbab=aabbbda caaabbb=aaabbabaaaa daaabbab=aaabbbda aaaabbb=bcbbdaaaa aaaabbab=cbcbbd bbbab=d

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

Σ	#	Presentation	Mapping
10	1381	⟨a, b \| aaabbbabaa=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

1381

⟨a, b | aaabbbabaa=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#1331 ⟨a, b \| aaaabbbaab=1⟩
Next:	#1333 ⟨a, b \| aaaabbbabb=1⟩

#1332 ⟨a, b | aaaabbbaba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances