⟨a, b | aaaabbbbaba=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. bbbbab=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.	a⁴b²ab ⇒ cbcb²d	[32]
9.	cb⁴ ⇒ b³aba⁴	[24]
10.	db³ab ⇒ b⁴da	[20]
11.	cab⁴ ⇒ ab³aba⁴	[25]
12.	dab³ab ⇒ ab⁴da	[23]
13.	ca²b⁴ ⇒ a²b³aba⁴	[34]
14.	da²b³ab ⇒ a²b⁴da	[22]
15.	ca³b⁴ ⇒ a³b³aba⁴	[37]
16.	da³b³ab ⇒ a³b⁴da	[35]
17.	a⁴b⁴ ⇒ bcb³da⁴	[39]
18.	a⁴b³ab ⇒ cbcb³d	[36]
19.	b⁴ab ⇒ d	[3]

# ab:aaaabbbbaba=1 cda/b aaaaa=c,bbbbab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaaa=c abcb=babc aaaabab=cbcbd aaaabbab=cbcbbd cbbbb=bbbabaaaa dbbbab=bbbbda cabbbb=abbbabaaaa dabbbab=abbbbda caabbbb=aabbbabaaaa daabbbab=aabbbbda caaabbbb=aaabbbabaaaa daaabbbab=aaabbbbda aaaabbbb=bcbbbdaaaa aaaabbbab=cbcbbbd bbbbab=d

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

Σ	#	Presentation	Mapping
11	2995	⟨a, b \| aaabbbbabaa=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

2995

⟨a, b | aaabbbbabaa=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2893 ⟨a, b \| aaaabbbbaab=1⟩
Next:	#2895 ⟨a, b \| aaaabbbbabb=1⟩

#2894 ⟨a, b | aaaabbbbaba=1⟩

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Properties

Rewriting system

Isomorphic instances