⟨a, b | aaaabbbaaba=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. bbbaab=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.	a²bcb ⇒ ba²bc	[28]
7.	a(a²b)² ⇒ (cb)²d	[30]
8.	cb³ ⇒ b²a²ba³	[24]
9.	db²a²b ⇒ b³da²	[20]
10.	cab³ ⇒ ab²a²ba³	[25]
11.	dab²a²b ⇒ ab³da²	[23]
12.	ca²b³ ⇒ a²b²a²ba³	[32]
13.	da²b²a²b ⇒ a²b³da²	[22]
14.	a³b³ ⇒ bcb²da³	[35]
15.	a³b²a²b ⇒ cbcb²d	[33]
16.	b³a²b ⇒ d	[3]

# ab:aaaabbbaaba=1 cda/b aaaaa=c,bbbaab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaaa=c aabcb=baabc aaabaab=cbcbd cbbb=bbaabaaa dbbaab=bbbdaa cabbb=abbaabaaa dabbaab=abbbdaa caabbb=aabbaabaaa daabbaab=aabbbdaa aaabbb=bcbbdaaa aaabbaab=cbcbbd bbbaab=d

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

Σ	#	Presentation	Mapping
11	2983	⟨a, b \| aaabbbaabaa=1⟩	φ(a) = a, φ(b) = b
11	3176	⟨a, b \| abaaaaabbba=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

2983

⟨a, b | aaabbbaabaa=1⟩

φ(a) = a, φ(b) = b

3176

⟨a, b | abaaaaabbba=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2885 ⟨a, b \| aaaabbbaaab=1⟩
Next:	#2887 ⟨a, b \| aaaabbbaabb=1⟩

#2886 ⟨a, b | aaaabbbaaba=1⟩

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Properties

Rewriting system

Isomorphic instances