⟨a, b | aaaaaabbaba=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. aaaaaaa=c
2. bbab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[14]
2.	dc ⇒ 1	[32]
3.	ac ⇒ ca	[6]
4.	ad ⇒ da	[31]
5.	a⁷ ⇒ c	[2]
6.	cb² ⇒ baba⁶	[27]
7.	dbab ⇒ b²da	[42]
8.	abcb ⇒ babc	[38]
9.	cab² ⇒ (ab)²a⁶	[26]
10.	d(ab)² ⇒ ab²da	[33]
11.	ca²b² ⇒ a(ab)²a⁶	[41]
12.	da(ab)² ⇒ a²b²da	[36]
13.	ca³b² ⇒ a³baba⁶	[46]
14.	da³bab ⇒ a³b²da	[35]
15.	ca⁴b² ⇒ a⁴baba⁶	[50]
16.	da⁴bab ⇒ a⁴b²da	[47]
17.	ca⁵b² ⇒ a⁵baba⁶	[52]
18.	da⁵bab ⇒ a⁵b²da	[45]
19.	a⁶b² ⇒ bcbda⁶	[54]
20.	a⁶bab ⇒ (cb)²d	[48]
21.	b²ab ⇒ d	[3]

# ab:aaaaaabbaba=1 cda/b aaaaaaa=c,bbab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaaaaa=c cbb=babaaaaaa dbab=bbda abcb=babc cabb=ababaaaaaa dabab=abbda caabb=aababaaaaaa daabab=aabbda caaabb=aaababaaaaaa daaabab=aaabbda caaaabb=aaaababaaaaaa daaaabab=aaaabbda caaaaabb=aaaaababaaaaaa daaaaabab=aaaaabbda aaaaaabb=bcbdaaaaaa aaaaaabab=cbcbd bbab=d

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

Σ	#	Presentation	Mapping
11	2829	⟨a, b \| aaaaabbabaa=1⟩	φ(a) = a, φ(b) = b
11	2877	⟨a, b \| aaaabbabaaa=1⟩	φ(a) = a, φ(b) = b
11	3268	⟨a, b \| ababbbbbbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

2829

⟨a, b | aaaaabbabaa=1⟩

φ(a) = a, φ(b) = b

2877

⟨a, b | aaaabbabaaa=1⟩

φ(a) = a, φ(b) = b

3268

⟨a, b | ababbbbbbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#2802 ⟨a, b \| aaaaaabbaab=1⟩
Next:	#2804 ⟨a, b \| aaaaaabbabb=1⟩

#2803 ⟨a, b | aaaaaabbaba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances