⟨a, b | aaaabbababa=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. bbabab=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 ⇒ cb²a	[27]
7.	a⁴b² ⇒ bcbda⁴	[32]
8.	cb²ab ⇒ (ba)³a³	[24]
9.	db(ab)² ⇒ b²abda	[20]
10.	cab²ab ⇒ (ab)³a⁴	[25]
11.	d(ab)³ ⇒ ab²abda	[23]
12.	ca²b²ab ⇒ a(ab)³a⁴	[33]
13.	da(ab)³ ⇒ a²b²abda	[22]
14.	ca³b²ab ⇒ a²(ab)³a⁴	[35]
15.	da²(ab)³ ⇒ a³b²abda	[34]
16.	a³(ab)³ ⇒ cbcb²da	[37]
17.	b²(ab)² ⇒ d	[3]
18.	(cb²)² ⇒ b(ab)²ca⁴bda⁴	[39]
19.	cab²cb² ⇒ (ab)³ca⁴bda⁴	[40]
20.	ca²b²cb² ⇒ a(ab)³ca⁴bda⁴	[41]
21.	ca³b²cb² ⇒ a²(ab)³ca⁴bda⁴	[42]

# ab:aaaabbababa=1 cda/b aaaaa=c,bbabab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaaa=c abcb=cbba aaaabb=bcbdaaaa cbbab=bababaaaa dbabab=bbabda cabbab=abababaaaa dababab=abbabda caabbab=aabababaaaa daababab=aabbabda caaabbab=aaabababaaaa daaababab=aaabbabda aaaababab=cbcbbda bbabab=d cbbcbb=bababcaaaabdaaaa cabbcbb=abababcaaaabdaaaa caabbcbb=aabababcaaaabdaaaa caaabbcbb=aaabababcaaaabdaaaa

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

Σ	#	Presentation	Mapping
11	2970	⟨a, b \| aaabbababaa=1⟩	φ(a) = a, φ(b) = b
11	3249	⟨a, b \| abababbbbba=1⟩	φ(a) = b, φ(b) = a
11	3266	⟨a, b \| ababbbbbaab=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

2970

⟨a, b | aaabbababaa=1⟩

φ(a) = a, φ(b) = b

3249

⟨a, b | abababbbbba=1⟩

φ(a) = b, φ(b) = a

3266

⟨a, b | ababbbbbaab=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#2878 ⟨a, b \| aaaabbabaab=1⟩
Next:	#2880 ⟨a, b \| aaaabbababb=1⟩

#2879 ⟨a, b | aaaabbababa=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances