⟨a, b | aaaaabbaba=1⟩

Up:

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. aaaaaa=c
2. bbab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[14]
2.	dc ⇒ 1	[23]
3.	ac ⇒ ca	[6]
4.	ad ⇒ da	[26]
5.	a⁶ ⇒ c	[2]
6.	cb² ⇒ baba⁵	[38]
7.	dbab ⇒ b²da	[31]
8.	abcb ⇒ babc	[36]
9.	cab² ⇒ (ab)²a⁵	[41]
10.	d(ab)² ⇒ ab²da	[27]
11.	ca²b² ⇒ a(ab)²a⁵	[43]
12.	da(ab)² ⇒ a²b²da	[35]
13.	ca³b² ⇒ a³baba⁵	[48]
14.	da³bab ⇒ a³b²da	[44]
15.	ca⁴b² ⇒ a⁴baba⁵	[53]
16.	da⁴bab ⇒ a⁴b²da	[34]
17.	a⁵b² ⇒ bcbda⁵	[52]
18.	a⁵bab ⇒ (cb)²d	[45]
19.	b²ab ⇒ d	[3]

# ab:aaaaabbaba=1 cda/b aaaaaa=c,bbab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaaaa=c cbb=babaaaaa dbab=bbda abcb=babc cabb=ababaaaaa dabab=abbda caabb=aababaaaaa daabab=aabbda caaabb=aaababaaaaa daaabab=aaabbda caaaabb=aaaababaaaaa daaaabab=aaaabbda aaaaabb=bcbdaaaaa aaaaabab=cbcbd bbab=d

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

Σ	#	Presentation	Mapping
10	1326	⟨a, b \| aaaabbabaa=1⟩	φ(a) = a, φ(b) = b
10	1526	⟨a, b \| ababbbbbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

1326

⟨a, b | aaaabbabaa=1⟩

φ(a) = a, φ(b) = b

1526

⟨a, b | ababbbbbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#1300 ⟨a, b \| aaaaabbaab=1⟩
Next:	#1302 ⟨a, b \| aaaaabbabb=1⟩

#1301 ⟨a, b | aaaaabbaba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances