⟨a, b | aaaaabbbaba=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. aaaaaa=c
2. bbbab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[12]
2.	dc ⇒ 1	[17]
3.	ac ⇒ ca	[6]
4.	ad ⇒ da	[18]
5.	a⁶ ⇒ c	[2]
6.	abcb ⇒ babc	[29]
7.	a⁵bab ⇒ (cb)²d	[31]
8.	cb³ ⇒ b²aba⁵	[24]
9.	db²ab ⇒ b³da	[19]
10.	cab³ ⇒ ab²aba⁵	[26]
11.	dab²ab ⇒ ab³da	[23]
12.	ca²b³ ⇒ a²b²aba⁵	[34]
13.	da²b²ab ⇒ a²b³da	[22]
14.	ca³b³ ⇒ a³b²aba⁵	[38]
15.	da³b²ab ⇒ a³b³da	[35]
16.	ca⁴b³ ⇒ a⁴b²aba⁵	[41]
17.	da⁴b²ab ⇒ a⁴b³da	[39]
18.	a⁵b³ ⇒ bcb²da⁵	[43]
19.	a⁵b²ab ⇒ cbcb²d	[36]
20.	b³ab ⇒ d	[3]

# ab:aaaaabbbaba=1 cda/b aaaaaa=c,bbbab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaaaa=c abcb=babc aaaaabab=cbcbd cbbb=bbabaaaaa dbbab=bbbda cabbb=abbabaaaaa dabbab=abbbda caabbb=aabbabaaaaa daabbab=aabbbda caaabbb=aaabbabaaaaa daaabbab=aaabbbda caaaabbb=aaaabbabaaaaa daaaabbab=aaaabbbda aaaaabbb=bcbbdaaaaa aaaaabbab=cbcbbd bbbab=d

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

Σ	#	Presentation	Mapping
11	2888	⟨a, b \| aaaabbbabaa=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

2888

⟨a, b | aaaabbbabaa=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2834 ⟨a, b \| aaaaabbbaab=1⟩
Next:	#2836 ⟨a, b \| aaaaabbbabb=1⟩

#2835 ⟨a, b | aaaaabbbaba=1⟩

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Properties

Rewriting system

Isomorphic instances