⟨a, b | aabbbababba=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. aaa=c
2. bbbababb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[9]
2.	dc ⇒ 1	[11]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[10]
5.	a³ ⇒ c	[2]
6.	cb³ab ⇒ (ba)²b²a²	[16]
7.	d(ba)²b² ⇒ b³abda	[12]
8.	ab²cb² ⇒ bcb³a	[33]
9.	abab²cb ⇒ (ba)²b²c	[25]
10.	cab³ab ⇒ (ab)³ba²	[17]
11.	d(ab)³b ⇒ ab³abda	[15]
12.	a²b³ab ⇒ bab²cbda²	[28]
13.	a²bcb³ ⇒ (cb²)²da²	[38]
14.	a(ab)³b ⇒ cbab²cbd	[24]
15.	db(ba)²b² ⇒ b³(ab)²d	[13]
16.	dab(ba)²b² ⇒ ab³(ab)²d	[22]
17.	a²b(ba)²b² ⇒ cb²cb³da	[40]
18.	b³abab² ⇒ d	[3]
19.	cb⁴cb³ ⇒ (ba)²b²a²bcb²da²	[42]
20.	cab⁴cb³ ⇒ (ab)³ba²bcb²da²	[43]
21.	a²b⁴cb³ ⇒ bab²cbda²bcb²da²	[45]

# ab:aabbbababba=1 cda/b aaa=c,bbbababb=d magic:0 cd=1 dc=1 ac=ca ad=da aaa=c cbbbab=bababbaa dbababb=bbbabda abbcbb=bcbbba ababbcb=bababbc cabbbab=abababbaa dabababb=abbbabda aabbbab=babbcbdaa aabcbbb=cbbcbbdaa aabababb=cbabbcbd dbbababb=bbbababd dabbababb=abbbababd aabbababb=cbbcbbbda bbbababb=d cbbbbcbbb=bababbaabcbbdaa cabbbbcbbb=abababbaabcbbdaa aabbbbcbbb=babbcbdaabcbbdaa

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

Σ	#	Presentation	Mapping
11	3220	⟨a, b \| abaabbbaaab=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

3220

⟨a, b | abaabbbaaab=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#3145 ⟨a, b \| aabbbababab=1⟩
Next:	#3147 ⟨a, b \| aabbbabbaab=1⟩

#3146 ⟨a, b | aabbbababba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances