⟨a, b | aabbabababa=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. aaa=c
2. bbababab=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.	abcb ⇒ cb²a	[18]
7.	a²b² ⇒ bcbda²	[23]
8.	cb²(ab)² ⇒ (ba)⁴a	[15]
9.	db(ab)³ ⇒ b²(ab)²da	[12]
10.	cab²(ab)² ⇒ (ab)⁴a²	[16]
11.	d(ab)⁴ ⇒ ab²(ab)²da	[14]
12.	a(ab)⁴ ⇒ cbcb²abda	[26]
13.	b²(ab)³ ⇒ d	[3]
14.	(cb²)²ab ⇒ b(ab)³ca²bda²	[28]
15.	cab²cb²ab ⇒ (ab)⁴ca²bda²	[30]
16.	(cb²)³ ⇒ b(ab)³c(a²b)²da²	[32]
17.	cab²(cb²)² ⇒ (ab)⁴c(a²b)²da²	[33]

# ab:aabbabababa=1 cda/b aaa=c,bbababab=d magic:0 cd=1 dc=1 ac=ca ad=da aaa=c abcb=cbba aabb=bcbdaa cbbabab=babababaa dbababab=bbababda cabbabab=ababababaa dabababab=abbababda aabababab=cbcbbabda bbababab=d cbbcbbab=babababcaabdaa cabbcbbab=ababababcaabdaa cbbcbbcbb=babababcaabaabdaa cabbcbbcbb=ababababcaabaabdaa

Up:	Monoids with two generators and one relation
Prev:	#3120 ⟨a, b \| aabbababaab=1⟩
Next:	#3123 ⟨a, b \| aabbababbab=1⟩

#3121 ⟨a, b | aabbabababa=1⟩

Quick links

Properties

Rewriting system