⟨a, b | aabababbaba=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:
- Right-to-left recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aaa=c
2. bababbab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[10]
2.	cd ⇒ 1	[8]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[9]
5.	a³ ⇒ c	[2]
6.	b²abc ⇒ a(ab)³	[14]
7.	b(ab)²d ⇒ adb²ab	[11]
8.	babcba ⇒ cb(ab)²	[19]
9.	b(ba)²c ⇒ a²(ba)³	[16]
10.	(ba)³d ⇒ adb(ba)²	[12]
11.	b²aba² ⇒ a²dbabcb	[26]
12.	(ba)³a ⇒ dba(bc)²	[24]
13.	(ba)²b²a ⇒ adbcb(ab)²	[17]
14.	bc(ba)²b² ⇒ a²d	[20]
15.	(ba)²b²cba ⇒ dbabc²b(ab)²	[27]

# ab:aabababbaba=1 reversed:cda/b aaa=c,bababbab=d magic:0 dc=1 cd=1 ca=ac da=ad aaa=c bbabc=aababab bababd=adbbab babcba=cbabab bbabac=aabababa bababad=adbbaba bbabaa=aadbabcb bababaa=dbabcbc bababba=adbcbabab bcbababb=aad bababbcba=dbabccbabab

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

Σ	#	Presentation	Mapping
11	3255	⟨a, b \| ababbabaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3255

⟨a, b | ababbabaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#3069 ⟨a, b \| aabababbaab=1⟩
Next:	#3071 ⟨a, b \| aabababbbaa=1⟩

#3070 ⟨a, b | aabababbaba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances