⟨a, b | aabbababa=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. bbabab=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.	cb²ab ⇒ (ba)³a	[15]
9.	db(ab)² ⇒ b²abda	[12]
10.	cab²ab ⇒ (ab)³a²	[16]
11.	d(ab)³ ⇒ ab²abda	[14]
12.	a(ab)³ ⇒ cbcb²da	[26]
13.	b²(ab)² ⇒ d	[3]
14.	(cb²)² ⇒ b(ab)²ca²bda²	[28]
15.	cab²cb² ⇒ (ab)³ca²bda²	[29]

# ab:aabbababa=1 cda/b aaa=c,bbabab=d magic:0 cd=1 dc=1 ac=ca ad=da aaa=c abcb=cbba aabb=bcbdaa cbbab=bababaa dbabab=bbabda cabbab=abababaa dababab=abbabda aababab=cbcbbda bbabab=d cbbcbb=bababcaabdaa cabbcbb=abababcaabdaa

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

Σ	#	Presentation	Mapping
9	715	⟨a, b \| abababbba=1⟩	φ(a) = b, φ(b) = a
9	718	⟨a, b \| ababbbaab=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

715

⟨a, b | abababbba=1⟩

φ(a) = b, φ(b) = a

718

⟨a, b | ababbbaab=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#681 ⟨a, b \| aabbabaab=1⟩
Next:	#683 ⟨a, b \| aabbabbaa=1⟩

#682 ⟨a, b | aabbababa=1⟩

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Properties

Rewriting system

Isomorphic instances