⟨a, b | aabbaabaaba=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. bbaabaab=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.	ab² ⇒ bcbda	[26]
7.	a²bcb ⇒ cb²a²	[18]
8.	cb²a²b ⇒ b(a²b)²a	[15]
9.	db(a²b)² ⇒ b²a²bda²	[12]
10.	ab(a²b)² ⇒ cbcb²da²	[28]
11.	b²(a²b)² ⇒ d	[3]
12.	(cb²)² ⇒ b(a²b)²cabda	[34]
13.	cb²abcb ⇒ b(a²b)²aba²	[24]
14.	dbcabcb² ⇒ b²a²(ba)²	[36]
15.	dba(ab)²cb ⇒ b²a²bda²ba²	[23]
16.	(abc)²b² ⇒ (cb)²(ba)²	[38]
17.	(aba)²bcb ⇒ cbcb²da²ba²	[39]
18.	b²cabcb² ⇒ da²ba	[31]
19.	b²a(ab)²cb ⇒ dba²	[17]

# ab:aabbaabaaba=1 cda/b aaa=c,bbaabaab=d magic:0 cd=1 dc=1 ac=ca ad=da aaa=c abb=bcbda aabcb=cbbaa cbbaab=baabaaba dbaabaab=bbaabdaa abaabaab=cbcbbdaa bbaabaab=d cbbcbb=baabaabcabda cbbabcb=baabaababaa dbcabcbb=bbaababa dbaababcb=bbaabdaabaa abcabcbb=cbcbbaba abaababcb=cbcbbdaabaa bbcabcbb=daaba bbaababcb=dbaa

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

Σ	#	Presentation	Mapping
11	3194	⟨a, b \| abaaabbaaba=1⟩	φ(a) = a, φ(b) = b
11	3202	⟨a, b \| abaabaaabba=1⟩	φ(a) = a, φ(b) = b
11	3291	⟨a, b \| abbabbabbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

3194

⟨a, b | abaaabbaaba=1⟩

φ(a) = a, φ(b) = b

3202

⟨a, b | abaabaaabba=1⟩

φ(a) = a, φ(b) = b

3291

⟨a, b | abbabbabbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#3105 ⟨a, b \| aabbaabaaab=1⟩
Next:	#3107 ⟨a, b \| aabbaabaabb=1⟩

#3106 ⟨a, b | aabbaabaaba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances