⟨a, b | aabaabaabba=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:
- 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. baabaabb=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.	b²a ⇒ adbcb	[23]
7.	bcba² ⇒ a²b²c	[19]
8.	ba²b²c ⇒ ab(a²b)²	[13]
9.	b(a²b)²d ⇒ a²dba²b²	[11]
10.	b(a²b)²a ⇒ a²db(bc)²	[30]
11.	(ba²)²b² ⇒ d	[3]
12.	(b²c)² ⇒ adbacb(a²b)²	[33]
13.	bcbab²c ⇒ a(ab)²(a²b)²	[22]
14.	b²cbacbd ⇒ (ab)²a²b²	[28]
15.	bcbaba²bd ⇒ a²ba²dba²b²	[21]
16.	b²(cba)² ⇒ (ab)²(bc)²	[29]
17.	bcb(aba)² ⇒ a²ba²db(bc)²	[34]
18.	b²cbacb² ⇒ aba²d	[27]
19.	bcbaba²b² ⇒ a²bd	[17]

# ab:aabaabaabba=1 reversed:cda/b aaa=c,baabaabb=d magic:0 dc=1 cd=1 ca=ac da=ad aaa=c bba=adbcb bcbaa=aabbc baabbc=abaabaab baabaabd=aadbaabb baabaaba=aadbbcbc baabaabb=d bbcbbc=adbacbaabaab bcbabbc=aababaabaab bbcbacbd=ababaabb bcbabaabd=aabaadbaabb bbcbacba=ababbcbc bcbabaaba=aabaadbbcbc bbcbacbb=abaad bcbabaabb=aabd

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

Σ	#	Presentation	Mapping
11	3041	⟨a, b \| aabaabbaaab=1⟩	φ(a) = a, φ(b) = b
11	3100	⟨a, b \| aabbaaabaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3041

⟨a, b | aabaabbaaab=1⟩

φ(a) = a, φ(b) = b

3100

⟨a, b | aabbaaabaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#3033 ⟨a, b \| aabaabaabab=1⟩
Next:	#3037 ⟨a, b \| aabaabababb=1⟩

#3034 ⟨a, b | aabaabaabba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances