⟨a, b | aaaaabbaaba=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. aaaaaa=c
2. bbaab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[12]
2.	dc ⇒ 1	[17]
3.	ac ⇒ ca	[6]
4.	ad ⇒ da	[18]
5.	a⁶ ⇒ c	[2]
6.	cb² ⇒ ba²ba⁴	[23]
7.	dba²b ⇒ b²da²	[19]
8.	cab² ⇒ aba²ba⁴	[24]
9.	daba²b ⇒ ab²da²	[22]
10.	a²bcb ⇒ ba²bc	[26]
11.	ca²b² ⇒ (a²b)²a⁴	[28]
12.	d(a²b)² ⇒ a²b²da²	[21]
13.	ca³b² ⇒ a(a²b)²a⁴	[31]
14.	da(a²b)² ⇒ a³b²da²	[30]
15.	a⁴b² ⇒ bcbda⁴	[33]
16.	a⁴ba²b ⇒ (cb)²d	[29]
17.	b²a²b ⇒ d	[3]

# ab:aaaaabbaaba=1 cda/b aaaaaa=c,bbaab=d magic:0 cd=1 dc=1 ac=ca ad=da aaaaaa=c cbb=baabaaaa dbaab=bbdaa cabb=abaabaaaa dabaab=abbdaa aabcb=baabc caabb=aabaabaaaa daabaab=aabbdaa caaabb=aaabaabaaaa daaabaab=aaabbdaa aaaabb=bcbdaaaa aaaabaab=cbcbd bbaab=d

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

Σ	#	Presentation	Mapping
11	2873	⟨a, b \| aaaabbaabaa=1⟩	φ(a) = a, φ(b) = b
11	3172	⟨a, b \| abaaaaaabba=1⟩	φ(a) = a, φ(b) = b
11	3294	⟨a, b \| abbabbbbbba=1⟩	φ(a) = b, φ(b) = a

Presentation

Mapping

2873

⟨a, b | aaaabbaabaa=1⟩

φ(a) = a, φ(b) = b

3172

⟨a, b | abaaaaaabba=1⟩

φ(a) = a, φ(b) = b

3294

⟨a, b | abbabbbbbba=1⟩

φ(a) = b, φ(b) = a

Up:	Monoids with two generators and one relation
Prev:	#2826 ⟨a, b \| aaaaabbaaab=1⟩
Next:	#2828 ⟨a, b \| aaaaabbaabb=1⟩

#2827 ⟨a, b | aaaaabbaaba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances