⟨a, b | aaa=1, ababb=bba⟩

Up:

Monoids with two generators and two relations

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(b) = 0; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	abab² ⇒ b²a	[2]
2.	a³ ⇒ 1	[1]
3.	bab²a² ⇒ a²b²	[4]
4.	a²b²a ⇒ bab²	[3]
5.	a²b⁴a ⇒ (bab²)²	[5]
6.	a²b³ab² ⇒ ba(b²a)²	[6]
7.	(bab²)³ ⇒ a²b⁶a	[9]
8.	bab(b²a)³ ⇒ a²b⁵ab²	[10]
9.	(a²b)²b ⇒ bab⁴a²	[8]
10.	(ab)²a²b² ⇒ b(b²a)²	[7]
11.	bab³aba²b² ⇒ a²b⁵ab²a	[14]
12.	a²b³a²b² ⇒ bab³ab⁴a²	[11]
13.	a²b⁴(bab²)² ⇒ (bab²)²ab⁴a	[12]
14.	a²b³(b²a)³ ⇒ b(ab³ab²)²	[16]
15.	(bab²)²aba²b² ⇒ a²b⁵ab⁴a²	[13]
16.	a²b³aba²b² ⇒ (bab)²(b²a)²	[15]
17.	a²b⁵aba²b² ⇒ ba(b(b²a)²)²	[18]
18.	a²b⁴(bab)²a²b² ⇒ (bab³ab)²b³a²	[17]

# ab:aaa=1,ababb=bba reversed:b/a ababb=bba aaa=1 babbaa=aabb aabba=babb aabbbba=babbbabb aabbbabb=babbabba babbbabbbabb=aabbbbbba babbbabbabba=aabbbbbabb aabaabb=babbbbaa ababaabb=bbbabba babbbabaabb=aabbbbbabba aabbbaabb=babbbabbbbaa aabbbbbabbbabb=babbbabbabbbba aabbbbbabbabba=babbbabbabbbabb babbbabbabaabb=aabbbbbabbbbaa aabbbabaabb=babbabbbabba aabbbbbabaabb=babbbabbabbbabba aabbbbbabbabaabb=babbbabbabbbabbbbaa

Up:	Monoids with two generators and two relations
Prev:	#22799 ⟨a, b \| aaa=1, ababb=bab⟩
Next:	#22801 ⟨a, b \| aaa=1, ababb=bbb⟩

#22800 ⟨a, b | aaa=1, ababb=bba⟩

Quick links

Properties

Rewriting system