#5890 ⟨a, b | ababba=abbab⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ bab²a = ab²ab and a ⋅ b²ab = ab²ab, however bab²a ≠ b²ab
Enveloping group: ⟨a, b | aaabb⟩

Rewriting system

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

Auxiliary generators:
1. c = abbab
Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	c(ca)² ⇒ c³	[16]
2.	c⁴a ⇒ c²ac²	[11]
3.	c²ac³a ⇒ c⁵	[17]
4.	cb ⇒ abc	[5]
5.	c²ab ⇒ abc²	[8]
6.	abcab ⇒ ab²c	[7]
7.	cab²a ⇒ ab²c	[6]
8.	cab²c ⇒ ab²c²a	[10]
9.	c²a²b²a ⇒ (ab)²c²	[12]
10.	c²a²b²c ⇒ (ab)²c³a	[15]
11.	ab²ab ⇒ c	[2]
12.	abab²a ⇒ c	[3]
13.	abab²c ⇒ c²a	[9]

# ab:ababba=abbab ac/b abbab=c magic:0
ccaca=ccc
cccca=ccacc
ccaccca=ccccc
cb=abc
ccab=abcc
abcab=abbc
cabba=abbc
cabbc=abbcca
ccaabba=ababcc
ccaabbc=ababccca
abbab=c
ababba=c
ababbc=cca