#5619 ⟨a, b | aaabba=babba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by a is not injective:
- a³b² ⋅ a = bab²a and bab² ⋅ a = bab²a, however a³b² ≠ bab²
Enveloping group is isomorphic to ℤ

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 = babba
Reduction order:
- Right-to-left recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	babc ⇒ cb²a	[4]
2.	bab²a ⇒ c	[2]
3.	ca²bc ⇒ bab²cb²a	[8]
4.	(bab²)²c ⇒ ca²b²c	[9]
5.	ca²b²a ⇒ bab²c	[7]
6.	a³bc ⇒ cb²a	[6]
7.	a³b²c ⇒ bab²c	[10]
8.	ca²b³ab²c ⇒ bab²ca²b²c	[12]
9.	a³b²a ⇒ c	[3]
10.	a³b³ab²c ⇒ ca²b²c	[11]

# ab:aaabba=babba reversed:bc/a babba=c magic:0
babc=cbba
babba=c
caabc=babbcbba
babbbabbc=caabbc
caabba=babbc
aaabc=cbba
aaabbc=babbc
caabbbabbc=babbcaabbc
aaabba=c
aaabbbabbc=caabbc