#5333 ⟨a, b | abaabba=baba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

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

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

#	Rule	Proof
1.	babc ⇒ abc²	[5]
2.	(ba)² ⇒ abca	[3]
3.	(abc)² ⇒ ba²bc²	[8]
4.	a²b² ⇒ c	[2]
5.	a³bc³ ⇒ cabc	[7]
6.	b²a²bc² ⇒ abc²abc	[11]
7.	abcaba ⇒ ba²bca	[6]
8.	a³bc²a ⇒ caba	[9]
9.	b²a²bca ⇒ abc²aba	[14]
10.	abcba²bc² ⇒ ba²bc²abc	[12]
11.	abcba²bca ⇒ ba²bc²aba	[15]
12.	a³bc²ba²bc² ⇒ ca²bc²abc	[10]
13.	a³bc²ba²bca ⇒ ca²bc²aba	[13]

# ab:abaabba=baba c/ba aabb=c morph:4/2
babc=abcc
baba=abca
abcabc=baabcc
aabb=c
aaabccc=cabc
bbaabcc=abccabc
abcaba=baabca
aaabcca=caba
bbaabca=abccaba
abcbaabcc=baabccabc
abcbaabca=baabccaba
aaabccbaabcc=caabccabc
aaabccbaabca=caabccaba