#5074 ⟨a, b | aaabbaa=abab⟩

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

#	Rule	Proof
1.	a²ca²b ⇒ aba²ca	[7]
2.	a²caba ⇒ abc	[6]
3.	(ab)² ⇒ a²ca	[3]
4.	ab²a ⇒ c	[2]
5.	a(ac)²b ⇒ ab(a²c)²a	[12]
6.	caca²b ⇒ cba²ca	[9]
7.	(ca)²ba ⇒ cbc	[8]
8.	abcb ⇒ (a²c)²a	[10]
9.	cbab ⇒ (ca)²	[5]
10.	cb²a ⇒ ab²c	[4]
11.	c(ac)²b ⇒ cb(a²c)²a	[13]
12.	(cb)² ⇒ c(aca)²	[11]

# ab:aaabbaa=abab reversed:a/cb abba=c morph:4/0
aacaab=abaaca
aacaba=abc
abab=aaca
abba=c
aacacb=abaacaaca
cacaab=cbaaca
cacaba=cbc
abcb=aacaaca
cbab=caca
cbba=abbc
cacacb=cbaacaaca
cbcb=cacaaca