#3601 ⟨a, b | aababbaaab=a⟩

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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) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. ababb=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a²(a²c)³ ⇒ aca³(ca²)²	[9]
2.	aca(a²c)³ ⇒ a	[7]
3.	ab ⇒ ac(a²c)²	[5]
4.	a³cb ⇒ aca³caca²c	[10]
5.	a(a²c)²b ⇒ aca²(aca²c)²	[11]
6.	(a²c)³b ⇒ aca²c	[8]
7.	a³cac(a²c)²b ⇒ aca³cac	[12]
8.	a³(ca²ca)²acb ⇒ (aca²)²cac	[13]
9.	(ac(a²c)²)²b ⇒ c	[6]

# ab:aababbaaab=a reversed:ac/b ababb=c morph:5/0
aaaacaacaac=acaaacaacaa
acaaacaacaac=a
ab=acaacaac
aaacb=acaaacacaac
aaacaacb=acaaacaacacaac
aacaacaacb=acaac
aaacacaacaacb=acaaacac
aaacaacacaacaacb=acaaacaacac
acaacaacacaacaacb=c