#4136 ⟨a, b | aababbaba=ab⟩

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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. bbaba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	abc ⇒ ac²aba	[10]
2.	cbc ⇒ c³aba	[12]
3.	a²bac ⇒ ab	[3]
4.	cabac ⇒ cb	[4]
5.	ab²c ⇒ ac²(ba)²	[11]
6.	cb²c ⇒ c³(ba)²	[13]
7.	b²ac ⇒ cbacaba	[14]
8.	a(ba)²c ⇒ ab²	[5]
9.	c(ba)²c ⇒ cb²	[6]
10.	ab³ ⇒ ac²	[8]
11.	cb³ ⇒ c³	[9]
12.	b(ba)² ⇒ c	[2]
13.	b²ab² ⇒ cbac	[7]

# ab:aababbaba=ab reversed:ac/b bbaba=c morph:5/0
abc=accaba
cbc=cccaba
aabac=ab
cabac=cb
abbc=accbaba
cbbc=cccbaba
bbac=cbacaba
ababac=abb
cbabac=cbb
abbb=acc
cbbb=ccc
bbaba=c
bbabb=cbac