#437 ⟨a, b | aaabba=ab⟩

Properties

Presentation has sum-of-sides 8
Infinite non-commutative monoid

Complete 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(c) = 0; deg(a) = deg(b) = 1, a < b
Auxiliary generator: ab=c

ab ⇒ c
cb² ⇒ cacbc
cacba ⇒ cb
a²cbc ⇒ cb
c(ac)²bc ⇒ (cb)²a
ca(cb)² ⇒ cbacbc
a²cba ⇒ c
(cba)² ⇒ cacbc
a(ac)²bc ⇒ c²ba
cb(ac)²bc ⇒ cacbc²ba
cba(cb)² ⇒ c(acbc)²

# ab:aaabba=ab reversed:c/ab ab=c magic:0
ab=c
cbb=cacbc
cacba=cb
aacbc=cb
cacacbc=cbcba
cacbcb=cbacbc
aacba=c
cbacba=cacbc
aacacbc=ccba
cbacacbc=cacbccba
cbacbcb=cacbcacbc

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#437 ⟨a, b | aaabba=ab⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)