#1729 ⟨a, b | aabbbaaab=a⟩

Properties

Presentation has sum-of-sides 10
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:
- Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Auxiliary generator: aaa=c

c²b³cb ⇒ cb³cbc
c²bcb³cb ⇒ c²b⁴cbc
(cb)³b²cb ⇒ cbcb⁴cbc
cb(bc)²b³cb ⇒ cb²cb⁴cbc
(cb³cb)² ⇒ c(b³cb)²c
c²b⁴cbcb³cb ⇒ cbcb⁴cbcb³c
cbcb⁴cbcb³cb ⇒ cb²cb⁴cbcb³c
cb²cb⁴cbcb³cb ⇒ c(b³cb)²cb³c
c(b³cb)²cb³cb ⇒ c
a ⇒ c(b³cb)²

# ab:aabbbaaab=a bc/a aaa=c frequency:3/3
ccbbbcb=cbbbcbc
ccbcbbbcb=ccbbbbcbc
cbcbcbbbcb=cbcbbbbcbc
cbbcbcbbbcb=cbbcbbbbcbc
cbbbcbcbbbcb=cbbbcbbbbcbc
ccbbbbcbcbbbcb=cbcbbbbcbcbbbc
cbcbbbbcbcbbbcb=cbbcbbbbcbcbbbc
cbbcbbbbcbcbbbcb=cbbbcbbbbcbcbbbc
cbbbcbbbbcbcbbbcb=c
a=cbbbcbbbbcb

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#1729 ⟨a, b | aabbbaaab=a⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)