#1986 ⟨a, b | aabbaaba=ab⟩

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

aca²ba ⇒ ab
aca²bc ⇒ cb
c²a²ba ⇒ cb
ab² ⇒ c
abca²ba ⇒ c
cb² ⇒ abca²bc
cba²ba ⇒ (ac)²
cbca²ba ⇒ abca²bc
c²a²bcb ⇒ cbca²bc
abca²bcb ⇒ c²a²bc
cba²bcb ⇒ acac²a²bc
cbca²bcb ⇒ ab(ca²bc)²

# ab:aabbaaba=ab ac/b abb=c frequency:3/0
acaaba=ab
acaabc=cb
ccaaba=cb
abb=c
abcaaba=c
cbb=abcaabc
cbaaba=acac
cbcaaba=abcaabc
ccaabcb=cbcaabc
abcaabcb=ccaabc
cbaabcb=acaccaabc
cbcaabcb=abcaabccaabc

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#1986 ⟨a, b | aabbaaba=ab⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)