#3777 ⟨a, b | abababbbba=b⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabbab^-1b^-1b^-1⟩
- Anti-isomorphic embedding: φ(a) = ab, φ(b) = b^-1

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

#	Rule	Proof
1.	(ab)³b⁴ ⇒ b(ba)²b⁴a	[2]
2.	(ab)³b³a ⇒ b	[1]

# ab:abababbbba=b ba - -
abababbbbb=bbababbbba
abababbbba=b

2 unique, 2 total

Σ	#	Presentation	Properties
9	1056	⟨a, b \| aaabba=bbb⟩	Can Inf
11	4305	⟨a, b \| abababbba=bb⟩	Can Inf

1 unique, 1 total

Σ	#	Presentation	Properties
9	924	⟨a, b \| aaabbba=bb⟩	Can Inf