#3733 ⟨a, b | abaabaabba=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^-1a^-1b^-1⟩
- Embedding: φ(a) = b^-1, φ(b) = bba

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.	a(ba²)²b³ ⇒ b(ba²)²b²a	[2]
2.	a(ba²)²b²a ⇒ b	[1]

# ab:abaabaabba=b ba - -
abaabaabbb=bbaabaabba
abaabaabba=b

2 unique, 2 total

Σ	#	Presentation	Properties
9	1054	⟨a, b \| aaabba=bab⟩	Can Inf
11	5046	⟨a, b \| aaababa=baab⟩	Can Inf