#5234 ⟨a, b | aabbaba=babb⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabab^-1ab^-1a^-1b^-1b^-1⟩
- Embedding: φ(a) = ab^-1, φ(b) = a^-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.	a²b(ba)² ⇒ bab²	[1]
2.	a(ab²)³ ⇒ (bab)³a	[2]

# ab:aabbaba=babb ba - -
aabbaba=babb
aabbabbabb=babbabbaba

1 unique, 1 total

Σ	#	Presentation	Properties
11	3604	⟨a, b \| aababbaaba=b⟩	Can Inf