#5144 ⟨a, b | aabaaba=babb⟩

Properties

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

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(ab²)² ⇒ (bab)²a	[2]
2.	(a²b)²a ⇒ bab²	[1]

# ab:aabaaba=babb ba - -
aabbabb=babbaba
aabaaba=babb

3 unique, 9 total

Σ	#	Presentation	Properties	φ
11	3048	⟨a, b \| aabaabbbaba=1⟩	Grp Inf	6
11	3655	⟨a, b \| aabbabbaba=b⟩	Can Inf
11	4115	⟨a, b \| aababaaba=bb⟩	Can Inf