#1702 ⟨a, b | aababbaba=b⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabaab^-1ab^-1b^-1⟩
- Anti-isomorphic embedding: φ(a) = ab^-1, φ(b) = aba^-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(ab²)² ⇒ ba(bab)²a	[2]
2.	a²(bab)²a ⇒ b	[1]

# ab:aababbaba=b ba - -
aababbabb=bababbaba
aababbaba=b

4 unique, 4 total

Σ	#	Presentation	Properties
9	807	⟨a, b \| aababbaa=b⟩	Can Inf
9	1205	⟨a, b \| aabaa=babb⟩	Can Inf
11	3564	⟨a, b \| aabaababaa=b⟩	Can Inf
11	5904	⟨a, b \| ababba=bbabb⟩	Can Inf