#3498 ⟨a, b | aaabbababa=b⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabab^-1b^-1b^-1a^-1b^-1⟩
- Anti-isomorphic embedding: φ(a) = a, φ(b) = b^-1a^-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.	a³b(ba)²b² ⇒ ba²b(ba)³	[2]
2.	a³b(ba)³ ⇒ b	[1]

# ab:aaabbababa=b ba - -
aaabbababb=baabbababa
aaabbababa=b

1 unique, 1 total

Σ	#	Presentation	Properties
10	2769	⟨a, b \| babbb=aaaba⟩	Can Inf