#5364 ⟨a, b | abababa=bbbb⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaaabbbb⟩
- Embedding: φ(a) = ba, 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.	b⁵a ⇒ ab⁵	[2]
2.	a(ba)³ ⇒ b⁴	[1]

# ab:abababa=bbbb ab - -
bbbbba=abbbbb
abababa=bbbb

2 unique, 5 total

Σ	#	Presentation	Properties	φ
9	625	⟨a, b \| aaaabbbba=1⟩	Grp Inf	3
9	1148	⟨a, b \| aaaaa=bbbb⟩	Can Inf