#11510 ⟨a, b | ababa=a, bbaaa=1⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ (ab)² = b and b ⋅ 1 = b, however (ab)² ≠ 1
Not right cancellative, because right multiplication by aba is not injective:
- (ab)² ⋅ aba = aba and 1 ⋅ aba = aba, however (ab)² ≠ 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.	(ba)² ⇒ 1	[3]
2.	b²a³ ⇒ 1	[2]

# ab:ababa=a,bbaaa=1 ab - -
baba=1
bbaaa=1

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ	#	Presentation	Mapping
11	17506	⟨a, b \| abab=1, aabbba=a⟩	φ(a) = b, φ(b) = a