#3898 ⟨a, b | aabb=ab, abab=1⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ (ba)² = a and a ⋅ 1 = a, however (ba)² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- a²b ⋅ b = ab and a ⋅ b = ab, however a²b ≠ a

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.	a²b² ⇒ ab	[1]
2.	(ab)² ⇒ 1	[2]

# ab:aabb=ab,abab=1 ab - -
aabb=ab
abab=1

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

1 total

Σ	#	Presentation	Mapping
10	5635	⟨a, b \| abab=1, aabbab=1⟩	φ(a) = a, φ(b) = b