#1789 ⟨a, b | aabb=1, aabab=1⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ab²a = a and a ⋅ 1 = a, however ab²a ≠ 1
Not right cancellative, because right multiplication by ab² is not injective:
- ab²a ⋅ ab² = ab² and 1 ⋅ ab² = ab², however ab²a ≠ 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.	a²b² ⇒ 1	[1]
2.	a(ab)² ⇒ 1	[2]

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

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

1 total

Σ	#	Presentation	Mapping
11	17435	⟨a, b \| aabb=1, aababa=a⟩	φ(a) = a, φ(b) = b