#1524 ⟨a, b | aab=bb, aaaa=1⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b² = b and b ⋅ 1 = b, however b² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b² ⋅ b = b and 1 ⋅ b = b, however b² ≠ 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

# ab:aab=bb,aaaa=1 ab - -
aab=bb
bbb=b
aaaa=1

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

2 total

Σ	#	Presentation	Mapping
11	17628	⟨a, b \| aaaa=1, aaabb=ab⟩	φ(a) = a, φ(b) = b
11	17640	⟨a, b \| aaaa=1, aabba=ba⟩	φ(a) = a, φ(b) = b