#4190 ⟨a, b | bab=aba, bba=a⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b³ = ab and a ⋅ b = ab, however b³ ≠ b
Not right cancellative, because right multiplication by a is not injective:
- b² ⋅ a = a and 1 ⋅ a = a, 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:bab=aba,bba=a ba - -
bba=a
aba=bab
aab=baa
aaa=abb
abbb=ab

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

1 total

Σ	#	Presentation	Mapping
10	6684	⟨a, b \| aab=b, abab=ba⟩	φ(a) = b, φ(b) = a