#5405 ⟨a, b | aab=bb, aba=ab⟩

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 = ab and a ⋅ b = ab, however ba ≠ b
Not right cancellative, because right multiplication by b is not injective:
- a² ⋅ b = b² and b ⋅ b = b², however a² ≠ b

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,aba=ab ab - -
aab=bb
aba=ab
bba=bb
abbb=abb
bbbb=bbb

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

1 total

Σ	#	Presentation	Mapping
11	16384	⟨a, b \| aba=ab, aaba=bb⟩	φ(a) = a, φ(b) = b