#3039 ⟨a, b, c | aba=b, bcb=a⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ bca = bcab and b ⋅ cab = bcab, however bca ≠ cab
Not right cancellative, because right multiplication by a is not injective:
- bac ⋅ a = bca² and bca ⋅ a = bca², however bac ≠ bca

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

# abc:aba=b,bcb=a cba - -
bcb=a
acb=bca
abb=bba
aba=b
bbca=bcab
baca=bcaa
abca=acab
aaca=acaa