#109 ⟨a, b, c | ab=a, bcc=1⟩

Properties

Sum of relation sides is 6
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
Not right cancellative, because right multiplication by c² is not injective:
- c²b ⋅ c² = c² and 1 ⋅ c² = c², however c²b ≠ 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

# abc:ab=a,bcc=1 abc - -
ab=a
acc=a
bcc=1

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

1 total

Σ	#	Presentation	Mapping
8	1942	⟨a, b, c \| abc=ab, caa=1⟩	φ(a) = c, φ(b) = a, φ(c) = b