#41 ⟨a, b, c | ba=ab, bc=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 b is not injective:
- b ⋅ cb = b and b ⋅ 1 = b, however cb ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- cb ⋅ c = c and 1 ⋅ c = c, however cb ≠ 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

#	Rule	Proof
1.	ba ⇒ ab	[1]
2.	bc ⇒ 1	[2]

# abc:ba=ab,bc=1 abc - -
ba=ab
bc=1

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

4 total

Σ	#	Presentation	Mapping
8	7310	⟨a, b, c \| ab=1, aabc=ca⟩	φ(a) = b, φ(b) = c, φ(c) = a
8	7354	⟨a, b, c \| ab=1, abac=ca⟩	φ(a) = b, φ(b) = c, φ(c) = a
8	7373	⟨a, b, c \| ab=1, abca=ac⟩	φ(a) = b, φ(b) = c, φ(c) = a
8	7789	⟨a, b, c \| ab=1, bca=bac⟩	φ(a) = b, φ(b) = c, φ(c) = a