#1311 ⟨a, b, c | ab=1, abcc=c⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by c is not injective:
- c ⋅ c = c and c ⋅ 1 = c, however c ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- c ⋅ c = c and 1 ⋅ c = c, however c ≠ 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.	ab ⇒ 1	[1]
2.	c² ⇒ c	[2]

# abc:ab=1,abcc=c abc - -
ab=1
cc=c

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

3 total

Σ	#	Presentation	Mapping
7	1374	⟨a, b, c \| ab=1, cabc=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	1467	⟨a, b, c \| ab=1, abc=cc⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	1526	⟨a, b, c \| ab=1, bcc=bc⟩	φ(a) = a, φ(b) = b, φ(c) = c