#1284 ⟨a, b, c | ab=1, aabc=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 a is not injective:
- a ⋅ ba = a and a ⋅ 1 = a, however ba ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- a ⋅ c = c and 1 ⋅ c = c, however a ≠ 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.	ac ⇒ c	[2]

# abc:ab=1,aabc=c abc - -
ab=1
ac=c

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

4 total

Σ	#	Presentation	Mapping
7	1298	⟨a, b, c \| ab=1, abac=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	1461	⟨a, b, c \| ab=1, abc=ac⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	1474	⟨a, b, c \| ab=1, aca=ca⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	1502	⟨a, b, c \| ab=1, bac=bc⟩	φ(a) = a, φ(b) = b, φ(c) = c