#3574 ⟨a, b, c | ac=ab, bc=ab⟩

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 a is not injective:
- a ⋅ c = ab and a ⋅ b = ab, however c ≠ b

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.	ac ⇒ ab	[1]
2.	bc ⇒ ab	[2]

# abc:ac=ab,bc=ab abc - -
ac=ab
bc=ab

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

1 total

Σ	#	Presentation	Mapping
8	3575	⟨a, b, c \| ac=ab, bc=ac⟩	φ(a) = a, φ(b) = b, φ(c) = c