#3270 ⟨a, b, c | bb=ac, aacc=1⟩

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 ⋅ b²ca = a and a ⋅ 1 = a, however b²ca ≠ 1
Not right cancellative, because right multiplication by b²c is not injective:
- b²ca ⋅ b²c = b²c and 1 ⋅ b²c = b²c, however b²ca ≠ 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.	ac ⇒ b²	[1]
2.	ab²c ⇒ 1	[2]

# abc:bb=ac,aacc=1 bac - -
ac=bb
abbc=1

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

1 total

Σ	#	Presentation	Mapping
8	3276	⟨a, b, c \| bb=ac, abbc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c