#2444 ⟨a, b, c | aab=b, bcac=1⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ cacb = b and b ⋅ 1 = b, however cacb ≠ 1
Not right cancellative, because right multiplication by cac is not injective:
- cacb ⋅ cac = cac and 1 ⋅ cac = cac, however cacb ≠ 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.	a² ⇒ 1	[3]
2.	bcac ⇒ 1	[2]

# abc:aab=b,bcac=1 abc - -
aa=1
bcac=1

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

3 total

Σ	#	Presentation	Mapping
8	6131	⟨a, b, c \| aa=1, aabcac=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6202	⟨a, b, c \| aa=1, baacac=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6678	⟨a, b, c \| aa=1, abcac=a⟩	φ(a) = a, φ(b) = b, φ(c) = c