#219 ⟨a, b, c | aa=1, bac=b⟩

Properties

Sum of relation sides is 6
Infinite non-cancellative non-commutative monoid
Element ab has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ac = b and b ⋅ 1 = b, however ac ≠ 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	[1]
2.	bac ⇒ b	[2]

# abc:aa=1,bac=b abc - -
aa=1
bac=b

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

4 total

Σ	#	Presentation	Mapping
8	6624	⟨a, b, c \| aa=1, aabac=b⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6698	⟨a, b, c \| aa=1, baaac=b⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7148	⟨a, b, c \| aa=1, abac=ab⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7643	⟨a, b, c \| aa=1, bac=aab⟩	φ(a) = a, φ(b) = b, φ(c) = c