#62 ⟨a, b, c | aab=1, acb=1⟩

Properties

Sum of relation sides is 6
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ aba = a and a ⋅ 1 = a, however aba ≠ 1
Not right cancellative, because right multiplication by ab is not injective:
- aba ⋅ ab = ab and 1 ⋅ ab = ab, however aba ≠ 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.	a²b ⇒ 1	[1]
2.	acb ⇒ 1	[2]

# abc:aab=1,acb=1 abc - -
aab=1
acb=1

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

3 total

Σ	#	Presentation	Mapping
8	4202	⟨a, b, c \| aab=1, acba=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	4234	⟨a, b, c \| aab=1, bacb=b⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	4499	⟨a, b, c \| abc=1, aaca=a⟩	φ(a) = a, φ(b) = c, φ(c) = b