#309 ⟨a, b, c | aab=b, bcc=1⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ c²b = b and b ⋅ 1 = b, however c²b ≠ 1
Not right cancellative, because right multiplication by c² is not injective:
- c²b ⋅ c² = c² and 1 ⋅ c² = c², however c²b ≠ 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.	bc² ⇒ 1	[2]

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

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

3 total

Σ	#	Presentation	Mapping
7	1070	⟨a, b, c \| aa=1, aabcc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	1091	⟨a, b, c \| aa=1, baacc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	1245	⟨a, b, c \| aa=1, abcc=a⟩	φ(a) = a, φ(b) = b, φ(c) = c