#6638 ⟨a, b, c | aa=1, aabcc=b⟩

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 ⋅ c² = b and b ⋅ 1 = b, however c² ≠ 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.	bc² ⇒ b	[2]

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

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

3 total

Σ	#	Presentation	Mapping
8	6707	⟨a, b, c \| aa=1, baacc=b⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7189	⟨a, b, c \| aa=1, abcc=ab⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7690	⟨a, b, c \| aa=1, bcc=aab⟩	φ(a) = a, φ(b) = b, φ(c) = c