#222 ⟨a, b, c | aa=1, bbc=b⟩

Properties

Sum of relation sides is 6
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ bc = b and b ⋅ 1 = b, however bc ≠ 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.	b²c ⇒ b	[2]

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

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

5 total

Σ	#	Presentation	Mapping
8	6629	⟨a, b, c \| aa=1, aabbc=b⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6701	⟨a, b, c \| aa=1, baabc=b⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7165	⟨a, b, c \| aa=1, abbc=ab⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7661	⟨a, b, c \| aa=1, bbc=aab⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7669	⟨a, b, c \| aa=1, bbc=baa⟩	φ(a) = a, φ(b) = b, φ(c) = c