#225 ⟨a, b, c | aa=1, bcb=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 ⋅ cb = b and b ⋅ 1 = b, however cb ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- bc ⋅ b = b and 1 ⋅ b = 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.	bcb ⇒ b	[2]

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

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

4 total

Σ	#	Presentation	Mapping
8	6635	⟨a, b, c \| aa=1, aabcb=b⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6704	⟨a, b, c \| aa=1, baacb=b⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7180	⟨a, b, c \| aa=1, abcb=ab⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7678	⟨a, b, c \| aa=1, bcb=aab⟩	φ(a) = a, φ(b) = b, φ(c) = c