#170 ⟨a, b, c | aa=1, bacc=1⟩

Properties

Sum of relation sides is 6
Infinite non-cancellative non-commutative monoid
Element ab has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ac²b = b and b ⋅ 1 = b, however ac²b ≠ 1
Not right cancellative, because right multiplication by ac² is not injective:
- ac²b ⋅ ac² = ac² and 1 ⋅ ac² = ac², however ac²b ≠ 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.	bac² ⇒ 1	[2]

# abc:aa=1,bacc=1 abc - -
aa=1
bacc=1

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

6 total

Σ	#	Presentation	Mapping
8	2436	⟨a, b, c \| aab=b, bacc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6123	⟨a, b, c \| aa=1, aabacc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6153	⟨a, b, c \| aa=1, abacca=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6196	⟨a, b, c \| aa=1, baaacc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6654	⟨a, b, c \| aa=1, abacc=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7229	⟨a, b, c \| aa=1, bacc=aa⟩	φ(a) = a, φ(b) = b, φ(c) = c