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

# abc:aa=a,bac=1 abc - -
aa=a
bac=1

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

3 total

Σ	#	Presentation	Mapping
7	731	⟨a, b, c \| aa=a, baac=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	1618	⟨a, b, c \| aab=ab, bac=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	4630	⟨a, b, c \| aa=a, baaac=1⟩	φ(a) = a, φ(b) = b, φ(c) = c