#103 ⟨a, b, c | ab=a, acb=1⟩

Properties

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

# abc:ab=a,acb=1 abc - -
ab=a
acb=1

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

4 total

Σ	#	Presentation	Mapping
7	783	⟨a, b, c \| ab=a, abcb=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	1797	⟨a, b, c \| aba=aa, acb=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	1813	⟨a, b, c \| aba=ab, bca=1⟩	φ(a) = b, φ(b) = a, φ(c) = c
8	4799	⟨a, b, c \| ab=a, abbcb=1⟩	φ(a) = a, φ(b) = b, φ(c) = c