#3453 ⟨a, b, c | ba=ac, acb=b⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ab = b and b ⋅ 1 = b, however ab ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- ba ⋅ b = b and 1 ⋅ b = b, however ba ≠ 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.	ac ⇒ ba	[1]
2.	bab ⇒ b	[2]

# abc:ba=ac,acb=b bac - -
ac=ba
bab=b

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

1 total

Σ	#	Presentation	Mapping
8	3459	⟨a, b, c \| ba=ac, bab=b⟩	φ(a) = a, φ(b) = b, φ(c) = c