#551 ⟨a, b, c | bb=ac, bc=b⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ c = b and b ⋅ 1 = b, however c ≠ 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.	bc ⇒ b	[2]
2.	ac ⇒ b²	[1]

# abc:bb=ac,bc=b bac - -
bc=b
ac=bb

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

2 total

Σ	#	Presentation	Mapping
8	5784	⟨a, b, c \| ab=a, aab=cb⟩	φ(a) = b, φ(b) = c, φ(c) = a
8	5798	⟨a, b, c \| ab=a, aba=cb⟩	φ(a) = b, φ(b) = c, φ(c) = a