#49 ⟨a, b, c | bb=ac, bc=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 ⋅ c³a = a and a ⋅ 1 = a, however c³a ≠ 1
Not right cancellative, because right multiplication by c³ is not injective:
- c³a ⋅ c³ = c³ and 1 ⋅ c³ = c³, however c³a ≠ 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

Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:bb=ac,bc=1 ac/b - -
accc=1
accac=acacc
b=acc

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

4 total

Σ	#	Presentation	Mapping
8	7285	⟨a, b, c \| ab=1, aaab=cb⟩	φ(a) = acc, φ(b) = c, φ(c) = a
8	7299	⟨a, b, c \| ab=1, aaba=cb⟩	φ(a) = acc, φ(b) = c, φ(c) = a
8	7343	⟨a, b, c \| ab=1, abaa=cb⟩	φ(a) = acc, φ(b) = c, φ(c) = a
8	7380	⟨a, b, c \| ab=1, abcb=aa⟩	φ(a) = acc, φ(b) = c, φ(c) = a