#47 ⟨a, b, c | bb=aa, 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 ⋅ ac²a = a and a ⋅ 1 = a, however ac²a ≠ 1
Not right cancellative, because right multiplication by ac² is not injective:
- ac²a ⋅ ac² = ac² and 1 ⋅ ac² = ac², however ac²a ≠ 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(c) = deg(a) = 0, c < a; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:bb=aa,bc=1 ca/b - -
aacc=1
aaaac=aacaa
aacaac=aa
b=aac

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

6 total

Σ	#	Presentation	Mapping
8	7286	⟨a, b, c \| ab=1, aaab=cc⟩	φ(a) = aac, φ(b) = c, φ(c) = a
8	7300	⟨a, b, c \| ab=1, aaba=cc⟩	φ(a) = aac, φ(b) = c, φ(c) = a
8	7344	⟨a, b, c \| ab=1, abaa=cc⟩	φ(a) = aac, φ(b) = c, φ(c) = a
8	7389	⟨a, b, c \| ab=1, abcc=aa⟩	φ(a) = aac, φ(b) = c, φ(c) = a
8	7583	⟨a, b, c \| ab=1, cabc=aa⟩	φ(a) = aac, φ(b) = c, φ(c) = a
8	7806	⟨a, b, c \| ab=1, bcc=baa⟩	φ(a) = aac, φ(b) = c, φ(c) = a