#545 ⟨a, b, c | bb=aa, bc=a⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ cbc = b² and b ⋅ b = b², however cbc ≠ b

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(b) = 0, c < b; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:bb=aa,bc=a cb/a - -
bcbc=bb
bbbc=bcbb
a=bc

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

3 total

Σ	#	Presentation	Mapping
8	3352	⟨a, b, c \| ab=aa, cac=b⟩	φ(a) = b, φ(b) = cbc, φ(c) = c
8	5200	⟨a, b, c \| aa=b, acac=b⟩	φ(a) = b, φ(b) = bb, φ(c) = c
8	6023	⟨a, b, c \| ab=c, abc=aa⟩	φ(a) = b, φ(b) = c, φ(c) = bc