#546 ⟨a, b, c | bb=aa, bc=b⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element ba 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

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

# abc:bb=aa,bc=b bc/a - -
bc=b
bba=abb
aa=bb

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

2 total

Σ	#	Presentation	Mapping
8	5785	⟨a, b, c \| ab=a, aab=cc⟩	φ(a) = b, φ(b) = c, φ(c) = a
8	5799	⟨a, b, c \| ab=a, aba=cc⟩	φ(a) = b, φ(b) = c, φ(c) = a