#7393 ⟨a, b, c | ab=1, abcc=bb⟩

Properties

Sum of relation sides is 8
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 c is not injective:
- ac²ac ⋅ c = c² and c ⋅ c = c², however ac²ac ≠ c

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:ab=1,abcc=bb ca/b - -
aacc=1
acccc=ccacc
accacc=cc
b=acc

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

1 total

Σ	#	Presentation	Mapping
8	7810	⟨a, b, c \| ab=1, bcc=bbb⟩	φ(a) = a, φ(b) = acc, φ(c) = c