#6670 ⟨a, b, c | aa=1, abbcb=b⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ bcab = b and b ⋅ 1 = b, however bcab ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b²ca ⋅ b = b and 1 ⋅ b = b, however b²ca ≠ 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

# abc:aa=1,abbcb=b abc - -
aa=1
bbcb=ab
bbcab=b

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

1 total

Σ	#	Presentation	Mapping
8	7251	⟨a, b, c \| aa=1, bbcb=ab⟩	φ(a) = a, φ(b) = b, φ(c) = c