#2194 ⟨a, b, c | aabc=1, abca=1⟩

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 a²b is not injective:
- a²b ⋅ ca²b = a²b and a²b ⋅ 1 = a²b, however ca²b ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- ca²b ⋅ c = c and 1 ⋅ c = c, however ca²b ≠ 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

#	Rule	Proof
1.	bca ⇒ abc	[3]
2.	a²bc ⇒ 1	[1]

# abc:aabc=1,abca=1 abc - -
bca=abc
aabc=1

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

1 total

Σ	#	Presentation	Mapping
8	2212	⟨a, b, c \| aabc=1, bcaa=1⟩	φ(a) = a, φ(b) = b, φ(c) = c