#1234 ⟨a, b, c | aa=1, abac=c⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element ab has infinite order
Not right cancellative, because right multiplication by c is not injective:
- ba ⋅ c = ac and a ⋅ c = ac, however ba ≠ a

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.	a² ⇒ 1	[1]
2.	bac ⇒ ac	[3]

# abc:aa=1,abac=c abc - -
aa=1
bac=ac

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

1 total

Σ	#	Presentation	Mapping
7	1413	⟨a, b, c \| aa=1, bac=ac⟩	φ(a) = a, φ(b) = b, φ(c) = c