#6004 ⟨a, b, c | ab=c, aab=cc⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by c is not injective:
- a ⋅ c = c² and c ⋅ c = c², however a ≠ 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

#	Rule	Proof
1.	ac ⇒ c²	[2]
2.	ab ⇒ c	[1]

# abc:ab=c,aab=cc cab - -
ac=cc
ab=c

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

1 total

Σ	#	Presentation	Mapping
8	6025	⟨a, b, c \| ab=c, abc=ac⟩	φ(a) = a, φ(b) = b, φ(c) = c