#6639 ⟨a, b, c | aa=1, aabcc=c⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not right cancellative, because right multiplication by c is not injective:
- bc ⋅ c = c and 1 ⋅ c = c, however bc ≠ 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.	a² ⇒ 1	[1]
2.	bc² ⇒ c	[2]

# abc:aa=1,aabcc=c abc - -
aa=1
bcc=c

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

2 total

Σ	#	Presentation	Mapping
8	6708	⟨a, b, c \| aa=1, baacc=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7190	⟨a, b, c \| aa=1, abcc=ac⟩	φ(a) = a, φ(b) = b, φ(c) = c