#216 ⟨a, b, c | aa=1, abc=c⟩

Properties

Sum of relation sides is 6
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not right cancellative, because right multiplication by c is not injective:
- b ⋅ c = ac and a ⋅ c = ac, however b ≠ 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.	bc ⇒ ac	[3]

# abc:aa=1,abc=c abc - -
aa=1
bc=ac

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

7 total

Σ	#	Presentation	Mapping
8	6620	⟨a, b, c \| aa=1, aaabc=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6643	⟨a, b, c \| aa=1, abaac=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7121	⟨a, b, c \| aa=1, aaab=cb⟩	φ(a) = a, φ(b) = c, φ(c) = b
8	7135	⟨a, b, c \| aa=1, aabc=ac⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7202	⟨a, b, c \| aa=1, baac=ac⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7624	⟨a, b, c \| aa=1, abc=aac⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7635	⟨a, b, c \| aa=1, baa=acb⟩	φ(a) = a, φ(b) = c, φ(c) = b