#4375 ⟨a, b, c | aba=1, aabc=c⟩

Properties

Sum of relation sides is 8
Isomorphic to ℕ ∗ ℤ
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | ⟩
- Embedding: φ(a) = a, φ(b) = a^-1a^-1, φ(c) = b

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.	ba ⇒ ab	[2]
2.	a²b ⇒ 1	[3]

# abc:aba=1,aabc=c abc - -
ba=ab
aab=1

2 unique, 6 total

Σ	#	Presentation	Properties	Description	φ
8	2272	⟨a, b, c \| abac=1, caba=1⟩	Grp Inf	ℤ ∗ ℤ	1
8	5674	⟨a, b, c \| aa=b, aac=bc⟩	Can Inf	ℕ ∗ ℕ	3

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

2 total

Σ	#	Presentation	Mapping
8	4388	⟨a, b, c \| aba=1, abac=c⟩	φ(a) = a, φ(b) = b, φ(c) = 1
8	4427	⟨a, b, c \| aba=1, baac=c⟩	φ(a) = a, φ(b) = b, φ(c) = 1