#5674 ⟨a, b, c | aa=b, aac=bc⟩

Properties

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

Format:	Pretty Plain
Word:
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Strategy:	Leftmost Rightmost
Result:	1 1

Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	b ⇒ a²	[1]

# abc:aa=b,aac=bc ac/b - -
b=aa

2 unique, 5 total

Σ	#	Presentation	Properties	Description	φ
8	2272	⟨a, b, c \| abac=1, caba=1⟩	Grp Inf	ℤ ∗ ℤ	1
8	4375	⟨a, b, c \| aba=1, aabc=c⟩	Can Inf	ℕ ∗ ℤ	2

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

3 total

Σ	#	Presentation	Mapping
8	5998	⟨a, b, c \| ab=c, aab=ac⟩	φ(a) = a, φ(b) = 1, φ(c) = a
8	6020	⟨a, b, c \| ab=c, aba=ca⟩	φ(a) = a, φ(b) = 1, φ(c) = a
8	6031	⟨a, b, c \| ab=c, abc=cc⟩	φ(a) = a, φ(b) = 1, φ(c) = a