#2845 ⟨a, b, c | aaa=b, bcc=a⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a²c² = a and a ⋅ 1 = a, however a²c² ≠ 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

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.	a³c² ⇒ a	[2]
2.	b ⇒ a³	[1]

# abc:aaa=b,bcc=a ac/b - -
aaacc=a
b=aaa

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

6 total

Σ	#	Presentation	Mapping
8	2870	⟨a, b, c \| aab=a, acc=b⟩	φ(a) = a, φ(b) = acc, φ(c) = c
8	2972	⟨a, b, c \| aab=c, acb=a⟩	φ(a) = a, φ(b) = c, φ(c) = aac
8	5193	⟨a, b, c \| aa=b, abcc=a⟩	φ(a) = a, φ(b) = aa, φ(c) = c
8	5228	⟨a, b, c \| aa=b, bacc=a⟩	φ(a) = a, φ(b) = aa, φ(c) = c
8	5291	⟨a, b, c \| ab=a, aacc=b⟩	φ(a) = a, φ(b) = aacc, φ(c) = c
8	5505	⟨a, b, c \| ab=c, aacb=a⟩	φ(a) = a, φ(b) = c, φ(c) = ac