#2823 ⟨a, b, c | aaa=b, abc=b⟩

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 ⋅ a³c = a³ and a ⋅ a² = a³, however a³c ≠ a²

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.	a⁴c ⇒ a³	[2]
2.	b ⇒ a³	[1]

# abc:aaa=b,abc=b ac/b - -
aaaac=aaa
b=aaa

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

3 total

Σ	#	Presentation	Mapping
8	2836	⟨a, b, c \| aaa=b, bac=b⟩	φ(a) = a, φ(b) = aaa, φ(c) = c
8	5735	⟨a, b, c \| aa=b, bbc=ab⟩	φ(a) = a, φ(b) = aa, φ(c) = c
8	5737	⟨a, b, c \| aa=b, bbc=ba⟩	φ(a) = a, φ(b) = aa, φ(c) = c