#145 ⟨a, b, c | aa=b, bc=c⟩

Properties

Sum of relation sides is 6
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by c is not injective:
- a² ⋅ c = c and 1 ⋅ c = c, however a² ≠ 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.	a²c ⇒ c	[2]
2.	b ⇒ a²	[1]

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

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

9 total

Σ	#	Presentation	Mapping
6	158	⟨a, b, c \| ab=c, ac=b⟩	φ(a) = a, φ(b) = c, φ(c) = ac
7	905	⟨a, b, c \| aa=b, aac=c⟩	φ(a) = a, φ(b) = aa, φ(c) = c
7	1012	⟨a, b, c \| ab=c, aab=b⟩	φ(a) = a, φ(b) = c, φ(c) = ac
8	2819	⟨a, b, c \| aaa=b, aac=c⟩	φ(a) = a, φ(b) = aaa, φ(c) = c
8	2914	⟨a, b, c \| aab=b, aba=c⟩	φ(a) = a, φ(b) = c, φ(c) = aca
8	2915	⟨a, b, c \| aab=b, abb=c⟩	φ(a) = a, φ(b) = c, φ(c) = acc
8	2927	⟨a, b, c \| aab=b, baa=c⟩	φ(a) = a, φ(b) = c, φ(c) = caa
8	2928	⟨a, b, c \| aab=b, bab=c⟩	φ(a) = a, φ(b) = c, φ(c) = cac
8	2932	⟨a, b, c \| aab=b, bba=c⟩	φ(a) = a, φ(b) = c, φ(c) = cca