#928 ⟨a, b, c | aa=b, bcb=a⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a²ca = a and a ⋅ 1 = a, however a²ca ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a³c ⋅ a = a and 1 ⋅ a = a, however a³c ≠ 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.

# abc:aa=b,bcb=a ac/b - -
acaa=aaca
aaaca=a
b=aa

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

5 total

Σ	#	Presentation	Mapping
8	2891	⟨a, b, c \| aab=a, caa=b⟩	φ(a) = a, φ(b) = caa, φ(c) = c
8	3010	⟨a, b, c \| aba=a, aca=b⟩	φ(a) = a, φ(b) = aca, φ(c) = c
8	5172	⟨a, b, c \| aa=b, aacb=a⟩	φ(a) = a, φ(b) = aa, φ(c) = c
8	5313	⟨a, b, c \| ab=a, acaa=b⟩	φ(a) = a, φ(b) = aaca, φ(c) = c
8	5534	⟨a, b, c \| ab=c, acaa=a⟩	φ(a) = a, φ(b) = c, φ(c) = ac