#7308 ⟨a, b, c | ab=1, aabc=bb⟩

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 ⋅ a²ca = a and a ⋅ 1 = a, however a²ca ≠ 1
Not right cancellative, because right multiplication by a²c is not injective:
- a²ca ⋅ a²c = a²c and 1 ⋅ a²c = a²c, however a²ca ≠ 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:ab=1,aabc=bb ac/b - -
aaac=1
acaac=aacac
b=aac

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

3 total

Σ	#	Presentation	Mapping
8	7352	⟨a, b, c \| ab=1, abac=bb⟩	φ(a) = a, φ(b) = aac, φ(c) = c
8	7758	⟨a, b, c \| ab=1, bba=aca⟩	φ(a) = a, φ(b) = aac, φ(c) = c
8	7765	⟨a, b, c \| ab=1, bbb=bac⟩	φ(a) = a, φ(b) = aac, φ(c) = c