#927 ⟨a, b, c | aa=b, bbc=c⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by c is not injective:
- a⁴ ⋅ c = c and 1 ⋅ c = c, however a⁴ ≠ 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.	a⁴c ⇒ c	[2]
2.	b ⇒ a²	[1]

# abc:aa=b,bbc=c ac/b - -
aaaac=c
b=aa

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

7 total

Σ	#	Presentation	Mapping
8	2824	⟨a, b, c \| aaa=b, abc=c⟩	φ(a) = a, φ(b) = aaa, φ(c) = c
8	2837	⟨a, b, c \| aaa=b, bac=c⟩	φ(a) = a, φ(b) = aaa, φ(c) = c
8	2961	⟨a, b, c \| aab=c, aac=b⟩	φ(a) = a, φ(b) = c, φ(c) = aac
8	5168	⟨a, b, c \| aa=b, aabc=c⟩	φ(a) = a, φ(b) = aa, φ(c) = c
8	5181	⟨a, b, c \| aa=b, abac=c⟩	φ(a) = a, φ(b) = aa, φ(c) = c
8	5220	⟨a, b, c \| aa=b, baac=c⟩	φ(a) = a, φ(b) = aa, φ(c) = c
8	5492	⟨a, b, c \| ab=c, aaac=b⟩	φ(a) = a, φ(b) = c, φ(c) = ac