#931 ⟨a, b, c | aa=b, bcc=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 ⋅ ac² = a and a ⋅ 1 = a, however ac² ≠ 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.	a²c² ⇒ a	[2]
2.	b ⇒ a²	[1]

# abc:aa=b,bcc=a ac/b - -
aacc=a
b=aa

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

6 total

Σ	#	Presentation	Mapping
7	960	⟨a, b, c \| ab=a, acc=b⟩	φ(a) = a, φ(b) = acc, φ(c) = c
7	1026	⟨a, b, c \| ab=c, acb=a⟩	φ(a) = a, φ(b) = c, φ(c) = ac
8	5175	⟨a, b, c \| aa=b, aacc=a⟩	φ(a) = a, φ(b) = aa, φ(c) = c
8	5310	⟨a, b, c \| ab=a, abcc=b⟩	φ(a) = a, φ(b) = acc, φ(c) = c
8	5497	⟨a, b, c \| ab=c, aabb=a⟩	φ(a) = a, φ(b) = c, φ(c) = ac
8	5528	⟨a, b, c \| ab=c, abcb=a⟩	φ(a) = aac, φ(b) = c, φ(c) = a