#919 ⟨a, b, c | aa=b, acc=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:
- ac ⋅ c = c and 1 ⋅ c = c, however ac ≠ 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.	ac² ⇒ c	[2]
2.	b ⇒ a²	[1]

# abc:aa=b,acc=c ac/b - -
acc=c
b=aa

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

4 total

Σ	#	Presentation	Mapping
7	1021	⟨a, b, c \| ab=c, abc=b⟩	φ(a) = a, φ(b) = cc, φ(c) = c
7	1031	⟨a, b, c \| ab=c, baa=a⟩	φ(a) = c, φ(b) = a, φ(c) = ca
8	2833	⟨a, b, c \| aaa=b, acc=c⟩	φ(a) = a, φ(b) = aaa, φ(c) = c
8	2967	⟨a, b, c \| aab=c, abc=b⟩	φ(a) = a, φ(b) = ccc, φ(c) = c