#1045 ⟨a, b, c | ab=c, cac=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 ⋅ ba²b = a and a ⋅ 1 = a, however ba²b ≠ 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(b) = deg(a) = 0, b < a; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:ab=c,cac=a ba/c - -
aaab=abaa
abaab=a
c=ab

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

5 total

Σ	#	Presentation	Mapping
8	2966	⟨a, b, c \| aab=c, abc=a⟩	φ(a) = a, φ(b) = b, φ(c) = aab
8	5205	⟨a, b, c \| aa=b, acbc=a⟩	φ(a) = a, φ(b) = aa, φ(c) = b
8	5411	⟨a, b, c \| ab=a, caac=b⟩	φ(a) = a, φ(b) = baab, φ(c) = b
8	5516	⟨a, b, c \| ab=c, abac=a⟩	φ(a) = a, φ(b) = b, φ(c) = ab
8	5606	⟨a, b, c \| ab=c, cbcc=a⟩	φ(a) = abaa, φ(b) = b, φ(c) = a