#988 ⟨a, b, c | ab=a, cac=b⟩

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.

# abc:ab=a,cac=b ac/b - -
aca=aac
aacc=a
b=cac

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

2 total

Σ	#	Presentation	Mapping
8	5199	⟨a, b, c \| aa=b, acac=a⟩	φ(a) = a, φ(b) = aa, φ(c) = c
8	5420	⟨a, b, c \| ab=a, cabc=b⟩	φ(a) = a, φ(b) = cac, φ(c) = c

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

3 total

Σ	#	Presentation	Mapping
7	1046	⟨a, b, c \| ab=c, cac=b⟩	φ(a) = c, φ(b) = caa, φ(c) = a
8	5201	⟨a, b, c \| aa=b, acac=c⟩	φ(a) = c, φ(b) = cc, φ(c) = a
8	5517	⟨a, b, c \| ab=c, abac=b⟩	φ(a) = c, φ(b) = caa, φ(c) = a