#1028 ⟨a, b, c | ab=c, acc=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 ⋅ (ab)² = a and a ⋅ 1 = a, however (ab)² ≠ 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(b) = 0, a < b; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	a(ab)² ⇒ a	[2]
2.	c ⇒ ab	[1]

# abc:ab=c,acc=a ab/c - -
aabab=a
c=ab

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

7 total

Σ	#	Presentation	Mapping
8	2897	⟨a, b, c \| aab=a, cac=b⟩	φ(a) = a, φ(b) = bab, φ(c) = b
8	2993	⟨a, b, c \| aab=c, cab=a⟩	φ(a) = a, φ(b) = b, φ(c) = aab
8	3048	⟨a, b, c \| aba=c, acb=a⟩	φ(a) = a, φ(b) = b, φ(c) = aba
8	5244	⟨a, b, c \| aa=b, bcac=a⟩	φ(a) = a, φ(b) = aa, φ(c) = b
8	5319	⟨a, b, c \| ab=a, acac=b⟩	φ(a) = a, φ(b) = abab, φ(c) = b
8	5499	⟨a, b, c \| ab=c, aabc=a⟩	φ(a) = a, φ(b) = b, φ(c) = ab
8	5580	⟨a, b, c \| ab=c, bbca=b⟩	φ(a) = b, φ(b) = a, φ(c) = ba