#325 ⟨a, b, c | aab=c, acc=1⟩

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 ⋅ (a²b)²a = a and a ⋅ 1 = a, however (a²b)²a ≠ 1
Not right cancellative, because right multiplication by (a²b)² is not injective:
- (a²b)²a ⋅ (a²b)² = (a²b)² and 1 ⋅ (a²b)² = (a²b)², however (a²b)²a ≠ 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(a²b)² ⇒ 1	[2]
2.	c ⇒ a²b	[1]

# abc:aab=c,acc=1 ab/c - -
aaabaab=1
c=aab

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

3 total

Σ	#	Presentation	Mapping
8	4690	⟨a, b, c \| aa=b, abcbc=1⟩	φ(a) = a, φ(b) = aa, φ(c) = b
8	4726	⟨a, b, c \| aa=b, bacbc=1⟩	φ(a) = a, φ(b) = aa, φ(c) = b
8	5002	⟨a, b, c \| ab=c, aacac=1⟩	φ(a) = a, φ(b) = b, φ(c) = ab