#2995 ⟨a, b, c | aab=c, cab=c⟩

Properties

Sum of relation sides is 8
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 = a²b and a ⋅ ab = a²b, however (ab)² ≠ ab
Not right cancellative, because right multiplication by b is not injective:
- a²ba ⋅ b = a²b and a² ⋅ b = a²b, however a²ba ≠ a²

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 ⇒ a²b	[2]
2.	c ⇒ a²b	[1]

# abc:aab=c,cab=c ab/c - -
aabab=aab
c=aab

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

1 total

Σ	#	Presentation	Mapping
8	6049	⟨a, b, c \| ab=c, acc=ac⟩	φ(a) = a, φ(b) = b, φ(c) = ab