#2933 ⟨a, b, c | aab=b, bbc=a⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ (bcb)² = b and b ⋅ 1 = b, however (bcb)² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- (b²c)² ⋅ b = b and 1 ⋅ b = b, however (b²c)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(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	(b²c)²b ⇒ b	[3]
2.	a ⇒ b²c	[2]

# abc:aab=b,bbc=a bc/a - -
bbcbbcb=b
a=bbc

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

1 total

Σ	#	Presentation	Mapping
8	2938	⟨a, b, c \| aab=b, bcb=a⟩	φ(a) = bcb, φ(b) = b, φ(c) = c