#1869 ⟨a, b, c | aba=bc, bba=1⟩

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 b is not injective:
- b ⋅ bab = b and b ⋅ 1 = b, however bab ≠ 1
Not right cancellative, because right multiplication by ba is not injective:
- bab ⋅ ba = ba and 1 ⋅ ba = ba, however bab ≠ 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.	b²a ⇒ 1	[2]
2.	bc ⇒ aba	[1]

# abc:aba=bc,bba=1 ab/c - -
bba=1
bc=aba