#2300 ⟨a, b | abaaaba=aab⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ba³ba = a²b and a ⋅ ab = a²b, however ba³ba ≠ ab

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

Auxiliary generators:
1. c = aaba
2. d = ab
Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(d) = 1; deg(b) = 2
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:abaaaba=aab ac/d/b aaba=c,ab=d morph:4/0,2/0
cca=ac
daca=c
ad=dac
cd=dcccc
ab=d
cb=ddaccccc