#1662 ⟨a, b, c | aab=ba, bac=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 e is not injective:
- e ⋅ ce = e and e ⋅ 1 = e, however ce ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- ce ⋅ c = c and 1 ⋅ c = c, however ce ≠ 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

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

# abc:aab=ba,bac=1 reversed:ac/edb ab=d,ad=e morph:2/3,2/1
ea=aae
ec=1
ad=e
da=ae
ab=d
ba=e
ed=be
eb=bd