#1670 ⟨a, b, c | aab=ba, cba=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 c is not injective:
- c ⋅ bac = c and c ⋅ 1 = c, however bac ≠ 1
Not right cancellative, because right multiplication by d is not injective:
- b ⋅ d = dcd and dc ⋅ d = dcd, however b ≠ dc

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

# abc:aab=ba,cba=1 reversed:cd/b/a bba=d morph:3/0
bd=dcd
cbcd=b
bbcd=db
cba=1
bba=d
ad=cdba
acd=ba
ab=cd