#2606 ⟨a, b, c | aba=b, acbb=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 ⋅ dac = c and c ⋅ 1 = c, however dac ≠ 1
Not right cancellative, because right multiplication by d is not injective:
- dac ⋅ d = d and 1 ⋅ d = d, however dac ≠ 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 = bb
Reduction order:
- Left-to-right recursive path with deg(c) = 0; deg(d) = deg(a) = deg(b) = 1, d < a < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# abc:aba=b,acbb=1 c/dab bb=d morph:2/0
cdd=dcd
cda=1
ad=da
acd=1
bd=db
bcd=ab
ba=cdb
bb=d