#1811 ⟨a, b, c | aba=ab, bac=1⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by d is not injective:
- d ⋅ dc = d and d ⋅ 1 = d, however dc ≠ 1
Not right cancellative, because right multiplication by dc² is not injective:
- dc²b ⋅ dc² = dc² and 1 ⋅ dc² = dc², however dc²b ≠ 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
Reduction order:
- Left-to-right recursive path with deg(d) = deg(b) = deg(c) = 0, d < b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# abc:aba=ab,bac=1 dbc/a ab=d morph:2/1
db=dd
ddc=d
dcb=d
bdcc=1
a=dc