#2783 ⟨a, b, c | abc=b, baca=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 b is not injective:
- b ⋅ d²ab = b and b ⋅ 1 = b, however d²ab ≠ 1
Not right cancellative, because right multiplication by d² is not injective:
- d²ab ⋅ d² = d² and 1 ⋅ d² = d², however d²ab ≠ 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 = ca
Reduction order:
- Left-to-right recursive path with deg(b) = deg(d) = 0, b < d; deg(a) = deg(c) = 1, a < c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# abc:abc=b,baca=1 bd/ac ca=d morph:2/1
bdbdd=bddb
abdd=1
ba=abd
bdda=1
c=dbdd