#1984 ⟨a, b, c | abc=ba, ccb=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 c is not injective:
- c ⋅ cbc = c and c ⋅ 1 = c, however cbc ≠ 1
Not right cancellative, because right multiplication by d is not injective:
- bc² ⋅ d = d and 1 ⋅ d = d, however bc² ≠ 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(c) = 0; deg(d) = deg(b) = deg(a) = 1, d < b < a
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# abc:abc=ba,ccb=1 c/dba ab=d morph:2/1
ccb=1
a=ccdc
ccdcd=dccd
ccdcb=d
bd=dcb
bccd=d