#5707 ⟨a, b, c | aa=b, acb=ca⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element c has infinite order
Not right cancellative, because right multiplication by a is not injective:
- c ⋅ a = bda and bd ⋅ a = bda, however c ≠ bd

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 = cb
Reduction order:
- Right-to-left 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:aa=b,acb=ca reversed:bd/ac cb=d morph:2/0
bdb=d
bdd=ddb
ab=ba
ad=bda
cb=d
cd=ddb
aa=b
ca=bda