#4278 ⟨a, b, c | aab=1, bcca=c⟩

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

# abc:aab=1,bcca=c cad/b bc=d morph:2/2
aac=cca
aad=c
dcc=cad
dca=c
bc=d
cb=ddc
db=bddc
cab=dc
aab=1
dab=bdc