#4414 ⟨a, b, c | aba=1, acbc=c⟩

Properties

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

# abc:aba=1,acbc=c d/cab bc=d morph:2/0
cdd=d
ad=cd
bd=ddd
acd=c
bc=d
ba=ab
aab=1