NO

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty)
(REPLACEMENT-MAP
(c)
(f 1)
(a)
(fSNonEmpty)
)
(RULES
c -> a
f(c) -> a
f(f(c)) -> c
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


Problem 1: 

Problem 1: 
Not CS-TRS Procedure:
R is not a CS-TRS

Problem 1: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty)
(REPLACEMENT-MAP
(c)
(f 1)
(a)
(fSNonEmpty)
)
(RULES
c -> a
f(c) -> a
f(f(c)) -> c
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Procedure:
-> Rules:
 c -> a
 f(c) -> a
 f(f(c)) -> c
-> Vars:


-> Rlps:
 (rule: c -> a, id: 1, possubterms: c->[])
 (rule: f(c) -> a, id: 2, possubterms: f(c)->[], c->[1])
 (rule: f(f(c)) -> c, id: 3, possubterms: f(f(c))->[], f(c)->[1], c->[1, 1])

-> Unifications:
(R2 unifies with R1 at p: [1], l: f(c), lp: c, sig: {}, l': c, r: a, r': a)
(R3 unifies with R2 at p: [1], l: f(f(c)), lp: f(c), sig: {}, l': f(c), r: c, r': a)
(R3 unifies with R1 at p: [1,1], l: f(f(c)), lp: c, sig: {}, l': c, r: c, r': a)

-> Critical pairs info:
<f(f(a)),c>   =>  Not trivial, Not overlay, Proper, NW0, N1
<f(a),c>   =>  Not trivial, Not overlay, Proper, NW0, N2
<f(a),a>   =>  Not trivial, Not overlay, Proper, NW0, N3

-> Problem conclusions:
 Left linear, Right linear, Linear
 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
 Not Huet-Levy confluent, Not Newman confluent
 R is a TRS 


Problem 1: 
No Convergence Brute Force Procedure:
-> Rewritings:
s: f(f(a))
Nodes: [0]
Edges: []
ID: 0 => ('f(f(a))', D0)
t: c
Nodes: [0,1]
Edges: [(0,1)]
ID: 0 => ('c', D0)
ID: 1 => ('a', D1, R1, P[], S{}), NR: 'a'
f(f(a)) ->* no union *<- c
"Not joinable"

The problem is not confluent.