NO

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x)
(REPLACEMENT-MAP
(0 1)
(1 1)
(2 1)
(3 1)
(4 1)
(5 1)
(fSNonEmpty)
)
(RULES
0(1(2(3(4(5(1(x))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x)))))))))))))))))))))))))
0(1(2(3(4(5(1(x))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x)))))))))))))))))))
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


Problem 1: 

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

Problem 1: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x)
(REPLACEMENT-MAP
(0 1)
(1 1)
(2 1)
(3 1)
(4 1)
(5 1)
(fSNonEmpty)
)
(RULES
0(1(2(3(4(5(1(x))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x)))))))))))))))))))))))))
0(1(2(3(4(5(1(x))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x)))))))))))))))))))
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Procedure:
-> Rules:
 0(1(2(3(4(5(1(x))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x)))))))))))))))))))))))))
 0(1(2(3(4(5(1(x))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x)))))))))))))))))))
-> Vars:
 x, x

-> Rlps:
 (rule: 0(1(2(3(4(5(1(x))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x))))))))))))))))))))))))), id: 1, possubterms: 0(1(2(3(4(5(1(x)))))))->[], 1(2(3(4(5(1(x))))))->[1], 2(3(4(5(1(x)))))->[1, 1], 3(4(5(1(x))))->[1, 1, 1], 4(5(1(x)))->[1, 1, 1, 1], 5(1(x))->[1, 1, 1, 1, 1], 1(x)->[1, 1, 1, 1, 1, 1])
 (rule: 0(1(2(3(4(5(1(x))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x))))))))))))))))))), id: 2, possubterms: 0(1(2(3(4(5(1(x)))))))->[], 1(2(3(4(5(1(x))))))->[1], 2(3(4(5(1(x)))))->[1, 1], 3(4(5(1(x))))->[1, 1, 1], 4(5(1(x)))->[1, 1, 1, 1], 5(1(x))->[1, 1, 1, 1, 1], 1(x)->[1, 1, 1, 1, 1, 1])

-> Unifications:
(R2 unifies with R1 at p: [], l: 0(1(2(3(4(5(1(x))))))), lp: 0(1(2(3(4(5(1(x))))))), sig: {x -> x'}, l': 0(1(2(3(4(5(1(x'))))))), r: 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x))))))))))))))))))), r': 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x'))))))))))))))))))))))))))

-> Critical pairs info:
<1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x'))))))))))))))))))))))))),1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x')))))))))))))))))))>   =>  Not trivial, Overlay, Proper, NW0, N1

-> 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: 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x')))))))))))))))))))))))))
Nodes: [0]
Edges: []
ID: 0 => ('1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x')))))))))))))))))))))))))', D0)
t: 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x')))))))))))))))))))
Nodes: [0]
Edges: []
ID: 0 => ('1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x')))))))))))))))))))', D0)
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x'))))))))))))))))))))))))) ->* no union *<- 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x')))))))))))))))))))
"Not joinable"

The problem is not confluent.