YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
++(nil,y:S) -> y:S
car(.(x:S,y:S)) -> x:S
cdr(.(x:S,y:S)) -> y:S
null(.(x:S,y:S)) -> ffalse
null(nil) -> ttrue
rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil))
rev(nil) -> nil
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 car(.(x:S,y:S)) -> x:S
 cdr(.(x:S,y:S)) -> y:S
 null(.(x:S,y:S)) -> ffalse
 null(nil) -> ttrue
 rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil))
 rev(nil) -> nil
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ++#(.(x:S,y:S),z:S) -> ++#(y:S,z:S)
 REV(.(x:S,y:S)) -> ++#(rev(y:S),.(x:S,nil))
 REV(.(x:S,y:S)) -> REV(y:S)
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 car(.(x:S,y:S)) -> x:S
 cdr(.(x:S,y:S)) -> y:S
 null(.(x:S,y:S)) -> ffalse
 null(nil) -> ttrue
 rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil))
 rev(nil) -> nil

Problem 1: 

SCC Processor:
-> Pairs:
 ++#(.(x:S,y:S),z:S) -> ++#(y:S,z:S)
 REV(.(x:S,y:S)) -> ++#(rev(y:S),.(x:S,nil))
 REV(.(x:S,y:S)) -> REV(y:S)
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 car(.(x:S,y:S)) -> x:S
 cdr(.(x:S,y:S)) -> y:S
 null(.(x:S,y:S)) -> ffalse
 null(nil) -> ttrue
 rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil))
 rev(nil) -> nil
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ++#(.(x:S,y:S),z:S) -> ++#(y:S,z:S)
->->-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 car(.(x:S,y:S)) -> x:S
 cdr(.(x:S,y:S)) -> y:S
 null(.(x:S,y:S)) -> ffalse
 null(nil) -> ttrue
 rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil))
 rev(nil) -> nil
->->Cycle:
->->-> Pairs:
 REV(.(x:S,y:S)) -> REV(y:S)
->->-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 car(.(x:S,y:S)) -> x:S
 cdr(.(x:S,y:S)) -> y:S
 null(.(x:S,y:S)) -> ffalse
 null(nil) -> ttrue
 rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil))
 rev(nil) -> nil


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ++#(.(x:S,y:S),z:S) -> ++#(y:S,z:S)
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 car(.(x:S,y:S)) -> x:S
 cdr(.(x:S,y:S)) -> y:S
 null(.(x:S,y:S)) -> ffalse
 null(nil) -> ttrue
 rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil))
 rev(nil) -> nil
->Projection:
 pi(++#) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 car(.(x:S,y:S)) -> x:S
 cdr(.(x:S,y:S)) -> y:S
 null(.(x:S,y:S)) -> ffalse
 null(nil) -> ttrue
 rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil))
 rev(nil) -> nil
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 REV(.(x:S,y:S)) -> REV(y:S)
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 car(.(x:S,y:S)) -> x:S
 cdr(.(x:S,y:S)) -> y:S
 null(.(x:S,y:S)) -> ffalse
 null(nil) -> ttrue
 rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil))
 rev(nil) -> nil
->Projection:
 pi(REV) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 car(.(x:S,y:S)) -> x:S
 cdr(.(x:S,y:S)) -> y:S
 null(.(x:S,y:S)) -> ffalse
 null(nil) -> ttrue
 rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil))
 rev(nil) -> nil
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.