YES

Problem 1: 

(VAR v_NonEmpty:S U:S V:S W:S X:S Y:S Z:S)
(RULES
concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S))
concat(leaf,Y:S) -> Y:S
lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S))
lessleaves(leaf,cons(W:S,Z:S)) -> ttrue
lessleaves(X:S,leaf) -> ffalse
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S))
 concat(leaf,Y:S) -> Y:S
 lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S))
 lessleaves(leaf,cons(W:S,Z:S)) -> ttrue
 lessleaves(X:S,leaf) -> ffalse
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 CONCAT(cons(U:S,V:S),Y:S) -> CONCAT(V:S,Y:S)
 LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> CONCAT(U:S,V:S)
 LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> CONCAT(W:S,Z:S)
 LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> LESSLEAVES(concat(U:S,V:S),concat(W:S,Z:S))
-> Rules:
 concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S))
 concat(leaf,Y:S) -> Y:S
 lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S))
 lessleaves(leaf,cons(W:S,Z:S)) -> ttrue
 lessleaves(X:S,leaf) -> ffalse

Problem 1: 

SCC Processor:
-> Pairs:
 CONCAT(cons(U:S,V:S),Y:S) -> CONCAT(V:S,Y:S)
 LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> CONCAT(U:S,V:S)
 LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> CONCAT(W:S,Z:S)
 LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> LESSLEAVES(concat(U:S,V:S),concat(W:S,Z:S))
-> Rules:
 concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S))
 concat(leaf,Y:S) -> Y:S
 lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S))
 lessleaves(leaf,cons(W:S,Z:S)) -> ttrue
 lessleaves(X:S,leaf) -> ffalse
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 CONCAT(cons(U:S,V:S),Y:S) -> CONCAT(V:S,Y:S)
->->-> Rules:
 concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S))
 concat(leaf,Y:S) -> Y:S
 lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S))
 lessleaves(leaf,cons(W:S,Z:S)) -> ttrue
 lessleaves(X:S,leaf) -> ffalse
->->Cycle:
->->-> Pairs:
 LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> LESSLEAVES(concat(U:S,V:S),concat(W:S,Z:S))
->->-> Rules:
 concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S))
 concat(leaf,Y:S) -> Y:S
 lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S))
 lessleaves(leaf,cons(W:S,Z:S)) -> ttrue
 lessleaves(X:S,leaf) -> ffalse


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 CONCAT(cons(U:S,V:S),Y:S) -> CONCAT(V:S,Y:S)
-> Rules:
 concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S))
 concat(leaf,Y:S) -> Y:S
 lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S))
 lessleaves(leaf,cons(W:S,Z:S)) -> ttrue
 lessleaves(X:S,leaf) -> ffalse
->Projection:
 pi(CONCAT) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S))
 concat(leaf,Y:S) -> Y:S
 lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S))
 lessleaves(leaf,cons(W:S,Z:S)) -> ttrue
 lessleaves(X:S,leaf) -> ffalse
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Reduction Pairs Processor:
-> Pairs:
 LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> LESSLEAVES(concat(U:S,V:S),concat(W:S,Z:S))
-> Rules:
 concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S))
 concat(leaf,Y:S) -> Y:S
 lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S))
 lessleaves(leaf,cons(W:S,Z:S)) -> ttrue
 lessleaves(X:S,leaf) -> ffalse
-> Usable rules:
 concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S))
 concat(leaf,Y:S) -> Y:S
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[concat](X1,X2) = X1 + X2 + 1
[lessleaves](X1,X2) = 0
[cons](X1,X2) = 2.X1 + X2 + 2
[fSNonEmpty] = 0
[false] = 0
[leaf] = 0
[true] = 0
[CONCAT](X1,X2) = 0
[LESSLEAVES](X1,X2) = 2.X1 + X2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S))
 concat(leaf,Y:S) -> Y:S
 lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S))
 lessleaves(leaf,cons(W:S,Z:S)) -> ttrue
 lessleaves(X:S,leaf) -> ffalse
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.