YES

We show the termination of the TRS R:

  concat(leaf(),Y) -> Y
  concat(cons(U,V),Y) -> cons(U,concat(V,Y))
  lessleaves(X,leaf()) -> false()
  lessleaves(leaf(),cons(W,Z)) -> true()
  lessleaves(cons(U,V),cons(W,Z)) -> lessleaves(concat(U,V),concat(W,Z))

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: concat#(cons(U,V),Y) -> concat#(V,Y)
p2: lessleaves#(cons(U,V),cons(W,Z)) -> lessleaves#(concat(U,V),concat(W,Z))
p3: lessleaves#(cons(U,V),cons(W,Z)) -> concat#(U,V)
p4: lessleaves#(cons(U,V),cons(W,Z)) -> concat#(W,Z)

and R consists of:

r1: concat(leaf(),Y) -> Y
r2: concat(cons(U,V),Y) -> cons(U,concat(V,Y))
r3: lessleaves(X,leaf()) -> false()
r4: lessleaves(leaf(),cons(W,Z)) -> true()
r5: lessleaves(cons(U,V),cons(W,Z)) -> lessleaves(concat(U,V),concat(W,Z))

The estimated dependency graph contains the following SCCs:

  {p2}
  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: lessleaves#(cons(U,V),cons(W,Z)) -> lessleaves#(concat(U,V),concat(W,Z))

and R consists of:

r1: concat(leaf(),Y) -> Y
r2: concat(cons(U,V),Y) -> cons(U,concat(V,Y))
r3: lessleaves(X,leaf()) -> false()
r4: lessleaves(leaf(),cons(W,Z)) -> true()
r5: lessleaves(cons(U,V),cons(W,Z)) -> lessleaves(concat(U,V),concat(W,Z))

The set of usable rules consists of

  r1, r2

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^4
    order: lexicographic order
    interpretations:
      lessleaves#_A(x1,x2) = ((1,0,0,0),(1,1,0,0),(0,0,1,0),(1,1,1,1)) x1 + ((0,0,0,0),(1,0,0,0),(0,1,0,0),(0,0,0,0)) x2
      cons_A(x1,x2) = ((1,0,0,0),(1,1,0,0),(1,1,1,0),(1,1,1,1)) x1 + ((1,0,0,0),(1,0,0,0),(1,1,0,0),(1,0,1,0)) x2 + (7,2,3,1)
      concat_A(x1,x2) = ((1,0,0,0),(1,1,0,0),(1,0,1,0),(0,1,1,1)) x1 + ((1,0,0,0),(1,0,0,0),(1,1,0,0),(1,0,0,0)) x2 + (6,3,1,1)
      leaf_A() = (1,1,1,1)

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: concat#(cons(U,V),Y) -> concat#(V,Y)

and R consists of:

r1: concat(leaf(),Y) -> Y
r2: concat(cons(U,V),Y) -> cons(U,concat(V,Y))
r3: lessleaves(X,leaf()) -> false()
r4: lessleaves(leaf(),cons(W,Z)) -> true()
r5: lessleaves(cons(U,V),cons(W,Z)) -> lessleaves(concat(U,V),concat(W,Z))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^4
    order: lexicographic order
    interpretations:
      concat#_A(x1,x2) = ((1,0,0,0),(0,1,0,0),(0,0,1,0),(1,1,1,1)) x1 + ((1,0,0,0),(0,1,0,0),(0,0,1,0),(0,1,1,1)) x2
      cons_A(x1,x2) = ((1,0,0,0),(0,1,0,0),(1,1,1,0),(1,1,1,1)) x1 + ((1,0,0,0),(1,1,0,0),(1,1,1,0),(1,1,1,1)) x2 + (1,1,1,1)

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5

We remove them from the problem.  Then no dependency pair remains.