YES
We show the termination of the TRS R:

  app(app(app(uncurry(),f),x),y) -> app(app(f,x),y)

Instead we prove termination of the uncurried system:

  app(uncurry_0(),y) -> uncurry_1(y)
  app(uncurry_1(x1),y) -> uncurry_2(x1,y)
  app(uncurry_2(x1,x2),y) -> uncurry_3(x1,x2,y)
  uncurry_3(f,x,y) -> app(app(f,x),y)


-- SCC decomposition.

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

p1: app#(uncurry_2(x1,x2),y) -> uncurry_3#(x1,x2,y)
p2: uncurry_3#(f,x,y) -> app#(app(f,x),y)
p3: uncurry_3#(f,x,y) -> app#(f,x)

and R consists of:

r1: app(uncurry_0(),y) -> uncurry_1(y)
r2: app(uncurry_1(x1),y) -> uncurry_2(x1,y)
r3: app(uncurry_2(x1,x2),y) -> uncurry_3(x1,x2,y)
r4: uncurry_3(f,x,y) -> app(app(f,x),y)

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3}


-- Reduction pair.

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

p1: app#(uncurry_2(x1,x2),y) -> uncurry_3#(x1,x2,y)
p2: uncurry_3#(f,x,y) -> app#(f,x)
p3: uncurry_3#(f,x,y) -> app#(app(f,x),y)

and R consists of:

r1: app(uncurry_0(),y) -> uncurry_1(y)
r2: app(uncurry_1(x1),y) -> uncurry_2(x1,y)
r3: app(uncurry_2(x1,x2),y) -> uncurry_3(x1,x2,y)
r4: uncurry_3(f,x,y) -> app(app(f,x),y)

The set of usable rules consists of

  r1, r2, r3, r4

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      trivial reduction triple (T x T, T x T, Φ)
  
    base order 2:
  
      lexicographic combination of reduction triples:
      
        1. marked-algebra reduction triple (>=A, >=A!, >A!):
        
          matrix interpretation with standard point-wise order:
          
            carrier: N^1
            order: standard order
            interpretations:
              app#_A(x1,x2) = x1
              uncurry_2_A(x1,x2) = x1 + x2 + 3
              uncurry_3#_A(x1,x2,x3) = x1 + x2 + 3
              app_A(x1,x2) = x1 + x2 + 1
              uncurry_0_A() = 5
              uncurry_1_A(x1) = x1 + 4
              uncurry_3_A(x1,x2,x3) = x1 + x2 + x3 + 2
              app#!_A(x1,x2) = x1
              uncurry_2!_A(x1,x2) = x1 + 3
              uncurry_3#!_A(x1,x2,x3) = x1 + x2 + 2
              app!_A(x1,x2) = x1
              uncurry_0!_A() = 0
              uncurry_1!_A(x1) = 4
              uncurry_3!_A(x1,x2,x3) = x1 + x2 + 2
        
        2. marked-algebra reduction triple (>=A, >=A!, >A!):
        
          max/plus interpretation on natural numbers:
          
            app#_A(x1,x2) = 1
            uncurry_2_A(x1,x2) = 2
            uncurry_3#_A(x1,x2,x3) = 1
            app_A(x1,x2) = 2
            uncurry_0_A = 0
            uncurry_1_A(x1) = 1
            uncurry_3_A(x1,x2,x3) = 2
            app#!_A(x1,x2) = 7
            uncurry_2!_A(x1,x2) = 4
            uncurry_3#!_A(x1,x2,x3) = max{8, x1 + 6, x2 + 4}
            app!_A(x1,x2) = x1 + 5
            uncurry_0!_A = 1
            uncurry_1!_A(x1) = 2
            uncurry_3!_A(x1,x2,x3) = 5
        
  
    partial status:
  
      pi(app#) = [1]
      pi(uncurry_2) = [1, 2]
      pi(uncurry_3#) = [1, 2]
      pi(app) = [1, 2]
      pi(uncurry_0) = []
      pi(uncurry_1) = [1]
      pi(uncurry_3) = [1, 2, 3]

The following rules are removed:

  p1, p2, p3

Then no dependency pair remains.