YES
We show the termination of the TRS R:

  app(D(),t()) -> |1|()
  app(D(),constant()) -> |0|()
  app(D(),app(app(+(),x),y)) -> app(app(+(),app(D(),x)),app(D(),y))
  app(D(),app(app(*(),x),y)) -> app(app(+(),app(app(*(),y),app(D(),x))),app(app(*(),x),app(D(),y)))
  app(D(),app(app(-(),x),y)) -> app(app(-(),app(D(),x)),app(D(),y))
  app(app(map(),f),nil()) -> nil()
  app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
  app(app(filter(),f),nil()) -> nil()
  app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
  app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
  app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)

Instead we prove termination of the uncurried system:

  app(*_0(),y) -> *_1(y)
  app(*_1(x1),y) -> *_2(x1,y)
  app(+_0(),y) -> +_1(y)
  app(+_1(x1),y) -> +_2(x1,y)
  app(-_0(),y) -> -_1(y)
  app(-_1(x1),y) -> -_2(x1,y)
  app(D_0(),y) -> D_1(y)
  app(cons_0(),y) -> cons_1(y)
  app(cons_1(x1),y) -> cons_2(x1,y)
  app(filter_0(),y) -> filter_1(y)
  app(filter_1(x1),y) -> filter_2(x1,y)
  app(filter2_0(),y) -> filter2_1(y)
  app(filter2_1(x1),y) -> filter2_2(x1,y)
  app(filter2_2(x1,x2),y) -> filter2_3(x1,x2,y)
  app(filter2_3(x1,x2,x3),y) -> filter2_4(x1,x2,x3,y)
  app(map_0(),y) -> map_1(y)
  app(map_1(x1),y) -> map_2(x1,y)
  D_1(t_0()) -> |1|_0()
  D_1(constant_0()) -> |0|_0()
  D_1(+_2(x,y)) -> +_2(D_1(x),D_1(y))
  D_1(*_2(x,y)) -> +_2(*_2(y,D_1(x)),*_2(x,D_1(y)))
  D_1(-_2(x,y)) -> -_2(D_1(x),D_1(y))
  map_2(f,nil_0()) -> nil_0()
  map_2(f,cons_2(x,xs)) -> cons_2(app(f,x),map_2(f,xs))
  filter_2(f,nil_0()) -> nil_0()
  filter_2(f,cons_2(x,xs)) -> filter2_4(app(f,x),f,x,xs)
  filter2_4(true_0(),f,x,xs) -> cons_2(x,filter_2(f,xs))
  filter2_4(false_0(),f,x,xs) -> filter_2(f,xs)


-- SCC decomposition.

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

p1: app#(D_0(),y) -> D_1#(y)
p2: app#(filter_1(x1),y) -> filter_2#(x1,y)
p3: app#(filter2_3(x1,x2,x3),y) -> filter2_4#(x1,x2,x3,y)
p4: app#(map_1(x1),y) -> map_2#(x1,y)
p5: D_1#(+_2(x,y)) -> D_1#(x)
p6: D_1#(+_2(x,y)) -> D_1#(y)
p7: D_1#(*_2(x,y)) -> D_1#(x)
p8: D_1#(*_2(x,y)) -> D_1#(y)
p9: D_1#(-_2(x,y)) -> D_1#(x)
p10: D_1#(-_2(x,y)) -> D_1#(y)
p11: map_2#(f,cons_2(x,xs)) -> app#(f,x)
p12: map_2#(f,cons_2(x,xs)) -> map_2#(f,xs)
p13: filter_2#(f,cons_2(x,xs)) -> filter2_4#(app(f,x),f,x,xs)
p14: filter_2#(f,cons_2(x,xs)) -> app#(f,x)
p15: filter2_4#(true_0(),f,x,xs) -> filter_2#(f,xs)
p16: filter2_4#(false_0(),f,x,xs) -> filter_2#(f,xs)

and R consists of:

r1: app(*_0(),y) -> *_1(y)
r2: app(*_1(x1),y) -> *_2(x1,y)
r3: app(+_0(),y) -> +_1(y)
r4: app(+_1(x1),y) -> +_2(x1,y)
r5: app(-_0(),y) -> -_1(y)
r6: app(-_1(x1),y) -> -_2(x1,y)
r7: app(D_0(),y) -> D_1(y)
r8: app(cons_0(),y) -> cons_1(y)
r9: app(cons_1(x1),y) -> cons_2(x1,y)
r10: app(filter_0(),y) -> filter_1(y)
r11: app(filter_1(x1),y) -> filter_2(x1,y)
r12: app(filter2_0(),y) -> filter2_1(y)
r13: app(filter2_1(x1),y) -> filter2_2(x1,y)
r14: app(filter2_2(x1,x2),y) -> filter2_3(x1,x2,y)
r15: app(filter2_3(x1,x2,x3),y) -> filter2_4(x1,x2,x3,y)
r16: app(map_0(),y) -> map_1(y)
r17: app(map_1(x1),y) -> map_2(x1,y)
r18: D_1(t_0()) -> |1|_0()
r19: D_1(constant_0()) -> |0|_0()
r20: D_1(+_2(x,y)) -> +_2(D_1(x),D_1(y))
r21: D_1(*_2(x,y)) -> +_2(*_2(y,D_1(x)),*_2(x,D_1(y)))
r22: D_1(-_2(x,y)) -> -_2(D_1(x),D_1(y))
r23: map_2(f,nil_0()) -> nil_0()
r24: map_2(f,cons_2(x,xs)) -> cons_2(app(f,x),map_2(f,xs))
r25: filter_2(f,nil_0()) -> nil_0()
r26: filter_2(f,cons_2(x,xs)) -> filter2_4(app(f,x),f,x,xs)
r27: filter2_4(true_0(),f,x,xs) -> cons_2(x,filter_2(f,xs))
r28: filter2_4(false_0(),f,x,xs) -> filter_2(f,xs)

The estimated dependency graph contains the following SCCs:

  {p2, p3, p4, p11, p12, p13, p14, p15, p16}
  {p5, p6, p7, p8, p9, p10}


-- Reduction pair.

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

p1: map_2#(f,cons_2(x,xs)) -> app#(f,x)
p2: app#(map_1(x1),y) -> map_2#(x1,y)
p3: map_2#(f,cons_2(x,xs)) -> map_2#(f,xs)
p4: app#(filter2_3(x1,x2,x3),y) -> filter2_4#(x1,x2,x3,y)
p5: filter2_4#(false_0(),f,x,xs) -> filter_2#(f,xs)
p6: filter_2#(f,cons_2(x,xs)) -> app#(f,x)
p7: app#(filter_1(x1),y) -> filter_2#(x1,y)
p8: filter_2#(f,cons_2(x,xs)) -> filter2_4#(app(f,x),f,x,xs)
p9: filter2_4#(true_0(),f,x,xs) -> filter_2#(f,xs)

and R consists of:

r1: app(*_0(),y) -> *_1(y)
r2: app(*_1(x1),y) -> *_2(x1,y)
r3: app(+_0(),y) -> +_1(y)
r4: app(+_1(x1),y) -> +_2(x1,y)
r5: app(-_0(),y) -> -_1(y)
r6: app(-_1(x1),y) -> -_2(x1,y)
r7: app(D_0(),y) -> D_1(y)
r8: app(cons_0(),y) -> cons_1(y)
r9: app(cons_1(x1),y) -> cons_2(x1,y)
r10: app(filter_0(),y) -> filter_1(y)
r11: app(filter_1(x1),y) -> filter_2(x1,y)
r12: app(filter2_0(),y) -> filter2_1(y)
r13: app(filter2_1(x1),y) -> filter2_2(x1,y)
r14: app(filter2_2(x1,x2),y) -> filter2_3(x1,x2,y)
r15: app(filter2_3(x1,x2,x3),y) -> filter2_4(x1,x2,x3,y)
r16: app(map_0(),y) -> map_1(y)
r17: app(map_1(x1),y) -> map_2(x1,y)
r18: D_1(t_0()) -> |1|_0()
r19: D_1(constant_0()) -> |0|_0()
r20: D_1(+_2(x,y)) -> +_2(D_1(x),D_1(y))
r21: D_1(*_2(x,y)) -> +_2(*_2(y,D_1(x)),*_2(x,D_1(y)))
r22: D_1(-_2(x,y)) -> -_2(D_1(x),D_1(y))
r23: map_2(f,nil_0()) -> nil_0()
r24: map_2(f,cons_2(x,xs)) -> cons_2(app(f,x),map_2(f,xs))
r25: filter_2(f,nil_0()) -> nil_0()
r26: filter_2(f,cons_2(x,xs)) -> filter2_4(app(f,x),f,x,xs)
r27: filter2_4(true_0(),f,x,xs) -> cons_2(x,filter_2(f,xs))
r28: filter2_4(false_0(),f,x,xs) -> filter_2(f,xs)

The set of usable rules consists of

  r1, r2, r3, r5, r14, r25

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          map_2#_A(x1,x2) = x2 + 3
          cons_2_A(x1,x2) = x1 + x2 + 6
          app#_A(x1,x2) = x2 + 8
          map_1_A(x1) = 4
          filter2_3_A(x1,x2,x3) = x3 + 1
          filter2_4#_A(x1,x2,x3,x4) = x4 + 7
          false_0_A() = 4
          filter_2#_A(x1,x2) = x2 + 5
          filter_1_A(x1) = x1 + 4
          app_A(x1,x2) = x2 + 5
          true_0_A() = 10
          *_0_A() = 1
          *_1_A(x1) = x1 + 4
          *_2_A(x1,x2) = 3
          +_0_A() = 3
          +_1_A(x1) = x1 + 2
          -_0_A() = 5
          -_1_A(x1) = x1 + 4
          filter2_2_A(x1,x2) = x1 + x2 + 3
          filter_2_A(x1,x2) = x1 + 3
          nil_0_A() = 1
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        max/plus interpretation on natural numbers:
        
          map_2#_A(x1,x2) = max{2, x1 - 12, x2 - 29}
          cons_2_A(x1,x2) = max{x1 + 28, x2}
          app#_A(x1,x2) = max{2, x1 - 20, x2 - 1}
          map_1_A(x1) = max{19, x1 + 8}
          filter2_3_A(x1,x2,x3) = max{x1 - 31, x2 + 1, x3 + 7}
          filter2_4#_A(x1,x2,x3,x4) = max{2, x2 - 19, x3 - 13, x4 - 27}
          false_0_A = 9
          filter_2#_A(x1,x2) = max{2, x1 - 19, x2 - 27}
          filter_1_A(x1) = max{10, x1 + 1}
          app_A(x1,x2) = max{9, x1 - 30, x2 + 7}
          true_0_A = 9
          *_0_A = 2
          *_1_A(x1) = max{2, x1 - 1}
          *_2_A(x1,x2) = max{8, x2 - 11}
          +_0_A = 0
          +_1_A(x1) = max{2, x1 - 11}
          -_0_A = 2
          -_1_A(x1) = x1 + 4
          filter2_2_A(x1,x2) = max{x1 - 1, x2 + 31}
          filter_2_A(x1,x2) = max{11, x1 - 41, x2 + 10}
          nil_0_A = 12
          map_2#!_A(x1,x2) = max{13, x2 - 29}
          cons_2!_A(x1,x2) = max{14, x2 + 1}
          app#!_A(x1,x2) = x1 + 32
          map_1!_A(x1) = max{12, x1 + 1}
          filter2_3!_A(x1,x2,x3) = max{1, x1 - 11, x2 - 1}
          filter2_4#!_A(x1,x2,x3,x4) = x3
          false_0!_A = 1
          filter_2#!_A(x1,x2) = max{43, x2 + 16}
          filter_1!_A(x1) = max{46, x1 + 18}
          app!_A(x1,x2) = max{45, x1 - 3, x2 - 6}
          true_0!_A = 13
          *_0!_A = 1
          *_1!_A(x1) = max{47, x1 - 5}
          *_2!_A(x1,x2) = max{46, x1 - 5}
          +_0!_A = 1
          +_1!_A(x1) = max{0, x1 - 14}
          -_0!_A = 1
          -_1!_A(x1) = max{2, x1 - 26}
          filter2_2!_A(x1,x2) = 47
          filter_2!_A(x1,x2) = max{x1 + 17, x2 - 13}
          nil_0!_A = 16
  
    partial status:
  
      pi(map_2#) = [2]
      pi(cons_2) = [2]
      pi(app#) = [2]
      pi(map_1) = []
      pi(filter2_3) = []
      pi(filter2_4#) = []
      pi(false_0) = []
      pi(filter_2#) = []
      pi(filter_1) = [1]
      pi(app) = [2]
      pi(true_0) = []
      pi(*_0) = []
      pi(*_1) = [1]
      pi(*_2) = []
      pi(+_0) = []
      pi(+_1) = [1]
      pi(-_0) = []
      pi(-_1) = [1]
      pi(filter2_2) = [1, 2]
      pi(filter_2) = []
      pi(nil_0) = []

The following rules are removed:

  p1, p2, p3, p4, p5, p6, p7, p8, p9

Then no dependency pair remains.

-- Reduction pair.

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

p1: D_1#(+_2(x,y)) -> D_1#(x)
p2: D_1#(-_2(x,y)) -> D_1#(y)
p3: D_1#(-_2(x,y)) -> D_1#(x)
p4: D_1#(*_2(x,y)) -> D_1#(y)
p5: D_1#(*_2(x,y)) -> D_1#(x)
p6: D_1#(+_2(x,y)) -> D_1#(y)

and R consists of:

r1: app(*_0(),y) -> *_1(y)
r2: app(*_1(x1),y) -> *_2(x1,y)
r3: app(+_0(),y) -> +_1(y)
r4: app(+_1(x1),y) -> +_2(x1,y)
r5: app(-_0(),y) -> -_1(y)
r6: app(-_1(x1),y) -> -_2(x1,y)
r7: app(D_0(),y) -> D_1(y)
r8: app(cons_0(),y) -> cons_1(y)
r9: app(cons_1(x1),y) -> cons_2(x1,y)
r10: app(filter_0(),y) -> filter_1(y)
r11: app(filter_1(x1),y) -> filter_2(x1,y)
r12: app(filter2_0(),y) -> filter2_1(y)
r13: app(filter2_1(x1),y) -> filter2_2(x1,y)
r14: app(filter2_2(x1,x2),y) -> filter2_3(x1,x2,y)
r15: app(filter2_3(x1,x2,x3),y) -> filter2_4(x1,x2,x3,y)
r16: app(map_0(),y) -> map_1(y)
r17: app(map_1(x1),y) -> map_2(x1,y)
r18: D_1(t_0()) -> |1|_0()
r19: D_1(constant_0()) -> |0|_0()
r20: D_1(+_2(x,y)) -> +_2(D_1(x),D_1(y))
r21: D_1(*_2(x,y)) -> +_2(*_2(y,D_1(x)),*_2(x,D_1(y)))
r22: D_1(-_2(x,y)) -> -_2(D_1(x),D_1(y))
r23: map_2(f,nil_0()) -> nil_0()
r24: map_2(f,cons_2(x,xs)) -> cons_2(app(f,x),map_2(f,xs))
r25: filter_2(f,nil_0()) -> nil_0()
r26: filter_2(f,cons_2(x,xs)) -> filter2_4(app(f,x),f,x,xs)
r27: filter2_4(true_0(),f,x,xs) -> cons_2(x,filter_2(f,xs))
r28: filter2_4(false_0(),f,x,xs) -> filter_2(f,xs)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          D_1#_A(x1) = x1
          +_2_A(x1,x2) = x1 + x2 + 10
          -_2_A(x1,x2) = x1 + x2 + 7
          *_2_A(x1,x2) = x1 + x2 + 10
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        max/plus interpretation on natural numbers:
        
          D_1#_A(x1) = max{0, x1 - 45}
          +_2_A(x1,x2) = max{41, x1 + 4, x2 + 6}
          -_2_A(x1,x2) = max{x1 + 41, x2 + 44}
          *_2_A(x1,x2) = max{44, x1 + 1, x2 + 41}
          D_1#!_A(x1) = max{1, x1 - 42}
          +_2!_A(x1,x2) = max{26, x1 + 7, x2 - 49}
          -_2!_A(x1,x2) = max{28, x1 - 23, x2 - 42}
          *_2!_A(x1,x2) = max{9, x1 - 42, x2 - 42}
  
    partial status:
  
      pi(D_1#) = []
      pi(+_2) = [2]
      pi(-_2) = [2]
      pi(*_2) = [1]

The following rules are removed:

  p1, p2, p3, p4, p5, p6

Then no dependency pair remains.