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(D(),app(minus(),x)) -> app(minus(),app(D(),x))
  app(D(),app(app(div(),x),y)) -> app(app(-(),app(app(div(),app(D(),x)),y)),app(app(div(),app(app(*(),x),app(D(),y))),app(app(pow(),y),|2|())))
  app(D(),app(ln(),x)) -> app(app(div(),app(D(),x)),x)
  app(D(),app(app(pow(),x),y)) -> app(app(+(),app(app(*(),app(app(*(),y),app(app(pow(),x),app(app(-(),y),|1|())))),app(D(),x))),app(app(*(),app(app(*(),app(app(pow(),x),y)),app(ln(),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(div_0(),y) -> div_1(y)
  app(div_1(x1),y) -> div_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(ln_0(),y) -> ln_1(y)
  app(map_0(),y) -> map_1(y)
  app(map_1(x1),y) -> map_2(x1,y)
  app(minus_0(),y) -> minus_1(y)
  app(pow_0(),y) -> pow_1(y)
  app(pow_1(x1),y) -> pow_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))
  D_1(minus_1(x)) -> minus_1(D_1(x))
  D_1(div_2(x,y)) -> -_2(div_2(D_1(x),y),div_2(*_2(x,D_1(y)),pow_2(y,|2|_0())))
  D_1(ln_1(x)) -> div_2(D_1(x),x)
  D_1(pow_2(x,y)) -> +_2(*_2(*_2(y,pow_2(x,-_2(y,|1|_0()))),D_1(x)),*_2(*_2(pow_2(x,y),ln_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: D_1#(minus_1(x)) -> D_1#(x)
p12: D_1#(div_2(x,y)) -> D_1#(x)
p13: D_1#(div_2(x,y)) -> D_1#(y)
p14: D_1#(ln_1(x)) -> D_1#(x)
p15: D_1#(pow_2(x,y)) -> D_1#(x)
p16: D_1#(pow_2(x,y)) -> D_1#(y)
p17: map_2#(f,cons_2(x,xs)) -> app#(f,x)
p18: map_2#(f,cons_2(x,xs)) -> map_2#(f,xs)
p19: filter_2#(f,cons_2(x,xs)) -> filter2_4#(app(f,x),f,x,xs)
p20: filter_2#(f,cons_2(x,xs)) -> app#(f,x)
p21: filter2_4#(true_0(),f,x,xs) -> filter_2#(f,xs)
p22: 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(div_0(),y) -> div_1(y)
r11: app(div_1(x1),y) -> div_2(x1,y)
r12: app(filter_0(),y) -> filter_1(y)
r13: app(filter_1(x1),y) -> filter_2(x1,y)
r14: app(filter2_0(),y) -> filter2_1(y)
r15: app(filter2_1(x1),y) -> filter2_2(x1,y)
r16: app(filter2_2(x1,x2),y) -> filter2_3(x1,x2,y)
r17: app(filter2_3(x1,x2,x3),y) -> filter2_4(x1,x2,x3,y)
r18: app(ln_0(),y) -> ln_1(y)
r19: app(map_0(),y) -> map_1(y)
r20: app(map_1(x1),y) -> map_2(x1,y)
r21: app(minus_0(),y) -> minus_1(y)
r22: app(pow_0(),y) -> pow_1(y)
r23: app(pow_1(x1),y) -> pow_2(x1,y)
r24: D_1(t_0()) -> |1|_0()
r25: D_1(constant_0()) -> |0|_0()
r26: D_1(+_2(x,y)) -> +_2(D_1(x),D_1(y))
r27: D_1(*_2(x,y)) -> +_2(*_2(y,D_1(x)),*_2(x,D_1(y)))
r28: D_1(-_2(x,y)) -> -_2(D_1(x),D_1(y))
r29: D_1(minus_1(x)) -> minus_1(D_1(x))
r30: D_1(div_2(x,y)) -> -_2(div_2(D_1(x),y),div_2(*_2(x,D_1(y)),pow_2(y,|2|_0())))
r31: D_1(ln_1(x)) -> div_2(D_1(x),x)
r32: D_1(pow_2(x,y)) -> +_2(*_2(*_2(y,pow_2(x,-_2(y,|1|_0()))),D_1(x)),*_2(*_2(pow_2(x,y),ln_1(x)),D_1(y)))
r33: map_2(f,nil_0()) -> nil_0()
r34: map_2(f,cons_2(x,xs)) -> cons_2(app(f,x),map_2(f,xs))
r35: filter_2(f,nil_0()) -> nil_0()
r36: filter_2(f,cons_2(x,xs)) -> filter2_4(app(f,x),f,x,xs)
r37: filter2_4(true_0(),f,x,xs) -> cons_2(x,filter_2(f,xs))
r38: filter2_4(false_0(),f,x,xs) -> filter_2(f,xs)

The estimated dependency graph contains the following SCCs:

  {p2, p3, p4, p17, p18, p19, p20, p21, p22}
  {p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15, p16}


-- 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(div_0(),y) -> div_1(y)
r11: app(div_1(x1),y) -> div_2(x1,y)
r12: app(filter_0(),y) -> filter_1(y)
r13: app(filter_1(x1),y) -> filter_2(x1,y)
r14: app(filter2_0(),y) -> filter2_1(y)
r15: app(filter2_1(x1),y) -> filter2_2(x1,y)
r16: app(filter2_2(x1,x2),y) -> filter2_3(x1,x2,y)
r17: app(filter2_3(x1,x2,x3),y) -> filter2_4(x1,x2,x3,y)
r18: app(ln_0(),y) -> ln_1(y)
r19: app(map_0(),y) -> map_1(y)
r20: app(map_1(x1),y) -> map_2(x1,y)
r21: app(minus_0(),y) -> minus_1(y)
r22: app(pow_0(),y) -> pow_1(y)
r23: app(pow_1(x1),y) -> pow_2(x1,y)
r24: D_1(t_0()) -> |1|_0()
r25: D_1(constant_0()) -> |0|_0()
r26: D_1(+_2(x,y)) -> +_2(D_1(x),D_1(y))
r27: D_1(*_2(x,y)) -> +_2(*_2(y,D_1(x)),*_2(x,D_1(y)))
r28: D_1(-_2(x,y)) -> -_2(D_1(x),D_1(y))
r29: D_1(minus_1(x)) -> minus_1(D_1(x))
r30: D_1(div_2(x,y)) -> -_2(div_2(D_1(x),y),div_2(*_2(x,D_1(y)),pow_2(y,|2|_0())))
r31: D_1(ln_1(x)) -> div_2(D_1(x),x)
r32: D_1(pow_2(x,y)) -> +_2(*_2(*_2(y,pow_2(x,-_2(y,|1|_0()))),D_1(x)),*_2(*_2(pow_2(x,y),ln_1(x)),D_1(y)))
r33: map_2(f,nil_0()) -> nil_0()
r34: map_2(f,cons_2(x,xs)) -> cons_2(app(f,x),map_2(f,xs))
r35: filter_2(f,nil_0()) -> nil_0()
r36: filter_2(f,cons_2(x,xs)) -> filter2_4(app(f,x),f,x,xs)
r37: filter2_4(true_0(),f,x,xs) -> cons_2(x,filter_2(f,xs))
r38: filter2_4(false_0(),f,x,xs) -> filter_2(f,xs)

The set of usable rules consists of

  r13, r17, r35, r36, r37, r38

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        map_2#_A(x1,x2) = max{26, x2 + 1}
        cons_2_A(x1,x2) = max{x1 + 29, x2 + 33}
        app#_A(x1,x2) = x2 + 27
        map_1_A(x1) = x1 + 31
        filter2_3_A(x1,x2,x3) = max{x1 - 33, x2 + 31, x3 + 60}
        filter2_4#_A(x1,x2,x3,x4) = max{26, x4 + 25}
        false_0_A = 63
        filter_2#_A(x1,x2) = max{26, x2 - 1}
        filter_1_A(x1) = max{4, x1 + 1}
        app_A(x1,x2) = max{x1 - 30, x2 + 98}
        true_0_A = 25
        filter_2_A(x1,x2) = x2 + 62
        filter2_4_A(x1,x2,x3,x4) = max{x3 + 30, x4 + 95}
        nil_0_A = 63
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        matrix interpretation with standard point-wise order:
        
          carrier: N^1
          order: standard order
          interpretations:
            map_2#_A(x1,x2) = x2
            cons_2_A(x1,x2) = x1 + x2 + 4
            app#_A(x1,x2) = x2
            map_1_A(x1) = x1 + 7
            filter2_3_A(x1,x2,x3) = x1 + x2 + x3
            filter2_4#_A(x1,x2,x3,x4) = x4
            false_0_A() = 1
            filter_2#_A(x1,x2) = x2
            filter_1_A(x1) = x1 + 7
            app_A(x1,x2) = x1 + x2 + 5
            true_0_A() = 1
            filter_2_A(x1,x2) = x2 + 1
            filter2_4_A(x1,x2,x3,x4) = x3 + x4 + 5
            nil_0_A() = 0
            map_2#!_A(x1,x2) = x1 + 1
            cons_2!_A(x1,x2) = x1 + x2 + 3
            app#!_A(x1,x2) = 0
            map_1!_A(x1) = 2
            filter2_3!_A(x1,x2,x3) = 24
            filter2_4#!_A(x1,x2,x3,x4) = x2 + x4 + 10
            false_0!_A() = 10
            filter_2#!_A(x1,x2) = x1 + x2 + 7
            filter_1!_A(x1) = 8
            app!_A(x1,x2) = x1 + x2 + 10
            true_0!_A() = 5
            filter_2!_A(x1,x2) = x2 + 9
            filter2_4!_A(x1,x2,x3,x4) = x3 + x4 + 9
            nil_0!_A() = 4
  
    partial status:
  
      pi(map_2#) = [2]
      pi(cons_2) = []
      pi(app#) = []
      pi(map_1) = [1]
      pi(filter2_3) = [3]
      pi(filter2_4#) = []
      pi(false_0) = []
      pi(filter_2#) = []
      pi(filter_1) = [1]
      pi(app) = [2]
      pi(true_0) = []
      pi(filter_2) = [2]
      pi(filter2_4) = [4]
      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#(pow_2(x,y)) -> D_1#(y)
p3: D_1#(pow_2(x,y)) -> D_1#(x)
p4: D_1#(ln_1(x)) -> D_1#(x)
p5: D_1#(div_2(x,y)) -> D_1#(y)
p6: D_1#(div_2(x,y)) -> D_1#(x)
p7: D_1#(minus_1(x)) -> 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: D_1#(*_2(x,y)) -> D_1#(x)
p12: 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(div_0(),y) -> div_1(y)
r11: app(div_1(x1),y) -> div_2(x1,y)
r12: app(filter_0(),y) -> filter_1(y)
r13: app(filter_1(x1),y) -> filter_2(x1,y)
r14: app(filter2_0(),y) -> filter2_1(y)
r15: app(filter2_1(x1),y) -> filter2_2(x1,y)
r16: app(filter2_2(x1,x2),y) -> filter2_3(x1,x2,y)
r17: app(filter2_3(x1,x2,x3),y) -> filter2_4(x1,x2,x3,y)
r18: app(ln_0(),y) -> ln_1(y)
r19: app(map_0(),y) -> map_1(y)
r20: app(map_1(x1),y) -> map_2(x1,y)
r21: app(minus_0(),y) -> minus_1(y)
r22: app(pow_0(),y) -> pow_1(y)
r23: app(pow_1(x1),y) -> pow_2(x1,y)
r24: D_1(t_0()) -> |1|_0()
r25: D_1(constant_0()) -> |0|_0()
r26: D_1(+_2(x,y)) -> +_2(D_1(x),D_1(y))
r27: D_1(*_2(x,y)) -> +_2(*_2(y,D_1(x)),*_2(x,D_1(y)))
r28: D_1(-_2(x,y)) -> -_2(D_1(x),D_1(y))
r29: D_1(minus_1(x)) -> minus_1(D_1(x))
r30: D_1(div_2(x,y)) -> -_2(div_2(D_1(x),y),div_2(*_2(x,D_1(y)),pow_2(y,|2|_0())))
r31: D_1(ln_1(x)) -> div_2(D_1(x),x)
r32: D_1(pow_2(x,y)) -> +_2(*_2(*_2(y,pow_2(x,-_2(y,|1|_0()))),D_1(x)),*_2(*_2(pow_2(x,y),ln_1(x)),D_1(y)))
r33: map_2(f,nil_0()) -> nil_0()
r34: map_2(f,cons_2(x,xs)) -> cons_2(app(f,x),map_2(f,xs))
r35: filter_2(f,nil_0()) -> nil_0()
r36: filter_2(f,cons_2(x,xs)) -> filter2_4(app(f,x),f,x,xs)
r37: filter2_4(true_0(),f,x,xs) -> cons_2(x,filter_2(f,xs))
r38: filter2_4(false_0(),f,x,xs) -> filter_2(f,xs)

The set of usable rules consists of

  r35

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        D_1#_A(x1) = 0
        +_2_A(x1,x2) = max{18, x1 - 17}
        pow_2_A(x1,x2) = max{5, x1 - 55, x2 - 55}
        ln_1_A(x1) = max{6, x1 - 72}
        div_2_A(x1,x2) = max{x1 + 37, x2 + 4}
        minus_1_A(x1) = max{73, x1 - 20}
        -_2_A(x1,x2) = max{0, x1 - 17, x2 - 92}
        *_2_A(x1,x2) = x2 + 17
        filter_2_A(x1,x2) = max{7, x1 - 1}
        nil_0_A = 2
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        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 + 5
            pow_2_A(x1,x2) = x1 + x2 + 5
            ln_1_A(x1) = x1 + 3
            div_2_A(x1,x2) = x1 + x2 + 5
            minus_1_A(x1) = x1 + 3
            -_2_A(x1,x2) = x1 + x2 + 5
            *_2_A(x1,x2) = x1 + x2 + 5
            filter_2_A(x1,x2) = x2 + 10
            nil_0_A() = 6
            D_1#!_A(x1) = x1 + 12
            +_2!_A(x1,x2) = 14
            pow_2!_A(x1,x2) = x2 + 13
            ln_1!_A(x1) = 18
            div_2!_A(x1,x2) = x1 + 19
            minus_1!_A(x1) = 19
            -_2!_A(x1,x2) = x1 + 14
            *_2!_A(x1,x2) = x1 + 15
            filter_2!_A(x1,x2) = x2 + 14
            nil_0!_A() = 0
  
    partial status:
  
      pi(D_1#) = []
      pi(+_2) = []
      pi(pow_2) = []
      pi(ln_1) = []
      pi(div_2) = [1, 2]
      pi(minus_1) = []
      pi(-_2) = []
      pi(*_2) = [2]
      pi(filter_2) = []
      pi(nil_0) = []

The following rules are removed:

  p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12

Then no dependency pair remains.