YES
We show the termination of the TRS R:

  app(rev(),nil()) -> nil()
  app(rev(),app(app(cons(),x),l)) -> app(app(cons(),app(app(rev1(),x),l)),app(app(rev2(),x),l))
  app(app(rev1(),|0|()),nil()) -> |0|()
  app(app(rev1(),app(s(),x)),nil()) -> app(s(),x)
  app(app(rev1(),x),app(app(cons(),y),l)) -> app(app(rev1(),y),l)
  app(app(rev2(),x),nil()) -> nil()
  app(app(rev2(),x),app(app(cons(),y),l)) -> app(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
  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(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)
  app(rev_0(),y) -> rev_1(y)
  app(rev1_0(),y) -> rev1_1(y)
  app(rev1_1(x1),y) -> rev1_2(x1,y)
  app(rev2_0(),y) -> rev2_1(y)
  app(rev2_1(x1),y) -> rev2_2(x1,y)
  app(s_0(),y) -> s_1(y)
  rev_1(nil_0()) -> nil_0()
  rev_1(cons_2(x,l)) -> cons_2(rev1_2(x,l),rev2_2(x,l))
  rev1_2(|0|_0(),nil_0()) -> |0|_0()
  rev1_2(s_1(x),nil_0()) -> s_1(x)
  rev1_2(x,cons_2(y,l)) -> rev1_2(y,l)
  rev2_2(x,nil_0()) -> nil_0()
  rev2_2(x,cons_2(y,l)) -> rev_1(cons_2(x,rev2_2(y,l)))
  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#(filter_1(x1),y) -> filter_2#(x1,y)
p2: app#(filter2_3(x1,x2,x3),y) -> filter2_4#(x1,x2,x3,y)
p3: app#(map_1(x1),y) -> map_2#(x1,y)
p4: app#(rev_0(),y) -> rev_1#(y)
p5: app#(rev1_1(x1),y) -> rev1_2#(x1,y)
p6: app#(rev2_1(x1),y) -> rev2_2#(x1,y)
p7: rev_1#(cons_2(x,l)) -> rev1_2#(x,l)
p8: rev_1#(cons_2(x,l)) -> rev2_2#(x,l)
p9: rev1_2#(x,cons_2(y,l)) -> rev1_2#(y,l)
p10: rev2_2#(x,cons_2(y,l)) -> rev_1#(cons_2(x,rev2_2(y,l)))
p11: rev2_2#(x,cons_2(y,l)) -> rev2_2#(y,l)
p12: map_2#(f,cons_2(x,xs)) -> app#(f,x)
p13: map_2#(f,cons_2(x,xs)) -> map_2#(f,xs)
p14: filter_2#(f,cons_2(x,xs)) -> filter2_4#(app(f,x),f,x,xs)
p15: filter_2#(f,cons_2(x,xs)) -> app#(f,x)
p16: filter2_4#(true_0(),f,x,xs) -> filter_2#(f,xs)
p17: filter2_4#(false_0(),f,x,xs) -> filter_2#(f,xs)

and R consists of:

r1: app(cons_0(),y) -> cons_1(y)
r2: app(cons_1(x1),y) -> cons_2(x1,y)
r3: app(filter_0(),y) -> filter_1(y)
r4: app(filter_1(x1),y) -> filter_2(x1,y)
r5: app(filter2_0(),y) -> filter2_1(y)
r6: app(filter2_1(x1),y) -> filter2_2(x1,y)
r7: app(filter2_2(x1,x2),y) -> filter2_3(x1,x2,y)
r8: app(filter2_3(x1,x2,x3),y) -> filter2_4(x1,x2,x3,y)
r9: app(map_0(),y) -> map_1(y)
r10: app(map_1(x1),y) -> map_2(x1,y)
r11: app(rev_0(),y) -> rev_1(y)
r12: app(rev1_0(),y) -> rev1_1(y)
r13: app(rev1_1(x1),y) -> rev1_2(x1,y)
r14: app(rev2_0(),y) -> rev2_1(y)
r15: app(rev2_1(x1),y) -> rev2_2(x1,y)
r16: app(s_0(),y) -> s_1(y)
r17: rev_1(nil_0()) -> nil_0()
r18: rev_1(cons_2(x,l)) -> cons_2(rev1_2(x,l),rev2_2(x,l))
r19: rev1_2(|0|_0(),nil_0()) -> |0|_0()
r20: rev1_2(s_1(x),nil_0()) -> s_1(x)
r21: rev1_2(x,cons_2(y,l)) -> rev1_2(y,l)
r22: rev2_2(x,nil_0()) -> nil_0()
r23: rev2_2(x,cons_2(y,l)) -> rev_1(cons_2(x,rev2_2(y,l)))
r24: map_2(f,nil_0()) -> nil_0()
r25: map_2(f,cons_2(x,xs)) -> cons_2(app(f,x),map_2(f,xs))
r26: filter_2(f,nil_0()) -> nil_0()
r27: filter_2(f,cons_2(x,xs)) -> filter2_4(app(f,x),f,x,xs)
r28: filter2_4(true_0(),f,x,xs) -> cons_2(x,filter_2(f,xs))
r29: filter2_4(false_0(),f,x,xs) -> filter_2(f,xs)

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3, p12, p13, p14, p15, p16, p17}
  {p8, p10, p11}
  {p9}


-- Reduction pair.

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

p1: app#(filter_1(x1),y) -> filter_2#(x1,y)
p2: filter_2#(f,cons_2(x,xs)) -> app#(f,x)
p3: app#(map_1(x1),y) -> map_2#(x1,y)
p4: map_2#(f,cons_2(x,xs)) -> map_2#(f,xs)
p5: map_2#(f,cons_2(x,xs)) -> app#(f,x)
p6: app#(filter2_3(x1,x2,x3),y) -> filter2_4#(x1,x2,x3,y)
p7: filter2_4#(false_0(),f,x,xs) -> filter_2#(f,xs)
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(cons_0(),y) -> cons_1(y)
r2: app(cons_1(x1),y) -> cons_2(x1,y)
r3: app(filter_0(),y) -> filter_1(y)
r4: app(filter_1(x1),y) -> filter_2(x1,y)
r5: app(filter2_0(),y) -> filter2_1(y)
r6: app(filter2_1(x1),y) -> filter2_2(x1,y)
r7: app(filter2_2(x1,x2),y) -> filter2_3(x1,x2,y)
r8: app(filter2_3(x1,x2,x3),y) -> filter2_4(x1,x2,x3,y)
r9: app(map_0(),y) -> map_1(y)
r10: app(map_1(x1),y) -> map_2(x1,y)
r11: app(rev_0(),y) -> rev_1(y)
r12: app(rev1_0(),y) -> rev1_1(y)
r13: app(rev1_1(x1),y) -> rev1_2(x1,y)
r14: app(rev2_0(),y) -> rev2_1(y)
r15: app(rev2_1(x1),y) -> rev2_2(x1,y)
r16: app(s_0(),y) -> s_1(y)
r17: rev_1(nil_0()) -> nil_0()
r18: rev_1(cons_2(x,l)) -> cons_2(rev1_2(x,l),rev2_2(x,l))
r19: rev1_2(|0|_0(),nil_0()) -> |0|_0()
r20: rev1_2(s_1(x),nil_0()) -> s_1(x)
r21: rev1_2(x,cons_2(y,l)) -> rev1_2(y,l)
r22: rev2_2(x,nil_0()) -> nil_0()
r23: rev2_2(x,cons_2(y,l)) -> rev_1(cons_2(x,rev2_2(y,l)))
r24: map_2(f,nil_0()) -> nil_0()
r25: map_2(f,cons_2(x,xs)) -> cons_2(app(f,x),map_2(f,xs))
r26: filter_2(f,nil_0()) -> nil_0()
r27: filter_2(f,cons_2(x,xs)) -> filter2_4(app(f,x),f,x,xs)
r28: filter2_4(true_0(),f,x,xs) -> cons_2(x,filter_2(f,xs))
r29: filter2_4(false_0(),f,x,xs) -> filter_2(f,xs)

The set of usable rules consists of

  r5, r6, r12, r14, r17, r19, r20, r26

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        app#_A(x1,x2) = max{43, x1 + 33, x2 + 35}
        filter_1_A(x1) = max{16, x1 + 2}
        filter_2#_A(x1,x2) = max{34, x1 + 33, x2 + 24}
        cons_2_A(x1,x2) = max{19, x1 + 13, x2 + 14}
        map_1_A(x1) = max{21, x1 + 12}
        map_2#_A(x1,x2) = max{x1 + 44, x2 + 23}
        filter2_3_A(x1,x2,x3) = max{x1 - 48, x2, x3 - 14}
        filter2_4#_A(x1,x2,x3,x4) = max{43, x2 + 33, x3 + 14, x4 + 33}
        false_0_A = 15
        app_A(x1,x2) = max{32, x1 + 14, x2 + 13}
        true_0_A = 15
        filter2_0_A = 12
        filter2_1_A(x1) = max{11, x1 - 48}
        filter2_2_A(x1,x2) = max{12, x1 - 47, x2 - 15}
        rev1_0_A = 1
        rev1_1_A(x1) = max{16, x1 - 1}
        rev2_0_A = 34
        rev2_1_A(x1) = max{33, x1 - 15}
        rev_1_A(x1) = max{33, x1}
        nil_0_A = 4
        rev1_2_A(x1,x2) = max{2, x1, x2}
        |0|_0_A = 3
        s_1_A(x1) = 33
        filter_2_A(x1,x2) = max{31, x1 - 34, x2 - 16}
  
    base order 2:
  
      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 + x2
            filter_1_A(x1) = x1 + 3
            filter_2#_A(x1,x2) = x1 + x2
            cons_2_A(x1,x2) = x1 + x2 + 6
            map_1_A(x1) = x1 + 2
            map_2#_A(x1,x2) = x1 + x2
            filter2_3_A(x1,x2,x3) = x1 + x2 + x3
            filter2_4#_A(x1,x2,x3,x4) = x2 + x4
            false_0_A() = 1
            app_A(x1,x2) = x1 + x2 + 1
            true_0_A() = 1
            filter2_0_A() = 1
            filter2_1_A(x1) = x1
            filter2_2_A(x1,x2) = x1 + x2
            rev1_0_A() = 0
            rev1_1_A(x1) = x1
            rev2_0_A() = 0
            rev2_1_A(x1) = 0
            rev_1_A(x1) = 2
            nil_0_A() = 0
            rev1_2_A(x1,x2) = x1 + x2 + 2
            |0|_0_A() = 1
            s_1_A(x1) = x1 + 2
            filter_2_A(x1,x2) = x1
            app#!_A(x1,x2) = x2 + 4
            filter_1!_A(x1) = 0
            filter_2#!_A(x1,x2) = x2 + 1
            cons_2!_A(x1,x2) = x2 + 3
            map_1!_A(x1) = 5
            map_2#!_A(x1,x2) = x2 + 6
            filter2_3!_A(x1,x2,x3) = x1 + x2 + x3 + 12
            filter2_4#!_A(x1,x2,x3,x4) = x4 + 2
            false_0!_A() = 11
            app!_A(x1,x2) = 6
            true_0!_A() = 2
            filter2_0!_A() = 0
            filter2_1!_A(x1) = 1
            filter2_2!_A(x1,x2) = 2
            rev1_0!_A() = 8
            rev1_1!_A(x1) = 7
            rev2_0!_A() = 9
            rev2_1!_A(x1) = 8
            rev_1!_A(x1) = 8
            nil_0!_A() = 9
            rev1_2!_A(x1,x2) = 2
            |0|_0!_A() = 0
            s_1!_A(x1) = 10
            filter_2!_A(x1,x2) = x2 + 10
  
    partial status:
  
      pi(app#) = []
      pi(filter_1) = []
      pi(filter_2#) = [1]
      pi(cons_2) = [2]
      pi(map_1) = []
      pi(map_2#) = [1, 2]
      pi(filter2_3) = [2]
      pi(filter2_4#) = [2, 4]
      pi(false_0) = []
      pi(app) = [2]
      pi(true_0) = []
      pi(filter2_0) = []
      pi(filter2_1) = []
      pi(filter2_2) = []
      pi(rev1_0) = []
      pi(rev1_1) = []
      pi(rev2_0) = []
      pi(rev2_1) = []
      pi(rev_1) = [1]
      pi(nil_0) = []
      pi(rev1_2) = [1, 2]
      pi(|0|_0) = []
      pi(s_1) = []
      pi(filter_2) = []

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: rev2_2#(x,cons_2(y,l)) -> rev_1#(cons_2(x,rev2_2(y,l)))
p2: rev_1#(cons_2(x,l)) -> rev2_2#(x,l)
p3: rev2_2#(x,cons_2(y,l)) -> rev2_2#(y,l)

and R consists of:

r1: app(cons_0(),y) -> cons_1(y)
r2: app(cons_1(x1),y) -> cons_2(x1,y)
r3: app(filter_0(),y) -> filter_1(y)
r4: app(filter_1(x1),y) -> filter_2(x1,y)
r5: app(filter2_0(),y) -> filter2_1(y)
r6: app(filter2_1(x1),y) -> filter2_2(x1,y)
r7: app(filter2_2(x1,x2),y) -> filter2_3(x1,x2,y)
r8: app(filter2_3(x1,x2,x3),y) -> filter2_4(x1,x2,x3,y)
r9: app(map_0(),y) -> map_1(y)
r10: app(map_1(x1),y) -> map_2(x1,y)
r11: app(rev_0(),y) -> rev_1(y)
r12: app(rev1_0(),y) -> rev1_1(y)
r13: app(rev1_1(x1),y) -> rev1_2(x1,y)
r14: app(rev2_0(),y) -> rev2_1(y)
r15: app(rev2_1(x1),y) -> rev2_2(x1,y)
r16: app(s_0(),y) -> s_1(y)
r17: rev_1(nil_0()) -> nil_0()
r18: rev_1(cons_2(x,l)) -> cons_2(rev1_2(x,l),rev2_2(x,l))
r19: rev1_2(|0|_0(),nil_0()) -> |0|_0()
r20: rev1_2(s_1(x),nil_0()) -> s_1(x)
r21: rev1_2(x,cons_2(y,l)) -> rev1_2(y,l)
r22: rev2_2(x,nil_0()) -> nil_0()
r23: rev2_2(x,cons_2(y,l)) -> rev_1(cons_2(x,rev2_2(y,l)))
r24: map_2(f,nil_0()) -> nil_0()
r25: map_2(f,cons_2(x,xs)) -> cons_2(app(f,x),map_2(f,xs))
r26: filter_2(f,nil_0()) -> nil_0()
r27: filter_2(f,cons_2(x,xs)) -> filter2_4(app(f,x),f,x,xs)
r28: filter2_4(true_0(),f,x,xs) -> cons_2(x,filter_2(f,xs))
r29: filter2_4(false_0(),f,x,xs) -> filter_2(f,xs)

The set of usable rules consists of

  r16, r17, r18, r19, r20, r21, r22, r23

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        rev2_2#_A(x1,x2) = max{20, x2 + 3}
        cons_2_A(x1,x2) = max{43, x2 + 19}
        rev_1#_A(x1) = max{23, x1 + 2}
        rev2_2_A(x1,x2) = max{21, x2}
        app_A(x1,x2) = max{x1 - 7, x2 + 6}
        s_0_A = 31
        s_1_A(x1) = 23
        rev_1_A(x1) = max{43, x1}
        nil_0_A = 22
        rev1_2_A(x1,x2) = max{24, x2 + 6}
        |0|_0_A = 27
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        matrix interpretation with standard point-wise order:
        
          carrier: N^1
          order: standard order
          interpretations:
            rev2_2#_A(x1,x2) = 0
            cons_2_A(x1,x2) = x1
            rev_1#_A(x1) = 0
            rev2_2_A(x1,x2) = x2 + 2
            app_A(x1,x2) = 2
            s_0_A() = 1
            s_1_A(x1) = 0
            rev_1_A(x1) = 2
            nil_0_A() = 1
            rev1_2_A(x1,x2) = 1
            |0|_0_A() = 0
            rev2_2#!_A(x1,x2) = 1
            cons_2!_A(x1,x2) = 2
            rev_1#!_A(x1) = 0
            rev2_2!_A(x1,x2) = x1 + x2 + 10
            app!_A(x1,x2) = 8
            s_0!_A() = 8
            s_1!_A(x1) = 7
            rev_1!_A(x1) = 3
            nil_0!_A() = 6
            rev1_2!_A(x1,x2) = x1 + x2 + 7
            |0|_0!_A() = 7
  
    partial status:
  
      pi(rev2_2#) = []
      pi(cons_2) = []
      pi(rev_1#) = [1]
      pi(rev2_2) = [2]
      pi(app) = []
      pi(s_0) = []
      pi(s_1) = []
      pi(rev_1) = []
      pi(nil_0) = []
      pi(rev1_2) = []
      pi(|0|_0) = []

The following rules are removed:

  p1, p2, p3

Then no dependency pair remains.

-- Reduction pair.

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

p1: rev1_2#(x,cons_2(y,l)) -> rev1_2#(y,l)

and R consists of:

r1: app(cons_0(),y) -> cons_1(y)
r2: app(cons_1(x1),y) -> cons_2(x1,y)
r3: app(filter_0(),y) -> filter_1(y)
r4: app(filter_1(x1),y) -> filter_2(x1,y)
r5: app(filter2_0(),y) -> filter2_1(y)
r6: app(filter2_1(x1),y) -> filter2_2(x1,y)
r7: app(filter2_2(x1,x2),y) -> filter2_3(x1,x2,y)
r8: app(filter2_3(x1,x2,x3),y) -> filter2_4(x1,x2,x3,y)
r9: app(map_0(),y) -> map_1(y)
r10: app(map_1(x1),y) -> map_2(x1,y)
r11: app(rev_0(),y) -> rev_1(y)
r12: app(rev1_0(),y) -> rev1_1(y)
r13: app(rev1_1(x1),y) -> rev1_2(x1,y)
r14: app(rev2_0(),y) -> rev2_1(y)
r15: app(rev2_1(x1),y) -> rev2_2(x1,y)
r16: app(s_0(),y) -> s_1(y)
r17: rev_1(nil_0()) -> nil_0()
r18: rev_1(cons_2(x,l)) -> cons_2(rev1_2(x,l),rev2_2(x,l))
r19: rev1_2(|0|_0(),nil_0()) -> |0|_0()
r20: rev1_2(s_1(x),nil_0()) -> s_1(x)
r21: rev1_2(x,cons_2(y,l)) -> rev1_2(y,l)
r22: rev2_2(x,nil_0()) -> nil_0()
r23: rev2_2(x,cons_2(y,l)) -> rev_1(cons_2(x,rev2_2(y,l)))
r24: map_2(f,nil_0()) -> nil_0()
r25: map_2(f,cons_2(x,xs)) -> cons_2(app(f,x),map_2(f,xs))
r26: filter_2(f,nil_0()) -> nil_0()
r27: filter_2(f,cons_2(x,xs)) -> filter2_4(app(f,x),f,x,xs)
r28: filter2_4(true_0(),f,x,xs) -> cons_2(x,filter_2(f,xs))
r29: filter2_4(false_0(),f,x,xs) -> filter_2(f,xs)

The set of usable rules consists of

  r19, r26

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        rev1_2#_A(x1,x2) = 0
        cons_2_A(x1,x2) = max{42, x1 - 44, x2 - 44}
        rev1_2_A(x1,x2) = max{88, x1 - 23}
        |0|_0_A = 1
        nil_0_A = 2
        filter_2_A(x1,x2) = 22
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        matrix interpretation with standard point-wise order:
        
          carrier: N^1
          order: standard order
          interpretations:
            rev1_2#_A(x1,x2) = x2
            cons_2_A(x1,x2) = x1 + x2 + 5
            rev1_2_A(x1,x2) = x1 + x2 + 5
            |0|_0_A() = 1
            nil_0_A() = 9
            filter_2_A(x1,x2) = x1 + x2 + 14
            rev1_2#!_A(x1,x2) = x2
            cons_2!_A(x1,x2) = x1 + x2 + 1
            rev1_2!_A(x1,x2) = x2 + 17
            |0|_0!_A() = 0
            nil_0!_A() = 12
            filter_2!_A(x1,x2) = 13
  
    partial status:
  
      pi(rev1_2#) = []
      pi(cons_2) = []
      pi(rev1_2) = []
      pi(|0|_0) = []
      pi(nil_0) = []
      pi(filter_2) = []

The following rules are removed:

  p1

Then no dependency pair remains.