YES
We show the termination of the TRS R:

  app(app(app(consif(),true()),x),ys) -> app(app(cons(),x),ys)
  app(app(app(consif(),false()),x),ys) -> ys
  app(app(filter(),f),nil()) -> nil()
  app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(consif(),app(f,x)),x),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(consif_0(),y) -> consif_1(y)
  app(consif_1(x1),y) -> consif_2(x1,y)
  app(consif_2(x1,x2),y) -> consif_3(x1,x2,y)
  app(filter_0(),y) -> filter_1(y)
  app(filter_1(x1),y) -> filter_2(x1,y)
  consif_3(true_0(),x,ys) -> cons_2(x,ys)
  consif_3(false_0(),x,ys) -> ys
  filter_2(f,nil_0()) -> nil_0()
  filter_2(f,cons_2(x,xs)) -> consif_3(app(f,x),x,filter_2(f,xs))


-- SCC decomposition.

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

p1: app#(consif_2(x1,x2),y) -> consif_3#(x1,x2,y)
p2: app#(filter_1(x1),y) -> filter_2#(x1,y)
p3: filter_2#(f,cons_2(x,xs)) -> consif_3#(app(f,x),x,filter_2(f,xs))
p4: filter_2#(f,cons_2(x,xs)) -> app#(f,x)
p5: filter_2#(f,cons_2(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(consif_0(),y) -> consif_1(y)
r4: app(consif_1(x1),y) -> consif_2(x1,y)
r5: app(consif_2(x1,x2),y) -> consif_3(x1,x2,y)
r6: app(filter_0(),y) -> filter_1(y)
r7: app(filter_1(x1),y) -> filter_2(x1,y)
r8: consif_3(true_0(),x,ys) -> cons_2(x,ys)
r9: consif_3(false_0(),x,ys) -> ys
r10: filter_2(f,nil_0()) -> nil_0()
r11: filter_2(f,cons_2(x,xs)) -> consif_3(app(f,x),x,filter_2(f,xs))

The estimated dependency graph contains the following SCCs:

  {p2, p4, p5}


-- 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)) -> filter_2#(f,xs)
p3: filter_2#(f,cons_2(x,xs)) -> app#(f,x)

and R consists of:

r1: app(cons_0(),y) -> cons_1(y)
r2: app(cons_1(x1),y) -> cons_2(x1,y)
r3: app(consif_0(),y) -> consif_1(y)
r4: app(consif_1(x1),y) -> consif_2(x1,y)
r5: app(consif_2(x1,x2),y) -> consif_3(x1,x2,y)
r6: app(filter_0(),y) -> filter_1(y)
r7: app(filter_1(x1),y) -> filter_2(x1,y)
r8: consif_3(true_0(),x,ys) -> cons_2(x,ys)
r9: consif_3(false_0(),x,ys) -> ys
r10: filter_2(f,nil_0()) -> nil_0()
r11: filter_2(f,cons_2(x,xs)) -> consif_3(app(f,x),x,filter_2(f,xs))

The set of usable rules consists of

  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11

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:
  
      model-based reduction triple (=A, >=A!, >A!):
      
        finite algebra:
        
          carrier: {0,1}
          interpretations:
            app#_A(0,0) = 0
            app#_A(0,1) = 0
            app#_A(1,0) = 0
            app#_A(1,1) = 0
            filter_1_A(0) = 0
            filter_1_A(1) = 1
            filter_2#_A(0,0) = 0
            filter_2#_A(0,1) = 0
            filter_2#_A(1,0) = 0
            filter_2#_A(1,1) = 0
            cons_2_A(0,0) = 0
            cons_2_A(0,1) = 1
            cons_2_A(1,0) = 0
            cons_2_A(1,1) = 1
            app_A(0,0) = 0
            app_A(0,1) = 1
            app_A(1,0) = 0
            app_A(1,1) = 1
            cons_0_A = 1
            cons_1_A(0) = 0
            cons_1_A(1) = 1
            consif_0_A = 0
            consif_1_A(0) = 0
            consif_1_A(1) = 1
            consif_2_A(0,0) = 0
            consif_2_A(0,1) = 1
            consif_2_A(1,0) = 0
            consif_2_A(1,1) = 1
            consif_3_A(0,0,0) = 0
            consif_3_A(0,0,1) = 1
            consif_3_A(0,1,0) = 0
            consif_3_A(0,1,1) = 1
            consif_3_A(1,0,0) = 0
            consif_3_A(1,0,1) = 1
            consif_3_A(1,1,0) = 0
            consif_3_A(1,1,1) = 1
            filter_0_A = 0
            filter_2_A(0,0) = 0
            filter_2_A(0,1) = 1
            filter_2_A(1,0) = 0
            filter_2_A(1,1) = 1
            true_0_A = 0
            false_0_A = 0
            nil_0_A = 0
            app#!_A(0,0) = 0
            app#!_A(0,1) = 0
            app#!_A(1,0) = 0
            app#!_A(1,1) = 0
            filter_1!_A(0) = 0
            filter_1!_A(1) = 0
            filter_2#!_A(0,0) = 0
            filter_2#!_A(0,1) = 0
            filter_2#!_A(1,0) = 0
            filter_2#!_A(1,1) = 0
            cons_2!_A(0,0) = 0
            cons_2!_A(0,1) = 0
            cons_2!_A(1,0) = 0
            cons_2!_A(1,1) = 0
            app!_A(0,0) = 1
            app!_A(0,1) = 1
            app!_A(1,0) = 1
            app!_A(1,1) = 1
            cons_0!_A = 1
            cons_1!_A(0) = 0
            cons_1!_A(1) = 0
            consif_0!_A = 0
            consif_1!_A(0) = 0
            consif_1!_A(1) = 0
            consif_2!_A(0,0) = 0
            consif_2!_A(0,1) = 1
            consif_2!_A(1,0) = 0
            consif_2!_A(1,1) = 0
            consif_3!_A(0,0,0) = 0
            consif_3!_A(0,0,1) = 0
            consif_3!_A(0,1,0) = 0
            consif_3!_A(0,1,1) = 1
            consif_3!_A(1,0,0) = 0
            consif_3!_A(1,0,1) = 0
            consif_3!_A(1,1,0) = 0
            consif_3!_A(1,1,1) = 0
            filter_0!_A = 0
            filter_2!_A(0,0) = 1
            filter_2!_A(0,1) = 1
            filter_2!_A(1,0) = 1
            filter_2!_A(1,1) = 1
            true_0!_A = 0
            false_0!_A = 1
            nil_0!_A = 1
  
    partial status:
  
      pi(app#) = [2]
      pi(filter_1) = [1]
      pi(filter_2#) = [2]
      pi(cons_2) = [1, 2]
      pi(app) = [1, 2]
      pi(cons_0) = []
      pi(cons_1) = [1]
      pi(consif_0) = []
      pi(consif_1) = [1]
      pi(consif_2) = [1, 2]
      pi(consif_3) = [2, 3]
      pi(filter_0) = []
      pi(filter_2) = [1, 2]
      pi(true_0) = []
      pi(false_0) = []
      pi(nil_0) = []

The following rules are removed:

  p3



-- SCC decomposition.

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)) -> 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(consif_0(),y) -> consif_1(y)
r4: app(consif_1(x1),y) -> consif_2(x1,y)
r5: app(consif_2(x1,x2),y) -> consif_3(x1,x2,y)
r6: app(filter_0(),y) -> filter_1(y)
r7: app(filter_1(x1),y) -> filter_2(x1,y)
r8: consif_3(true_0(),x,ys) -> cons_2(x,ys)
r9: consif_3(false_0(),x,ys) -> ys
r10: filter_2(f,nil_0()) -> nil_0()
r11: filter_2(f,cons_2(x,xs)) -> consif_3(app(f,x),x,filter_2(f,xs))

The estimated dependency graph contains the following SCCs:

  {p2}


-- Reduction pair.

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

p1: filter_2#(f,cons_2(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(consif_0(),y) -> consif_1(y)
r4: app(consif_1(x1),y) -> consif_2(x1,y)
r5: app(consif_2(x1,x2),y) -> consif_3(x1,x2,y)
r6: app(filter_0(),y) -> filter_1(y)
r7: app(filter_1(x1),y) -> filter_2(x1,y)
r8: consif_3(true_0(),x,ys) -> cons_2(x,ys)
r9: consif_3(false_0(),x,ys) -> ys
r10: filter_2(f,nil_0()) -> nil_0()
r11: filter_2(f,cons_2(x,xs)) -> consif_3(app(f,x),x,filter_2(f,xs))

The set of usable rules consists of

  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11

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:
  
      model-based reduction triple (=A, >=A!, >A!):
      
        finite algebra:
        
          carrier: {0,1}
          interpretations:
            filter_2#_A(0,0) = 1
            filter_2#_A(0,1) = 0
            filter_2#_A(1,0) = 0
            filter_2#_A(1,1) = 0
            cons_2_A(0,0) = 0
            cons_2_A(0,1) = 1
            cons_2_A(1,0) = 0
            cons_2_A(1,1) = 1
            app_A(0,0) = 1
            app_A(0,1) = 1
            app_A(1,0) = 0
            app_A(1,1) = 1
            cons_0_A = 0
            cons_1_A(0) = 1
            cons_1_A(1) = 1
            consif_0_A = 1
            consif_1_A(0) = 0
            consif_1_A(1) = 1
            consif_2_A(0,0) = 1
            consif_2_A(0,1) = 1
            consif_2_A(1,0) = 0
            consif_2_A(1,1) = 1
            consif_3_A(0,0,0) = 0
            consif_3_A(0,0,1) = 1
            consif_3_A(0,1,0) = 0
            consif_3_A(0,1,1) = 1
            consif_3_A(1,0,0) = 1
            consif_3_A(1,0,1) = 1
            consif_3_A(1,1,0) = 0
            consif_3_A(1,1,1) = 1
            filter_0_A = 1
            filter_1_A(0) = 0
            filter_1_A(1) = 1
            filter_2_A(0,0) = 1
            filter_2_A(0,1) = 1
            filter_2_A(1,0) = 0
            filter_2_A(1,1) = 1
            true_0_A = 0
            false_0_A = 0
            nil_0_A = 1
            filter_2#!_A(0,0) = 1
            filter_2#!_A(0,1) = 0
            filter_2#!_A(1,0) = 1
            filter_2#!_A(1,1) = 0
            cons_2!_A(0,0) = 1
            cons_2!_A(0,1) = 1
            cons_2!_A(1,0) = 1
            cons_2!_A(1,1) = 1
            app!_A(0,0) = 1
            app!_A(0,1) = 0
            app!_A(1,0) = 1
            app!_A(1,1) = 1
            cons_0!_A = 1
            cons_1!_A(0) = 0
            cons_1!_A(1) = 0
            consif_0!_A = 0
            consif_1!_A(0) = 1
            consif_1!_A(1) = 1
            consif_2!_A(0,0) = 0
            consif_2!_A(0,1) = 0
            consif_2!_A(1,0) = 0
            consif_2!_A(1,1) = 0
            consif_3!_A(0,0,0) = 1
            consif_3!_A(0,0,1) = 1
            consif_3!_A(0,1,0) = 1
            consif_3!_A(0,1,1) = 1
            consif_3!_A(1,0,0) = 1
            consif_3!_A(1,0,1) = 0
            consif_3!_A(1,1,0) = 1
            consif_3!_A(1,1,1) = 0
            filter_0!_A = 1
            filter_1!_A(0) = 1
            filter_1!_A(1) = 1
            filter_2!_A(0,0) = 1
            filter_2!_A(0,1) = 0
            filter_2!_A(1,0) = 1
            filter_2!_A(1,1) = 1
            true_0!_A = 1
            false_0!_A = 1
            nil_0!_A = 0
  
    partial status:
  
      pi(filter_2#) = [2]
      pi(cons_2) = [2]
      pi(app) = [2]
      pi(cons_0) = []
      pi(cons_1) = []
      pi(consif_0) = []
      pi(consif_1) = [1]
      pi(consif_2) = []
      pi(consif_3) = [3]
      pi(filter_0) = []
      pi(filter_1) = []
      pi(filter_2) = [2]
      pi(true_0) = []
      pi(false_0) = []
      pi(nil_0) = []

The following rules are removed:

  p1

Then no dependency pair remains.