Input TRS:
    1: app(app(:(),app(app(:(),x),y)),z) -> app(app(:(),x),app(app(:(),y),z))
    2: app(app(:(),app(app(+(),x),y)),z) -> app(app(+(),app(app(:(),x),z)),app(app(:(),y),z))
    3: app(app(:(),z),app(app(+(),x),app(f,y))) -> app(app(:(),app(app(g(),z),y)),app(app(+(),x),a()))
    4: app(app(map(),f),nil()) -> nil()
    5: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    6: app(app(filter(),f),nil()) -> nil()
    7: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
    8: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
    9: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #app(app(:(),app(app(+(),x),y)),z) -> #app(app(+(),app(app(:(),x),z)),app(app(:(),y),z))
   #2: #app(app(:(),app(app(+(),x),y)),z) -> #app(+(),app(app(:(),x),z))
   #3: #app(app(:(),app(app(+(),x),y)),z) -> #app(app(:(),x),z)
   #4: #app(app(:(),app(app(+(),x),y)),z) -> #app(:(),x)
   #5: #app(app(:(),app(app(+(),x),y)),z) -> #app(app(:(),y),z)
   #6: #app(app(:(),app(app(+(),x),y)),z) -> #app(:(),y)
   #7: #app(app(app(app(filter2(),false()),f),x),xs) -> #app(app(filter(),f),xs)
   #8: #app(app(app(app(filter2(),false()),f),x),xs) -> #app(filter(),f)
   #9: #app(app(filter(),f),app(app(cons(),x),xs)) -> #app(app(app(app(filter2(),app(f,x)),f),x),xs)
   #10: #app(app(filter(),f),app(app(cons(),x),xs)) -> #app(app(app(filter2(),app(f,x)),f),x)
   #11: #app(app(filter(),f),app(app(cons(),x),xs)) -> #app(app(filter2(),app(f,x)),f)
   #12: #app(app(filter(),f),app(app(cons(),x),xs)) -> #app(filter2(),app(f,x))
   #13: #app(app(filter(),f),app(app(cons(),x),xs)) -> #app(f,x)
   #14: #app(app(map(),f),app(app(cons(),x),xs)) -> #app(app(cons(),app(f,x)),app(app(map(),f),xs))
   #15: #app(app(map(),f),app(app(cons(),x),xs)) -> #app(cons(),app(f,x))
   #16: #app(app(map(),f),app(app(cons(),x),xs)) -> #app(f,x)
   #17: #app(app(map(),f),app(app(cons(),x),xs)) -> #app(app(map(),f),xs)
   #18: #app(app(:(),z),app(app(+(),x),app(f,y))) -> #app(app(:(),app(app(g(),z),y)),app(app(+(),x),a()))
   #19: #app(app(:(),z),app(app(+(),x),app(f,y))) -> #app(:(),app(app(g(),z),y))
   #20: #app(app(:(),z),app(app(+(),x),app(f,y))) -> #app(app(g(),z),y)
   #21: #app(app(:(),z),app(app(+(),x),app(f,y))) -> #app(g(),z)
   #22: #app(app(:(),z),app(app(+(),x),app(f,y))) -> #app(app(+(),x),a())
   #23: #app(app(:(),app(app(:(),x),y)),z) -> #app(app(:(),x),app(app(:(),y),z))
   #24: #app(app(:(),app(app(:(),x),y)),z) -> #app(app(:(),y),z)
   #25: #app(app(:(),app(app(:(),x),y)),z) -> #app(:(),y)
   #26: #app(app(app(app(filter2(),true()),f),x),xs) -> #app(app(cons(),x),app(app(filter(),f),xs))
   #27: #app(app(app(app(filter2(),true()),f),x),xs) -> #app(cons(),x)
   #28: #app(app(app(app(filter2(),true()),f),x),xs) -> #app(app(filter(),f),xs)
   #29: #app(app(app(app(filter2(),true()),f),x),xs) -> #app(filter(),f)
Number of SCCs: 2, DPs: 9, edges: 30
	SCC { #3 #5 #23 #24 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
 false()	weight: 0
  true()	weight: 0
filter2()	weight: 0
     :()	weight: 0
   nil()	weight: 0
 #app(x1,x2)	weight: x1
   map()	weight: 0
  cons()	weight: 0
filter()	weight: 0
     +()	weight: 0
     g()	weight: 0
   app(x1,x2)	weight: (/ 1 8) + x1 + x2
    Usable rules: { }
    Removed DPs: #3 #5 #23 #24
Number of SCCs: 1, DPs: 5, edges: 14
	SCC { #7 #13 #16 #17 #28 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
 false()	weight: 0
  true()	weight: 0
filter2()	weight: 0
     :()	weight: 0
   nil()	weight: 0
 #app(x1,x2)	weight: x1
   map()	weight: 0
  cons()	weight: 0
filter()	weight: 0
     +()	weight: 0
     g()	weight: 0
   app(x1,x2)	weight: (/ 1 8) + x1 + x2
    Usable rules: { }
    Removed DPs: #7 #13 #16 #28
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #17 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     a()	weight: 0
 false()	weight: 0
  true()	weight: 0
filter2()	weight: 0
     :()	weight: 0
   nil()	weight: 0
 #app(x1,x2)	weight: max{0, (/ 1 4) + x2}
   map()	weight: (/ 1 2)
  cons()	weight: 0
filter()	weight: 0
     +()	weight: 0
     g()	weight: 0
   app(x1,x2)	weight: max{(/ 1 4) + x2, x1}
    Usable rules: { }
    Removed DPs: #17
Number of SCCs: 0, DPs: 0, edges: 0
YES