/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
Input TRS:
    1: app(f(),app(app(cons(),nil()),y)) -> y
    2: app(f(),app(app(cons(),app(f(),app(app(cons(),nil()),y))),z)) -> app(app(app(copy(),n()),y),z)
    3: app(app(app(copy(),0()),y),z) -> app(f(),z)
    4: app(app(app(copy(),app(s(),x)),y),z) -> app(app(app(copy(),x),y),app(app(cons(),app(f(),y)),z))
    5: app(app(map(),fun),nil()) -> nil()
    6: app(app(map(),fun),app(app(cons(),x),xs)) -> app(app(cons(),app(fun,x)),app(app(map(),fun),xs))
    7: app(app(filter(),fun),nil()) -> nil()
    8: app(app(filter(),fun),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(fun,x)),fun),x),xs)
    9: app(app(app(app(filter2(),true()),fun),x),xs) -> app(app(cons(),x),app(app(filter(),fun),xs))
    10: app(app(app(app(filter2(),false()),fun),x),xs) -> app(app(filter(),fun),xs)
Number of strict rules: 10
Direct poly ... failed.
Freezing app
1: app❆1_f(app❆2_cons(nil(),y)) -> y
2: app❆1_f(app❆2_cons(app❆1_f(app❆2_cons(nil(),y)),z)) -> app❆3_copy(n(),y,z)
3: app❆3_copy(0(),y,z) -> app❆1_f(z)
4: app❆3_copy(app❆1_s(x),y,z) -> app❆3_copy(x,y,app❆2_cons(app❆1_f(y),z))
5: app❆2_map(fun,nil()) -> nil()
6: app❆2_map(fun,app❆2_cons(x,xs)) -> app❆2_cons(app(fun,x),app❆2_map(fun,xs))
7: app❆2_filter(fun,nil()) -> nil()
8: app❆2_filter(fun,app❆2_cons(x,xs)) -> app❆4_filter2(app(fun,x),fun,x,xs)
9: app❆4_filter2(true(),fun,x,xs) -> app❆2_cons(x,app❆2_filter(fun,xs))
10: app❆4_filter2(false(),fun,x,xs) -> app❆2_filter(fun,xs)
11: app(cons(),_1) ->= app❆1_cons(_1)
12: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
13: app(s(),_1) ->= app❆1_s(_1)
14: app(filter(),_1) ->= app❆1_filter(_1)
15: app(app❆1_filter(_1),_2) ->= app❆2_filter(_1,_2)
16: app(map(),_1) ->= app❆1_map(_1)
17: app(app❆1_map(_1),_2) ->= app❆2_map(_1,_2)
18: app(f(),_1) ->= app❆1_f(_1)
19: app(filter2(),_1) ->= app❆1_filter2(_1)
20: app(app❆1_filter2(_1),_2) ->= app❆2_filter2(_1,_2)
21: app(app❆2_filter2(_1,_2),_3) ->= app❆3_filter2(_1,_2,_3)
22: app(app❆3_filter2(_1,_2,_3),_4) ->= app❆4_filter2(_1,_2,_3,_4)
23: app(copy(),_1) ->= app❆1_copy(_1)
24: app(app❆1_copy(_1),_2) ->= app❆2_copy(_1,_2)
25: app(app❆2_copy(_1,_2),_3) ->= app❆3_copy(_1,_2,_3)
Number of strict rules: 10
Direct poly ... failed.
Dependency Pairs:
   #1: #app❆1_f(app❆2_cons(app❆1_f(app❆2_cons(nil(),y)),z)) -> #app❆3_copy(n(),y,z)
   #2: #app❆2_map(fun,app❆2_cons(x,xs)) -> #app(fun,x)
   #3: #app❆2_map(fun,app❆2_cons(x,xs)) -> #app❆2_map(fun,xs)
   #4: #app❆4_filter2(true(),fun,x,xs) -> #app❆2_filter(fun,xs)
   #5: #app(app❆2_copy(_1,_2),_3) ->? #app❆3_copy(_1,_2,_3)
   #6: #app❆4_filter2(false(),fun,x,xs) -> #app❆2_filter(fun,xs)
   #7: #app(app❆3_filter2(_1,_2,_3),_4) ->? #app❆4_filter2(_1,_2,_3,_4)
   #8: #app(app❆1_map(_1),_2) ->? #app❆2_map(_1,_2)
   #9: #app❆3_copy(0(),y,z) -> #app❆1_f(z)
   #10: #app❆2_filter(fun,app❆2_cons(x,xs)) -> #app❆4_filter2(app(fun,x),fun,x,xs)
   #11: #app❆2_filter(fun,app❆2_cons(x,xs)) -> #app(fun,x)
   #12: #app(app❆1_filter(_1),_2) ->? #app❆2_filter(_1,_2)
   #13: #app❆3_copy(app❆1_s(x),y,z) -> #app❆3_copy(x,y,app❆2_cons(app❆1_f(y),z))
   #14: #app❆3_copy(app❆1_s(x),y,z) -> #app❆1_f(y)
   #15: #app(f(),_1) ->? #app❆1_f(_1)
Number of SCCs: 2, DPs: 10
	SCC { #13 }
Sum... succeeded.
  #app❆2_map(x1,x2)		w: (0)
  s()		w: (0)
  app❆1_map(x1)		w: (0)
  n()		w: (3)
  app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_map(x1,x2)		w: (0)
  false()		w: (0)
  true()		w: (0)
  f()		w: (0)
  filter2()		w: (0)
  app❆2_filter(x1,x2)		w: (0)
  app❆1_copy(x1)		w: (0)
  0()		w: (0)
  app❆1_f(x1)		w: (8366 + x1)
  nil()		w: (1)
  app❆1_filter(x1)		w: (0)
  #app(x1,x2)		w: (0)
  map()		w: (0)
  #app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_filter2(x1,x2)		w: (0)
  #app❆2_filter(x1,x2)		w: (0)
  #app❆3_copy(x1,x2,x3)		w: (x2 + x1)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (1 + x2 + x1)
  app❆3_copy(x1,x2,x3)		w: (16733 + x1)
  app❆2_copy(x1,x2)		w: (0)
  #app❆1_f(x1)		w: (0)
  filter()		w: (0)
  app❆1_s(x1)		w: (3 + x1)
  app❆1_filter2(x1)		w: (0)
  app❆1_cons(x1)		w: (0)
  app❆3_filter2(x1,x2,x3)		w: (0)
  copy()		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #13
Number of SCCs: 1, DPs: 9
	SCC { #2..4 #6..8 #10..12 }
Sum... succeeded.
  #app❆2_map(x1,x2)		w: (2997 + x2)
  s()		w: (7550)
  app❆1_map(x1)		w: (3)
  n()		w: (8376)
  app❆4_filter2(x1,x2,x3,x4)		w: (35665 + x1)
  app❆2_map(x1,x2)		w: (5 + x2 + x1)
  false()		w: (1)
  true()		w: (1)
  f()		w: (1)
  filter2()		w: (20977)
  app❆2_filter(x1,x2)		w: (35667 + x2 + x1)
  app❆1_copy(x1)		w: (4950)
  0()		w: (1)
  app❆1_f(x1)		w: (8362 + x1)
  nil()		w: (1)
  app❆1_filter(x1)		w: (31894)
  #app(x1,x2)		w: (2998 + x2)
  map()		w: (1)
  #app❆4_filter2(x1,x2,x3,x4)		w: (2998 + x4)
  app❆2_filter2(x1,x2)		w: (35661 + x2 + x1)
  #app❆2_filter(x1,x2)		w: (2998 + x2)
  #app❆3_copy(x1,x2,x3)		w: (0)
  cons()		w: (1)
  app❆2_cons(x1,x2)		w: (5 + x2 + x1)
  app❆3_copy(x1,x2,x3)		w: (8360 + x3 + x1)
  app❆2_copy(x1,x2)		w: (8358 + x2 + x1)
  #app❆1_f(x1)		w: (0)
  filter()		w: (31892)
  app❆1_s(x1)		w: (7552 + x1)
  app❆1_filter2(x1)		w: (20979 + x1)
  app❆1_cons(x1)		w: (3)
  app❆3_filter2(x1,x2,x3)		w: (35663 + x3)
  copy()		w: (4948)
  app(x1,x2)		w: (1 + x1)
    USABLE RULES: { }
    Removed DPs: #2 #3 #8 #10 #11
Number of SCCs: 0, DPs: 0