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


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YES
Input TRS:
    1: app(app(minus(),x),0()) -> x
    2: app(app(minus(),app(s(),x)),app(s(),y)) -> app(app(minus(),x),y)
    3: app(double(),0()) -> 0()
    4: app(double(),app(s(),x)) -> app(s(),app(s(),app(double(),x)))
    5: app(app(plus(),0()),y) -> y
    6: app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
    7: app(app(plus(),app(s(),x)),y) -> app(app(plus(),x),app(s(),y))
    8: app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),app(app(minus(),x),y)),app(double(),y)))
    9: app(app(map(),f),nil()) -> nil()
    10: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    11: app(app(filter(),f),nil()) -> nil()
    12: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
    13: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
    14: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)
Number of strict rules: 14
Direct poly ... failed.
Freezing app
1: app❆2_minus(x,0()) -> x
2: app❆2_minus(app❆1_s(x),app❆1_s(y)) -> app❆2_minus(x,y)
3: app❆1_double(0()) -> 0()
4: app❆1_double(app❆1_s(x)) -> app❆1_s(app❆1_s(app❆1_double(x)))
5: app❆2_plus(0(),y) -> y
6: app❆2_plus(app❆1_s(x),y) -> app❆1_s(app❆2_plus(x,y))
7: app❆2_plus(app❆1_s(x),y) -> app❆2_plus(x,app❆1_s(y))
8: app❆2_plus(app❆1_s(x),y) -> app❆1_s(app❆2_plus(app❆2_minus(x,y),app❆1_double(y)))
9: app❆2_map(f,nil()) -> nil()
10: app❆2_map(f,app❆2_cons(x,xs)) -> app❆2_cons(app(f,x),app❆2_map(f,xs))
11: app❆2_filter(f,nil()) -> nil()
12: app❆2_filter(f,app❆2_cons(x,xs)) -> app❆4_filter2(app(f,x),f,x,xs)
13: app❆4_filter2(true(),f,x,xs) -> app❆2_cons(x,app❆2_filter(f,xs))
14: app❆4_filter2(false(),f,x,xs) -> app❆2_filter(f,xs)
15: app(plus(),_1) ->= app❆1_plus(_1)
16: app(app❆1_plus(_1),_2) ->= app❆2_plus(_1,_2)
17: app(cons(),_1) ->= app❆1_cons(_1)
18: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
19: app(double(),_1) ->= app❆1_double(_1)
20: app(s(),_1) ->= app❆1_s(_1)
21: app(filter(),_1) ->= app❆1_filter(_1)
22: app(app❆1_filter(_1),_2) ->= app❆2_filter(_1,_2)
23: app(map(),_1) ->= app❆1_map(_1)
24: app(app❆1_map(_1),_2) ->= app❆2_map(_1,_2)
25: app(minus(),_1) ->= app❆1_minus(_1)
26: app(app❆1_minus(_1),_2) ->= app❆2_minus(_1,_2)
27: app(filter2(),_1) ->= app❆1_filter2(_1)
28: app(app❆1_filter2(_1),_2) ->= app❆2_filter2(_1,_2)
29: app(app❆2_filter2(_1,_2),_3) ->= app❆3_filter2(_1,_2,_3)
30: app(app❆3_filter2(_1,_2,_3),_4) ->= app❆4_filter2(_1,_2,_3,_4)
Number of strict rules: 14
Direct poly ... failed.
Dependency Pairs:
   #1: #app❆2_minus(app❆1_s(x),app❆1_s(y)) -> #app❆2_minus(x,y)
   #2: #app❆2_plus(app❆1_s(x),y) -> #app❆2_plus(x,y)
   #3: #app❆4_filter2(true(),f,x,xs) -> #app❆2_filter(f,xs)
   #4: #app(app❆1_map(_1),_2) ->? #app❆2_map(_1,_2)
   #5: #app❆2_filter(f,app❆2_cons(x,xs)) -> #app❆4_filter2(app(f,x),f,x,xs)
   #6: #app❆2_filter(f,app❆2_cons(x,xs)) -> #app(f,x)
   #7: #app❆4_filter2(false(),f,x,xs) -> #app❆2_filter(f,xs)
   #8: #app(app❆3_filter2(_1,_2,_3),_4) ->? #app❆4_filter2(_1,_2,_3,_4)
   #9: #app❆2_plus(app❆1_s(x),y) -> #app❆2_plus(x,app❆1_s(y))
   #10: #app❆2_map(f,app❆2_cons(x,xs)) -> #app(f,x)
   #11: #app❆2_map(f,app❆2_cons(x,xs)) -> #app❆2_map(f,xs)
   #12: #app(app❆1_filter(_1),_2) ->? #app❆2_filter(_1,_2)
   #13: #app(double(),_1) ->? #app❆1_double(_1)
   #14: #app(app❆1_minus(_1),_2) ->? #app❆2_minus(_1,_2)
   #15: #app(app❆1_plus(_1),_2) ->? #app❆2_plus(_1,_2)
   #16: #app❆2_plus(app❆1_s(x),y) -> #app❆2_plus(app❆2_minus(x,y),app❆1_double(y))
   #17: #app❆2_plus(app❆1_s(x),y) -> #app❆2_minus(x,y)
   #18: #app❆2_plus(app❆1_s(x),y) -> #app❆1_double(y)
   #19: #app❆1_double(app❆1_s(x)) -> #app❆1_double(x)
Number of SCCs: 4, DPs: 14
	SCC { #19 }
Sum... succeeded.
  app❆2_minus(x1,x2)		w: (0)
  #app❆2_map(x1,x2)		w: (0)
  #app❆1_double(x1)		w: (x1)
  s()		w: (0)
  app❆1_map(x1)		w: (0)
  app❆1_minus(x1)		w: (0)
  app❆1_plus(x1)		w: (0)
  minus()		w: (0)
  app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_plus(x1,x2)		w: (0)
  app❆2_map(x1,x2)		w: (0)
  #app❆2_minus(x1,x2)		w: (0)
  false()		w: (0)
  true()		w: (0)
  filter2()		w: (0)
  app❆2_filter(x1,x2)		w: (0)
  0()		w: (0)
  #app❆2_plus(x1,x2)		w: (0)
  double()		w: (0)
  nil()		w: (0)
  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)
  plus()		w: (0)
  #app❆2_filter(x1,x2)		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (0)
  app❆1_double(x1)		w: (0)
  filter()		w: (0)
  app❆1_s(x1)		w: (1 + x1)
  app❆1_filter2(x1)		w: (0)
  app❆1_cons(x1)		w: (0)
  app❆3_filter2(x1,x2,x3)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #19
Number of SCCs: 3, DPs: 13
	SCC { #1 }
Sum... succeeded.
  app❆2_minus(x1,x2)		w: (0)
  #app❆2_map(x1,x2)		w: (0)
  #app❆1_double(x1)		w: (0)
  s()		w: (0)
  app❆1_map(x1)		w: (0)
  app❆1_minus(x1)		w: (0)
  app❆1_plus(x1)		w: (0)
  minus()		w: (0)
  app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_plus(x1,x2)		w: (0)
  app❆2_map(x1,x2)		w: (0)
  #app❆2_minus(x1,x2)		w: (x2)
  false()		w: (0)
  true()		w: (0)
  filter2()		w: (0)
  app❆2_filter(x1,x2)		w: (0)
  0()		w: (0)
  #app❆2_plus(x1,x2)		w: (0)
  double()		w: (0)
  nil()		w: (0)
  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)
  plus()		w: (0)
  #app❆2_filter(x1,x2)		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (0)
  app❆1_double(x1)		w: (0)
  filter()		w: (0)
  app❆1_s(x1)		w: (1 + x1)
  app❆1_filter2(x1)		w: (0)
  app❆1_cons(x1)		w: (0)
  app❆3_filter2(x1,x2,x3)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 12
	SCC { #2 #9 #16 }
Sum... succeeded.
  app❆2_minus(x1,x2)		w: (39 + x1)
  #app❆2_map(x1,x2)		w: (0)
  #app❆1_double(x1)		w: (0)
  s()		w: (0)
  app❆1_map(x1)		w: (0)
  app❆1_minus(x1)		w: (0)
  app❆1_plus(x1)		w: (0)
  minus()		w: (0)
  app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_plus(x1,x2)		w: (0)
  app❆2_map(x1,x2)		w: (0)
  #app❆2_minus(x1,x2)		w: (0)
  false()		w: (0)
  true()		w: (0)
  filter2()		w: (0)
  app❆2_filter(x1,x2)		w: (0)
  0()		w: (1)
  #app❆2_plus(x1,x2)		w: (x1)
  double()		w: (0)
  nil()		w: (0)
  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)
  plus()		w: (0)
  #app❆2_filter(x1,x2)		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (0)
  app❆1_double(x1)		w: (1 + x1)
  filter()		w: (0)
  app❆1_s(x1)		w: (40 + x1)
  app❆1_filter2(x1)		w: (0)
  app❆1_cons(x1)		w: (0)
  app❆3_filter2(x1,x2,x3)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { 1 2 }
    Removed DPs: #2 #9 #16
Number of SCCs: 1, DPs: 9
	SCC { #3..8 #10..12 }
Sum... succeeded.
  app❆2_minus(x1,x2)		w: (39 + x2)
  #app❆2_map(x1,x2)		w: (17 + x2 + x1)
  #app❆1_double(x1)		w: (0)
  s()		w: (1)
  app❆1_map(x1)		w: (18 + x1)
  app❆1_minus(x1)		w: (18 + x1)
  app❆1_plus(x1)		w: (18 + x1)
  minus()		w: (1)
  app❆4_filter2(x1,x2,x3,x4)		w: (69 + x1)
  app❆2_plus(x1,x2)		w: (35 + x2)
  app❆2_map(x1,x2)		w: (35 + x2 + x1)
  #app❆2_minus(x1,x2)		w: (0)
  false()		w: (1)
  true()		w: (1)
  filter2()		w: (1)
  app❆2_filter(x1,x2)		w: (71 + x2 + x1)
  0()		w: (1)
  #app❆2_plus(x1,x2)		w: (0)
  double()		w: (1)
  nil()		w: (1)
  app❆1_filter(x1)		w: (18 + x1)
  #app(x1,x2)		w: (x2 + x1)
  map()		w: (1)
  #app❆4_filter2(x1,x2,x3,x4)		w: (1 + x4 + x3 + x2)
  app❆2_filter2(x1,x2)		w: (35)
  plus()		w: (1)
  #app❆2_filter(x1,x2)		w: (x2 + x1)
  cons()		w: (1)
  app❆2_cons(x1,x2)		w: (2 + x2 + x1)
  app❆1_double(x1)		w: (18 + x1)
  filter()		w: (1)
  app❆1_s(x1)		w: (18 + x1)
  app❆1_filter2(x1)		w: (18 + x1)
  app❆1_cons(x1)		w: (18 + x1)
  app❆3_filter2(x1,x2,x3)		w: (52 + x3 + x2 + x1)
  app(x1,x2)		w: (16 + x1)
    USABLE RULES: { }
    Removed DPs: #3..8 #10..12
Number of SCCs: 0, DPs: 0