/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(f(),0()) -> true()
    2: app(f(),1()) -> false()
    3: app(f(),app(s(),x)) -> app(f(),x)
    4: app(app(app(if(),true()),app(s(),x)),app(s(),y)) -> app(s(),x)
    5: app(app(app(if(),false()),app(s(),x)),app(s(),y)) -> app(s(),y)
    6: app(app(g(),x),app(c(),y)) -> app(c(),app(app(g(),x),y))
    7: app(app(g(),x),app(c(),y)) -> app(app(g(),x),app(app(app(if(),app(f(),x)),app(c(),app(app(g(),app(s(),x)),y))),app(c(),y)))
    8: app(app(map(),fun),nil()) -> nil()
    9: app(app(map(),fun),app(app(cons(),x),xs)) -> app(app(cons(),app(fun,x)),app(app(map(),fun),xs))
    10: app(app(filter(),fun),nil()) -> nil()
    11: app(app(filter(),fun),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(fun,x)),fun),x),xs)
    12: app(app(app(app(filter2(),true()),fun),x),xs) -> app(app(cons(),x),app(app(filter(),fun),xs))
    13: app(app(app(app(filter2(),false()),fun),x),xs) -> app(app(filter(),fun),xs)
Number of strict rules: 13
Direct poly ... failed.
Freezing app
1: app❆1_f(0()) -> true()
2: app❆1_f(1()) -> false()
3: app❆1_f(app❆1_s(x)) -> app❆1_f(x)
4: app❆3_if(true(),app❆1_s(x),app❆1_s(y)) -> app❆1_s(x)
5: app❆3_if(false(),app❆1_s(x),app❆1_s(y)) -> app❆1_s(y)
6: app❆2_g(x,app❆1_c(y)) -> app❆1_c(app❆2_g(x,y))
7: app❆2_g(x,app❆1_c(y)) -> app❆2_g(x,app❆3_if(app❆1_f(x),app❆1_c(app❆2_g(app❆1_s(x),y)),app❆1_c(y)))
8: app❆2_map(fun,nil()) -> nil()
9: app❆2_map(fun,app❆2_cons(x,xs)) -> app❆2_cons(app(fun,x),app❆2_map(fun,xs))
10: app❆2_filter(fun,nil()) -> nil()
11: app❆2_filter(fun,app❆2_cons(x,xs)) -> app❆4_filter2(app(fun,x),fun,x,xs)
12: app❆4_filter2(true(),fun,x,xs) -> app❆2_cons(x,app❆2_filter(fun,xs))
13: app❆4_filter2(false(),fun,x,xs) -> app❆2_filter(fun,xs)
14: app(if(),_1) ->= app❆1_if(_1)
15: app(app❆1_if(_1),_2) ->= app❆2_if(_1,_2)
16: app(app❆2_if(_1,_2),_3) ->= app❆3_if(_1,_2,_3)
17: app(cons(),_1) ->= app❆1_cons(_1)
18: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
19: app(s(),_1) ->= app❆1_s(_1)
20: app(filter(),_1) ->= app❆1_filter(_1)
21: app(app❆1_filter(_1),_2) ->= app❆2_filter(_1,_2)
22: app(c(),_1) ->= app❆1_c(_1)
23: app(map(),_1) ->= app❆1_map(_1)
24: app(app❆1_map(_1),_2) ->= app❆2_map(_1,_2)
25: app(g(),_1) ->= app❆1_g(_1)
26: app(app❆1_g(_1),_2) ->= app❆2_g(_1,_2)
27: app(f(),_1) ->= app❆1_f(_1)
28: app(filter2(),_1) ->= app❆1_filter2(_1)
29: app(app❆1_filter2(_1),_2) ->= app❆2_filter2(_1,_2)
30: app(app❆2_filter2(_1,_2),_3) ->= app❆3_filter2(_1,_2,_3)
31: app(app❆3_filter2(_1,_2,_3),_4) ->= app❆4_filter2(_1,_2,_3,_4)
Number of strict rules: 13
Direct poly ... failed.
Dependency Pairs:
   #1: #app❆2_g(x,app❆1_c(y)) -> #app❆2_g(x,y)
   #2: #app❆4_filter2(false(),fun,x,xs) -> #app❆2_filter(fun,xs)
   #3: #app❆2_map(fun,app❆2_cons(x,xs)) -> #app(fun,x)
   #4: #app❆2_map(fun,app❆2_cons(x,xs)) -> #app❆2_map(fun,xs)
   #5: #app❆2_filter(fun,app❆2_cons(x,xs)) -> #app❆4_filter2(app(fun,x),fun,x,xs)
   #6: #app❆2_filter(fun,app❆2_cons(x,xs)) -> #app(fun,x)
   #7: #app(app❆1_map(_1),_2) ->? #app❆2_map(_1,_2)
   #8: #app❆4_filter2(true(),fun,x,xs) -> #app❆2_filter(fun,xs)
   #9: #app(app❆3_filter2(_1,_2,_3),_4) ->? #app❆4_filter2(_1,_2,_3,_4)
   #10: #app❆2_g(x,app❆1_c(y)) -> #app❆2_g(x,app❆3_if(app❆1_f(x),app❆1_c(app❆2_g(app❆1_s(x),y)),app❆1_c(y)))
   #11: #app❆2_g(x,app❆1_c(y)) -> #app❆3_if(app❆1_f(x),app❆1_c(app❆2_g(app❆1_s(x),y)),app❆1_c(y))
   #12: #app❆2_g(x,app❆1_c(y)) -> #app❆1_f(x)
   #13: #app❆2_g(x,app❆1_c(y)) -> #app❆2_g(app❆1_s(x),y)
   #14: #app(f(),_1) ->? #app❆1_f(_1)
   #15: #app(app❆1_g(_1),_2) ->? #app❆2_g(_1,_2)
   #16: #app(app❆1_filter(_1),_2) ->? #app❆2_filter(_1,_2)
   #17: #app(app❆2_if(_1,_2),_3) ->? #app❆3_if(_1,_2,_3)
   #18: #app❆1_f(app❆1_s(x)) -> #app❆1_f(x)
Number of SCCs: 3, DPs: 12
	SCC { #18 }
Sum... succeeded.
  1()		w: (0)
  #app❆2_map(x1,x2)		w: (0)
  s()		w: (0)
  app❆1_c(x1)		w: (0)
  app❆1_map(x1)		w: (0)
  app❆1_if(x1)		w: (0)
  #app❆3_if(x1,x2,x3)		w: (0)
  app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_map(x1,x2)		w: (0)
  false()		w: (0)
  c()		w: (0)
  app❆2_if(x1,x2)		w: (0)
  true()		w: (0)
  f()		w: (0)
  filter2()		w: (0)
  app❆2_filter(x1,x2)		w: (0)
  0()		w: (0)
  if()		w: (0)
  app❆1_f(x1)		w: (0)
  nil()		w: (0)
  app❆1_filter(x1)		w: (0)
  app❆3_if(x1,x2,x3)		w: (0)
  #app(x1,x2)		w: (0)
  map()		w: (0)
  #app❆2_g(x1,x2)		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)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (0)
  #app❆1_f(x1)		w: (x1)
  filter()		w: (0)
  app❆1_s(x1)		w: (1 + x1)
  app❆1_g(x1)		w: (0)
  app❆1_filter2(x1)		w: (0)
  app❆1_cons(x1)		w: (0)
  app❆3_filter2(x1,x2,x3)		w: (0)
  g()		w: (0)
  app❆2_g(x1,x2)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #18
Number of SCCs: 2, DPs: 11
	SCC { #1 #13 }
Sum... succeeded.
  1()		w: (0)
  #app❆2_map(x1,x2)		w: (0)
  s()		w: (0)
  app❆1_c(x1)		w: (1 + x1)
  app❆1_map(x1)		w: (0)
  app❆1_if(x1)		w: (0)
  #app❆3_if(x1,x2,x3)		w: (0)
  app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_map(x1,x2)		w: (0)
  false()		w: (0)
  c()		w: (0)
  app❆2_if(x1,x2)		w: (0)
  true()		w: (0)
  f()		w: (0)
  filter2()		w: (0)
  app❆2_filter(x1,x2)		w: (0)
  0()		w: (0)
  if()		w: (0)
  app❆1_f(x1)		w: (0)
  nil()		w: (0)
  app❆1_filter(x1)		w: (0)
  app❆3_if(x1,x2,x3)		w: (0)
  #app(x1,x2)		w: (0)
  map()		w: (0)
  #app❆2_g(x1,x2)		w: (x2)
  #app❆4_filter2(x1,x2,x3,x4)		w: (0)
  app❆2_filter2(x1,x2)		w: (0)
  #app❆2_filter(x1,x2)		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (0)
  #app❆1_f(x1)		w: (0)
  filter()		w: (0)
  app❆1_s(x1)		w: (1)
  app❆1_g(x1)		w: (0)
  app❆1_filter2(x1)		w: (0)
  app❆1_cons(x1)		w: (0)
  app❆3_filter2(x1,x2,x3)		w: (0)
  g()		w: (0)
  app❆2_g(x1,x2)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1 #13
Number of SCCs: 1, DPs: 9
	SCC { #2..9 #16 }
Sum... succeeded.
  1()		w: (1)
  #app❆2_map(x1,x2)		w: (x2 + x1)
  s()		w: (1)
  app❆1_c(x1)		w: (102218)
  app❆1_map(x1)		w: (51109 + x1)
  app❆1_if(x1)		w: (51109 + x1)
  #app❆3_if(x1,x2,x3)		w: (0)
  app❆4_filter2(x1,x2,x3,x4)		w: (204433 + x3 + x1)
  app❆2_map(x1,x2)		w: (102217 + x2 + x1)
  false()		w: (32288)
  c()		w: (1)
  app❆2_if(x1,x2)		w: (102217)
  true()		w: (32288)
  f()		w: (1)
  filter2()		w: (1)
  app❆2_filter(x1,x2)		w: (245087 + x2 + x1)
  0()		w: (1)
  if()		w: (1)
  app❆1_f(x1)		w: (32286 + x1)
  nil()		w: (1)
  app❆1_filter(x1)		w: (51109 + x1)
  app❆3_if(x1,x2,x3)		w: (153325 + x3 + x2 + x1)
  #app(x1,x2)		w: (10451 + x2 + x1)
  map()		w: (1)
  #app❆2_g(x1,x2)		w: (0)
  #app❆4_filter2(x1,x2,x3,x4)		w: (1 + x4 + x3 + x2)
  app❆2_filter2(x1,x2)		w: (102217 + x2 + x1)
  #app❆2_filter(x1,x2)		w: (x2 + x1)
  cons()		w: (1)
  app❆2_cons(x1,x2)		w: (10452 + x2 + x1)
  #app❆1_f(x1)		w: (0)
  filter()		w: (1)
  app❆1_s(x1)		w: (51109)
  app❆1_g(x1)		w: (51109 + x1)
  app❆1_filter2(x1)		w: (51109)
  app❆1_cons(x1)		w: (51109 + x1)
  app❆3_filter2(x1,x2,x3)		w: (153325 + x3 + x2)
  g()		w: (1)
  app❆2_g(x1,x2)		w: (102217 + x1)
  app(x1,x2)		w: (51107 + x1)
    USABLE RULES: { }
    Removed DPs: #2..9 #16
Number of SCCs: 0, DPs: 0