/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(twice(),f),x) -> app(f,app(f,x))
    2: app(app(map(),f),nil()) -> nil()
    3: app(app(map(),f),app(app(cons(),h),t)) -> app(app(cons(),app(f,h)),app(app(map(),f),t))
    4: app(app(fmap(),nil()),x) -> nil()
    5: app(app(fmap(),app(app(cons(),f),t_f())),x) -> app(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))
Number of strict rules: 5
Direct poly ... failed.
Freezing app
1: app❆2_twice(f,x) -> app(f,app(f,x))
2: app❆2_map(f,nil()) -> nil()
3: app❆2_map(f,app❆2_cons(h,t)) -> app❆2_cons(app(f,h),app❆2_map(f,t))
4: app❆2_fmap(nil(),x) -> nil()
5: app❆2_fmap(app❆2_cons(f,t_f()),x) -> app❆2_cons(app(f,x),app❆2_fmap(t_f(),x))
6: app(fmap(),_1) ->= app❆1_fmap(_1)
7: app(app❆1_fmap(_1),_2) ->= app❆2_fmap(_1,_2)
8: app(cons(),_1) ->= app❆1_cons(_1)
9: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
10: app(twice(),_1) ->= app❆1_twice(_1)
11: app(app❆1_twice(_1),_2) ->= app❆2_twice(_1,_2)
12: app(map(),_1) ->= app❆1_map(_1)
13: app(app❆1_map(_1),_2) ->= app❆2_map(_1,_2)
Number of strict rules: 5
Direct poly ... failed.
Dependency Pairs:
   #1: #app(app❆1_map(_1),_2) ->? #app❆2_map(_1,_2)
   #2: #app(app❆1_twice(_1),_2) ->? #app❆2_twice(_1,_2)
   #3: #app(app❆1_fmap(_1),_2) ->? #app❆2_fmap(_1,_2)
   #4: #app❆2_fmap(app❆2_cons(f,t_f()),x) -> #app(f,x)
   #5: #app❆2_fmap(app❆2_cons(f,t_f()),x) -> #app❆2_fmap(t_f(),x)
   #6: #app❆2_map(f,app❆2_cons(h,t)) -> #app(f,h)
   #7: #app❆2_map(f,app❆2_cons(h,t)) -> #app❆2_map(f,t)
   #8: #app❆2_twice(f,x) -> #app(f,app(f,x))
   #9: #app❆2_twice(f,x) -> #app(f,x)
Number of SCCs: 1, DPs: 8
	SCC { #1..4 #6..9 }
Sum... succeeded.
  #app❆2_map(x1,x2)		w: (1043 + x1)
  t_f()		w: (1)
  app❆2_fmap(x1,x2)		w: (8857 + x2 + x1)
  #app❆2_twice(x1,x2)		w: (1043 + x1)
  app❆1_map(x1)		w: (2 + x1)
  twice()		w: (1)
  app❆1_fmap(x1)		w: (2 + x1)
  app❆2_map(x1,x2)		w: (11799 + x2)
  app❆2_twice(x1,x2)		w: (2 + x2 + x1)
  fmap()		w: (1)
  #app❆2_fmap(x1,x2)		w: (1 + x1)
  nil()		w: (1)
  #app(x1,x2)		w: (1042 + x1)
  map()		w: (1)
  cons()		w: (1)
  app❆2_cons(x1,x2)		w: (2439 + x2 + x1)
  app❆1_cons(x1)		w: (2)
  app❆1_twice(x1)		w: (2 + x1)
  app(x1,x2)		w: (1)
    USABLE RULES: { }
    Removed DPs: #1..4 #6 #8 #9
Number of SCCs: 1, DPs: 1
	SCC { #7 }
Sum... succeeded.
  #app❆2_map(x1,x2)		w: (1043 + x2)
  t_f()		w: (30690)
  app❆2_fmap(x1,x2)		w: (10452 + x2 + x1)
  #app❆2_twice(x1,x2)		w: (1043)
  app❆1_map(x1)		w: (2 + x1)
  twice()		w: (1)
  app❆1_fmap(x1)		w: (2 + x1)
  app❆2_map(x1,x2)		w: (11799 + x2)
  app❆2_twice(x1,x2)		w: (2 + x2 + x1)
  fmap()		w: (1)
  #app❆2_fmap(x1,x2)		w: (1)
  nil()		w: (1)
  #app(x1,x2)		w: (1042)
  map()		w: (1)
  cons()		w: (1)
  app❆2_cons(x1,x2)		w: (2 + x2 + x1)
  app❆1_cons(x1)		w: (2)
  app❆1_twice(x1)		w: (2 + x1)
  app(x1,x2)		w: (1)
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 0, DPs: 0