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


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YES
Input TRS:
    1: app(app(plus(),0()),y) -> y
    2: app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
    3: app(app(times(),0()),y) -> 0()
    4: app(app(times(),app(s(),x)),y) -> app(app(plus(),app(app(times(),x),y)),y)
    5: app(inc(),xs) -> app(app(map(),app(plus(),app(s(),0()))),xs)
    6: app(double(),xs) -> app(app(map(),app(times(),app(s(),app(s(),0())))),xs)
    7: app(app(map(),f),nil()) -> nil()
    8: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Uncurrying app
1: app^2_plus(0(),y) -> y
2: app^2_plus(app^1_s(x),y) -> app^1_s(app^2_plus(x,y))
3: app^2_times(0(),y) -> 0()
4: app^2_times(app^1_s(x),y) -> app^2_plus(app^2_times(x,y),y)
5: app^1_inc(xs) -> app^2_map(app^1_plus(app^1_s(0())),xs)
6: app^1_double(xs) -> app^2_map(app^1_times(app^1_s(app^1_s(0()))),xs)
7: app^2_map(f,nil()) -> nil()
8: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs))
9: app(plus(),_1) ->= app^1_plus(_1)
10: app(app^1_plus(_1),_2) ->= app^2_plus(_1,_2)
11: app(cons(),_1) ->= app^1_cons(_1)
12: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
13: app(double(),_1) ->= app^1_double(_1)
14: app(times(),_1) ->= app^1_times(_1)
15: app(app^1_times(_1),_2) ->= app^2_times(_1,_2)
16: app(s(),_1) ->= app^1_s(_1)
17: app(inc(),_1) ->= app^1_inc(_1)
18: app(map(),_1) ->= app^1_map(_1)
19: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #app^2_plus(app^1_s(x),y) -> #app^2_plus(x,y)
   #2: #app^1_double(xs) -> #app^2_map(app^1_times(app^1_s(app^1_s(0()))),xs)
   #3: #app(double(),_1) ->? #app^1_double(_1)
   #4: #app(app^1_plus(_1),_2) ->? #app^2_plus(_1,_2)
   #5: #app^1_inc(xs) -> #app^2_map(app^1_plus(app^1_s(0())),xs)
   #6: #app(inc(),_1) ->? #app^1_inc(_1)
   #7: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
   #8: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x)
   #9: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs)
   #10: #app(app^1_times(_1),_2) ->? #app^2_times(_1,_2)
   #11: #app^2_times(app^1_s(x),y) -> #app^2_plus(app^2_times(x,y),y)
   #12: #app^2_times(app^1_s(x),y) -> #app^2_times(x,y)
Number of SCCs: 3, DPs: 9
  SCC { #12 }
POLO(Sum)... succeeded.
      #app^1_inc	w: 0
      s 	w: 0
      app^1_cons	w: 0
      app^1_plus	w: 0
      #app^2_map	w: 0
      inc	w: 0
      #app^2_plus	w: 0
      app^2_plus	w: 0
      0 	w: 0
      double	w: 0
      times	w: 0
      nil	w: 0
      #app	w: 0
      map	w: 0
      app^1_double	w: 0
      plus	w: 0
      cons	w: 0
      app^1_inc	w: 0
      app^1_times	w: 0
      #app^2_times	w: x1
      #app^1_double	w: 0
      app^1_map	w: 0
      app^2_cons	w: 0
      app^1_s	w: x1 + 1
      app^2_map	w: 0
      app	w: 0
      app^2_times	w: 0
    USABLE RULES: { }
    Removed DPs: #12
Number of SCCs: 2, DPs: 8
  SCC { #1 }
POLO(Sum)... succeeded.
      #app^1_inc	w: 0
      s 	w: 0
      app^1_cons	w: 0
      app^1_plus	w: 0
      #app^2_map	w: 0
      inc	w: 0
      #app^2_plus	w: x1
      app^2_plus	w: 0
      0 	w: 0
      double	w: 0
      times	w: 0
      nil	w: 0
      #app	w: 0
      map	w: 0
      app^1_double	w: 0
      plus	w: 0
      cons	w: 0
      app^1_inc	w: 0
      app^1_times	w: 0
      #app^2_times	w: 0
      #app^1_double	w: 0
      app^1_map	w: 0
      app^2_cons	w: 0
      app^1_s	w: x1 + 1
      app^2_map	w: 0
      app	w: 0
      app^2_times	w: 0
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 7
  SCC { #2 #3 #5..9 }
POLO(Sum)... succeeded.
      #app^1_inc	w: 3
      s 	w: 0
      app^1_cons	w: 0
      app^1_plus	w: x1
      #app^2_map	w: x1 + 1
      inc	w: 4
      #app^2_plus	w: 0
      app^2_plus	w: 0
      0 	w: 1
      double	w: 4
      times	w: 0
      nil	w: 0
      #app	w: x1
      map	w: 0
      app^1_double	w: 0
      plus	w: 0
      cons	w: 0
      app^1_inc	w: 0
      app^1_times	w: x1
      #app^2_times	w: 0
      #app^1_double	w: 3
      app^1_map	w: x1 + 2
      app^2_cons	w: 1
      app^1_s	w: x1
      app^2_map	w: 0
      app	w: 0
      app^2_times	w: 0
    USABLE RULES: { }
    Removed DPs: #2 #3 #5..8
Number of SCCs: 1, DPs: 1
  SCC { #9 }
POLO(Sum)... succeeded.
      #app^1_inc	w: 3
      s 	w: 0
      app^1_cons	w: 0
      app^1_plus	w: 0
      #app^2_map	w: x2 + 1
      inc	w: 4
      #app^2_plus	w: 0
      app^2_plus	w: 0
      0 	w: 1
      double	w: 4
      times	w: 0
      nil	w: 0
      #app	w: 0
      map	w: 0
      app^1_double	w: 0
      plus	w: 0
      cons	w: 0
      app^1_inc	w: 0
      app^1_times	w: 0
      #app^2_times	w: 0
      #app^1_double	w: 3
      app^1_map	w: 2
      app^2_cons	w: x2 + 1
      app^1_s	w: 0
      app^2_map	w: 0
      app	w: 0
      app^2_times	w: 0
    USABLE RULES: { }
    Removed DPs: #9
Number of SCCs: 0, DPs: 0