/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(app(app(curry(),g),x),y) -> app(app(g,x),y)
    6: app(app(map(),f),nil()) -> nil()
    7: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    8: inc() -> app(map(),app(app(curry(),plus()),app(s(),0())))
    9: double() -> app(map(),app(app(curry(),times()),app(s(),app(s(),0()))))
Number of strict rules: 9
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^3_curry(g,x,y) -> app(app(g,x),y)
6: app^2_map(f,nil()) -> nil()
7: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs))
8: inc() -> app^1_map(app^2_curry(plus(),app^1_s(0())))
9: double() -> app^1_map(app^2_curry(times(),app^1_s(app^1_s(0()))))
10: app(plus(),_1) ->= app^1_plus(_1)
11: app(app^1_plus(_1),_2) ->= app^2_plus(_1,_2)
12: app(curry(),_1) ->= app^1_curry(_1)
13: app(app^1_curry(_1),_2) ->= app^2_curry(_1,_2)
14: app(app^2_curry(_1,_2),_3) ->= app^3_curry(_1,_2,_3)
15: app(cons(),_1) ->= app^1_cons(_1)
16: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
17: app(times(),_1) ->= app^1_times(_1)
18: app(app^1_times(_1),_2) ->= app^2_times(_1,_2)
19: app(s(),_1) ->= app^1_s(_1)
20: app(map(),_1) ->= app^1_map(_1)
21: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
Number of strict rules: 9
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #app^2_plus(app^1_s(x),y) -> #app^2_plus(x,y)
   #2: #app(app^1_plus(_1),_2) ->? #app^2_plus(_1,_2)
   #3: #app(app^2_curry(_1,_2),_3) ->? #app^3_curry(_1,_2,_3)
   #4: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x)
   #5: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs)
   #6: #app^3_curry(g,x,y) -> #app(app(g,x),y)
   #7: #app^3_curry(g,x,y) -> #app(g,x)
   #8: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
   #9: #app^2_times(app^1_s(x),y) -> #app^2_plus(app^2_times(x,y),y)
   #10: #app^2_times(app^1_s(x),y) -> #app^2_times(x,y)
   #11: #app(app^1_times(_1),_2) ->? #app^2_times(_1,_2)
Number of SCCs: 3, DPs: 8
  SCC { #10 }
POLO(Sum)... succeeded.
      s 	w: 0
      app^1_cons	w: 0
      app^1_plus	w: 0
      #app^2_map	w: 0
      curry	w: 0
      #inc	w: 0
      inc	w: 0
      #app^2_plus	w: 0
      #app^3_curry	w: 0
      app^2_plus	w: 0
      0 	w: 0
      #double	w: 0
      double	w: 0
      times	w: 0
      app^1_curry	w: 0
      nil	w: 0
      #app	w: 0
      app^2_curry	w: 0
      map	w: 0
      plus	w: 0
      cons	w: 0
      app^1_times	w: 0
      #app^2_times	w: x1
      app^3_curry	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: #10
Number of SCCs: 2, DPs: 7
  SCC { #1 }
POLO(Sum)... succeeded.
      s 	w: 0
      app^1_cons	w: 0
      app^1_plus	w: 0
      #app^2_map	w: 0
      curry	w: 0
      #inc	w: 0
      inc	w: 0
      #app^2_plus	w: x1
      #app^3_curry	w: 0
      app^2_plus	w: 0
      0 	w: 0
      #double	w: 0
      double	w: 0
      times	w: 0
      app^1_curry	w: 0
      nil	w: 0
      #app	w: 0
      app^2_curry	w: 0
      map	w: 0
      plus	w: 0
      cons	w: 0
      app^1_times	w: 0
      #app^2_times	w: 0
      app^3_curry	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: 6
  SCC { #3..8 }
POLO(Sum)... succeeded.
      s 	w: 1
      app^1_cons	w: 2
      app^1_plus	w: x1 + 1
      #app^2_map	w: x1 + 1
      curry	w: 1
      #inc	w: 0
      inc	w: 0
      #app^2_plus	w: 0
      #app^3_curry	w: x1 + x2 + 2
      app^2_plus	w: x2 + 2
      0 	w: 1
      #double	w: 0
      double	w: 0
      times	w: 1
      app^1_curry	w: x1 + 2
      nil	w: 1
      #app	w: x1
      app^2_curry	w: x1 + x2 + 3
      map	w: 1
      plus	w: 1
      cons	w: 1
      app^1_times	w: x1 + 1
      #app^2_times	w: 0
      app^3_curry	w: x1 + x2 + x3 + 2
      app^1_map	w: x1 + 2
      app^2_cons	w: 3
      app^1_s	w: x1
      app^2_map	w: 3
      app	w: x1 + x2 + 1
      app^2_times	w: x2 + 2
    USABLE RULES: { 1..7 10..21 }
    Removed DPs: #3 #4 #6..8
Number of SCCs: 1, DPs: 1
  SCC { #5 }
POLO(Sum)... succeeded.
      s 	w: 1
      app^1_cons	w: 2
      app^1_plus	w: x1 + 1
      #app^2_map	w: x2 + 1
      curry	w: 1
      #inc	w: 0
      inc	w: 0
      #app^2_plus	w: 0
      #app^3_curry	w: 2
      app^2_plus	w: x2 + 2
      0 	w: 1
      #double	w: 0
      double	w: 0
      times	w: 1
      app^1_curry	w: x1 + 2
      nil	w: 1
      #app	w: x1
      app^2_curry	w: x1 + x2 + 3
      map	w: 1
      plus	w: 1
      cons	w: 1
      app^1_times	w: x1 + 1
      #app^2_times	w: 0
      app^3_curry	w: x1 + x2 + x3 + 2
      app^1_map	w: x1 + 2
      app^2_cons	w: x2 + 1
      app^1_s	w: x1
      app^2_map	w: x1 + x2 + 3
      app	w: x1 + x2 + 1
      app^2_times	w: x2 + 2
    USABLE RULES: { 1..7 10..21 }
    Removed DPs: #5
Number of SCCs: 0, DPs: 0