/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(),app(g(),x)) -> app(g(),app(f(),app(f(),x)))
    2: app(f(),app(h(),x)) -> app(h(),app(g(),x))
    3: app(app(map(),fun),nil()) -> nil()
    4: app(app(map(),fun),app(app(cons(),x),xs)) -> app(app(cons(),app(fun,x)),app(app(map(),fun),xs))
    5: app(app(filter(),fun),nil()) -> nil()
    6: app(app(filter(),fun),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(fun,x)),fun),x),xs)
    7: app(app(app(app(filter2(),true()),fun),x),xs) -> app(app(cons(),x),app(app(filter(),fun),xs))
    8: app(app(app(app(filter2(),false()),fun),x),xs) -> app(app(filter(),fun),xs)
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Uncurrying app
1: app^1_f(app^1_g(x)) -> app^1_g(app^1_f(app^1_f(x)))
2: app^1_f(app^1_h(x)) -> app^1_h(app^1_g(x))
3: app^2_map(fun,nil()) -> nil()
4: app^2_map(fun,app^2_cons(x,xs)) -> app^2_cons(app(fun,x),app^2_map(fun,xs))
5: app^2_filter(fun,nil()) -> nil()
6: app^2_filter(fun,app^2_cons(x,xs)) -> app^4_filter2(app(fun,x),fun,x,xs)
7: app^4_filter2(true(),fun,x,xs) -> app^2_cons(x,app^2_filter(fun,xs))
8: app^4_filter2(false(),fun,x,xs) -> app^2_filter(fun,xs)
9: app(h(),_1) ->= app^1_h(_1)
10: app(cons(),_1) ->= app^1_cons(_1)
11: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
12: app(filter(),_1) ->= app^1_filter(_1)
13: app(app^1_filter(_1),_2) ->= app^2_filter(_1,_2)
14: app(map(),_1) ->= app^1_map(_1)
15: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
16: app(g(),_1) ->= app^1_g(_1)
17: app(f(),_1) ->= app^1_f(_1)
18: app(filter2(),_1) ->= app^1_filter2(_1)
19: app(app^1_filter2(_1),_2) ->= app^2_filter2(_1,_2)
20: app(app^2_filter2(_1,_2),_3) ->= app^3_filter2(_1,_2,_3)
21: app(app^3_filter2(_1,_2,_3),_4) ->= app^4_filter2(_1,_2,_3,_4)
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #app^2_filter(fun,app^2_cons(x,xs)) -> #app^4_filter2(app(fun,x),fun,x,xs)
   #2: #app^2_filter(fun,app^2_cons(x,xs)) -> #app(fun,x)
   #3: #app(app^1_filter(_1),_2) ->? #app^2_filter(_1,_2)
   #4: #app^4_filter2(true(),fun,x,xs) -> #app^2_filter(fun,xs)
   #5: #app(f(),_1) ->? #app^1_f(_1)
   #6: #app(app^3_filter2(_1,_2,_3),_4) ->? #app^4_filter2(_1,_2,_3,_4)
   #7: #app^1_f(app^1_g(x)) -> #app^1_f(app^1_f(x))
   #8: #app^1_f(app^1_g(x)) -> #app^1_f(x)
   #9: #app^4_filter2(false(),fun,x,xs) -> #app^2_filter(fun,xs)
   #10: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
   #11: #app^2_map(fun,app^2_cons(x,xs)) -> #app(fun,x)
   #12: #app^2_map(fun,app^2_cons(x,xs)) -> #app^2_map(fun,xs)
Number of SCCs: 2, DPs: 10
  SCC { #7 #8 }
POLO(Sum)... succeeded.
      h 	w: 0
      app^1_cons	w: 0
      #app^2_map	w: 0
      app^2_filter2	w: 0
      app^4_filter2	w: 0
      false	w: 0
      app^1_h	w: 1
      #app^1_f	w: x1
      app^1_filter2	w: 0
      true	w: 0
      f 	w: 0
      filter2	w: 0
      #app^4_filter2	w: 0
      nil	w: 0
      #app	w: 0
      map	w: 0
      app^1_filter	w: 0
      cons	w: 0
      app^1_f	w: x1
      filter	w: 0
      app^3_filter2	w: 0
      app^2_filter	w: 0
      g 	w: 0
      app^1_map	w: 0
      app^2_cons	w: 0
      app^2_map	w: 0
      #app^2_filter	w: 0
      app	w: 0
      app^1_g	w: x1 + 1
    USABLE RULES: { 1 2 }
    Removed DPs: #7 #8
Number of SCCs: 1, DPs: 8
  SCC { #2..4 #6 #9..12 }
POLO(Sum)... succeeded.
      h 	w: 0
      app^1_cons	w: 0
      #app^2_map	w: x1 + 1
      app^2_filter2	w: 0
      app^4_filter2	w: 0
      false	w: 2
      app^1_h	w: 1
      #app^1_f	w: x1
      app^1_filter2	w: 0
      true	w: 2
      f 	w: 0
      filter2	w: 0
      #app^4_filter2	w: x1 + x2
      nil	w: 0
      #app	w: x1
      map	w: 0
      app^1_filter	w: x1 + 2
      cons	w: 0
      app^1_f	w: x1
      filter	w: 0
      app^3_filter2	w: x1 + x2 + x3 + 1
      app^2_filter	w: 0
      g 	w: 0
      app^1_map	w: x1 + 2
      app^2_cons	w: 1
      app^2_map	w: 0
      #app^2_filter	w: x1 + 1
      app	w: 0
      app^1_g	w: x1 + 1
    USABLE RULES: { 1 2 }
    Removed DPs: #2..4 #6 #9..11
Number of SCCs: 1, DPs: 1
  SCC { #12 }
POLO(Sum)... succeeded.
      h 	w: 0
      app^1_cons	w: 0
      #app^2_map	w: x2 + 1
      app^2_filter2	w: 0
      app^4_filter2	w: 0
      false	w: 2
      app^1_h	w: 1
      #app^1_f	w: x1
      app^1_filter2	w: 0
      true	w: 2
      f 	w: 0
      filter2	w: 0
      #app^4_filter2	w: 0
      nil	w: 0
      #app	w: 0
      map	w: 0
      app^1_filter	w: 2
      cons	w: 0
      app^1_f	w: x1
      filter	w: 0
      app^3_filter2	w: 1
      app^2_filter	w: 0
      g 	w: 0
      app^1_map	w: 2
      app^2_cons	w: x2 + 1
      app^2_map	w: 0
      #app^2_filter	w: 1
      app	w: 0
      app^1_g	w: x1 + 1
    USABLE RULES: { 1 2 }
    Removed DPs: #12
Number of SCCs: 0, DPs: 0