/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(append(),nil()),ys) -> ys
    2: app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
    3: app(app(flatwith(),f),app(leaf(),x)) -> app(app(cons(),app(f,x)),nil())
    4: app(app(flatwith(),f),app(node(),xs)) -> app(app(flatwithsub(),f),xs)
    5: app(app(flatwithsub(),f),nil()) -> nil()
    6: app(app(flatwithsub(),f),app(app(cons(),x),xs)) -> app(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs))
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Uncurrying app
1: app^2_append(nil(),ys) -> ys
2: app^2_append(app^2_cons(x,xs),ys) -> app^2_cons(x,app^2_append(xs,ys))
3: app^2_flatwith(f,app^1_leaf(x)) -> app^2_cons(app(f,x),nil())
4: app^2_flatwith(f,app^1_node(xs)) -> app^2_flatwithsub(f,xs)
5: app^2_flatwithsub(f,nil()) -> nil()
6: app^2_flatwithsub(f,app^2_cons(x,xs)) -> app^2_append(app^2_flatwith(f,x),app^2_flatwithsub(f,xs))
7: app(flatwithsub(),_1) ->= app^1_flatwithsub(_1)
8: app(app^1_flatwithsub(_1),_2) ->= app^2_flatwithsub(_1,_2)
9: app(append(),_1) ->= app^1_append(_1)
10: app(app^1_append(_1),_2) ->= app^2_append(_1,_2)
11: app(cons(),_1) ->= app^1_cons(_1)
12: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
13: app(flatwith(),_1) ->= app^1_flatwith(_1)
14: app(app^1_flatwith(_1),_2) ->= app^2_flatwith(_1,_2)
15: app(leaf(),_1) ->= app^1_leaf(_1)
16: app(node(),_1) ->= app^1_node(_1)
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #app^2_append(app^2_cons(x,xs),ys) -> #app^2_append(xs,ys)
   #2: #app^2_flatwithsub(f,app^2_cons(x,xs)) -> #app^2_append(app^2_flatwith(f,x),app^2_flatwithsub(f,xs))
   #3: #app^2_flatwithsub(f,app^2_cons(x,xs)) -> #app^2_flatwith(f,x)
   #4: #app^2_flatwithsub(f,app^2_cons(x,xs)) -> #app^2_flatwithsub(f,xs)
   #5: #app(app^1_flatwith(_1),_2) ->? #app^2_flatwith(_1,_2)
   #6: #app(app^1_append(_1),_2) ->? #app^2_append(_1,_2)
   #7: #app^2_flatwith(f,app^1_leaf(x)) -> #app(f,x)
   #8: #app(app^1_flatwithsub(_1),_2) ->? #app^2_flatwithsub(_1,_2)
   #9: #app^2_flatwith(f,app^1_node(xs)) -> #app^2_flatwithsub(f,xs)
Number of SCCs: 2, DPs: 7
  SCC { #1 }
POLO(Sum)... succeeded.
      flatwithsub	w: 0
      app^1_flatwithsub	w: 0
      flatwith	w: 0
      app^1_cons	w: 0
      app^2_flatwithsub	w: 0
      app^1_flatwith	w: 0
      app^1_append	w: 0
      #app^2_flatwithsub	w: 0
      #app^2_append	w: x1
      append	w: 0
      nil	w: 0
      #app	w: 0
      #app^2_flatwith	w: 0
      cons	w: 0
      app^2_flatwith	w: 0
      leaf	w: 0
      app^2_cons	w: x2 + 1
      node	w: 0
      app^2_append	w: 0
      app^1_leaf	w: 0
      app	w: 0
      app^1_node	w: 0
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 6
  SCC { #3..5 #7..9 }
POLO(Sum)... succeeded.
      flatwithsub	w: 0
      app^1_flatwithsub	w: 1
      flatwith	w: 0
      app^1_cons	w: 0
      app^2_flatwithsub	w: 0
      app^1_flatwith	w: 1
      app^1_append	w: 0
      #app^2_flatwithsub	w: x2
      #app^2_append	w: 0
      append	w: 0
      nil	w: 0
      #app	w: x2 + 1
      #app^2_flatwith	w: x2
      cons	w: 0
      app^2_flatwith	w: 0
      leaf	w: 0
      app^2_cons	w: x1 + x2 + 1
      node	w: 0
      app^2_append	w: 0
      app^1_leaf	w: x1 + 2
      app	w: 0
      app^1_node	w: x1 + 1
    USABLE RULES: { }
    Removed DPs: #3..5 #7..9
Number of SCCs: 0, DPs: 0