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


--------------------------------------------------------------------------------


YES
Input TRS:
    1: app(app(map(),f),nil()) -> nil()
    2: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    3: app(app(le(),0()),y) -> true()
    4: app(app(le(),app(s(),x)),0()) -> false()
    5: app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
    6: app(app(maxlist(),x),app(app(cons(),y),ys)) -> app(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
    7: app(app(maxlist(),x),nil()) -> x
    8: app(height(),app(app(node(),x),xs)) -> app(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Uncurrying app
1: app^2_map(f,nil()) -> nil()
2: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs))
3: app^2_le(0(),y) -> true()
4: app^2_le(app^1_s(x),0()) -> false()
5: app^2_le(app^1_s(x),app^1_s(y)) -> app^2_le(x,y)
6: app^2_maxlist(x,app^2_cons(y,ys)) -> app^2_if(app^2_le(x,y),app^2_maxlist(y,ys))
7: app^2_maxlist(x,nil()) -> x
8: app^1_height(app^2_node(x,xs)) -> app^1_s(app^2_maxlist(0(),app^2_map(height(),xs)))
9: app(le(),_1) ->= app^1_le(_1)
10: app(app^1_le(_1),_2) ->= app^2_le(_1,_2)
11: app(if(),_1) ->= app^1_if(_1)
12: app(app^1_if(_1),_2) ->= app^2_if(_1,_2)
13: app(cons(),_1) ->= app^1_cons(_1)
14: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
15: app(s(),_1) ->= app^1_s(_1)
16: app(map(),_1) ->= app^1_map(_1)
17: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
18: app(maxlist(),_1) ->= app^1_maxlist(_1)
19: app(app^1_maxlist(_1),_2) ->= app^2_maxlist(_1,_2)
20: app(height(),_1) ->= app^1_height(_1)
21: app(node(),_1) ->= app^1_node(_1)
22: app(app^1_node(_1),_2) ->= app^2_node(_1,_2)
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x)
   #2: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs)
   #3: #app^2_maxlist(x,app^2_cons(y,ys)) -> #app^2_le(x,y)
   #4: #app^2_maxlist(x,app^2_cons(y,ys)) -> #app^2_maxlist(y,ys)
   #5: #app(height(),_1) ->? #app^1_height(_1)
   #6: #app(app^1_le(_1),_2) ->? #app^2_le(_1,_2)
   #7: #app^2_le(app^1_s(x),app^1_s(y)) -> #app^2_le(x,y)
   #8: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
   #9: #app(app^1_maxlist(_1),_2) ->? #app^2_maxlist(_1,_2)
   #10: #app^1_height(app^2_node(x,xs)) -> #app^2_maxlist(0(),app^2_map(height(),xs))
   #11: #app^1_height(app^2_node(x,xs)) -> #app^2_map(height(),xs)
Number of SCCs: 3, DPs: 7
  SCC { #4 }
POLO(Sum)... succeeded.
      le	w: 0
      s 	w: 0
      app^1_cons	w: 0
      app^1_height	w: 0
      #app^2_map	w: 0
      height	w: 0
      false	w: 0
      #app^2_le	w: 0
      #app^1_height	w: 0
      app^1_le	w: 0
      true	w: 0
      app^2_node	w: 0
      0 	w: 0
      if	w: 0
      nil	w: 0
      app^2_le	w: 0
      #app	w: 0
      map	w: 0
      maxlist	w: 0
      app^1_maxlist	w: 0
      cons	w: 0
      app^2_if	w: 0
      #app^2_maxlist	w: x2
      app^1_map	w: 0
      app^2_cons	w: x1 + x2 + 1
      app^2_maxlist	w: 0
      app^1_if	w: 0
      node	w: 0
      app^1_s	w: 0
      app^2_map	w: 0
      app	w: 0
      app^1_node	w: 0
    USABLE RULES: { }
    Removed DPs: #4
Number of SCCs: 2, DPs: 6
  SCC { #7 }
POLO(Sum)... succeeded.
      le	w: 0
      s 	w: 0
      app^1_cons	w: 0
      app^1_height	w: 0
      #app^2_map	w: 0
      height	w: 0
      false	w: 0
      #app^2_le	w: x2
      #app^1_height	w: 0
      app^1_le	w: 0
      true	w: 0
      app^2_node	w: 0
      0 	w: 0
      if	w: 0
      nil	w: 0
      app^2_le	w: 0
      #app	w: 0
      map	w: 0
      maxlist	w: 0
      app^1_maxlist	w: 0
      cons	w: 0
      app^2_if	w: 0
      #app^2_maxlist	w: 0
      app^1_map	w: 0
      app^2_cons	w: 1
      app^2_maxlist	w: 0
      app^1_if	w: 0
      node	w: 0
      app^1_s	w: x1 + 1
      app^2_map	w: 0
      app	w: 0
      app^1_node	w: 0
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 1, DPs: 5
  SCC { #1 #2 #5 #8 #11 }
POLO(Sum)... succeeded.
      le	w: 0
      s 	w: 0
      app^1_cons	w: 0
      app^1_height	w: 0
      #app^2_map	w: x1
      height	w: 1
      false	w: 0
      #app^2_le	w: 0
      #app^1_height	w: 1
      app^1_le	w: 0
      true	w: 0
      app^2_node	w: 1
      0 	w: 0
      if	w: 0
      nil	w: 0
      app^2_le	w: 0
      #app	w: x1
      map	w: 0
      maxlist	w: 0
      app^1_maxlist	w: 0
      cons	w: 0
      app^2_if	w: 0
      #app^2_maxlist	w: 0
      app^1_map	w: x1 + 1
      app^2_cons	w: 1
      app^2_maxlist	w: 0
      app^1_if	w: 0
      node	w: 0
      app^1_s	w: 1
      app^2_map	w: 0
      app	w: 0
      app^1_node	w: 0
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 1, DPs: 4
  SCC { #1 #2 #5 #11 }
POLO(Sum)... succeeded.
      le	w: 0
      s 	w: 0
      app^1_cons	w: 0
      app^1_height	w: 0
      #app^2_map	w: x1 + x2
      height	w: 1
      false	w: 0
      #app^2_le	w: 0
      #app^1_height	w: x1
      app^1_le	w: 0
      true	w: 0
      app^2_node	w: x2 + 2
      0 	w: 0
      if	w: 0
      nil	w: 0
      app^2_le	w: 0
      #app	w: x2 + 1
      map	w: 0
      maxlist	w: 0
      app^1_maxlist	w: 0
      cons	w: 0
      app^2_if	w: 0
      #app^2_maxlist	w: 0
      app^1_map	w: 1
      app^2_cons	w: x1 + x2 + 2
      app^2_maxlist	w: 0
      app^1_if	w: 0
      node	w: 0
      app^1_s	w: 1
      app^2_map	w: 0
      app	w: 0
      app^1_node	w: 0
    USABLE RULES: { }
    Removed DPs: #1 #2 #5 #11
Number of SCCs: 0, DPs: 0