/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: min(0(),y) -> 0()
    2: min(s(x),0()) -> 0()
    3: min(s(x),s(y)) -> min(x,y)
    4: len(nil()) -> 0()
    5: len(cons(x,xs)) -> s(len(xs))
    6: sum(x,0()) -> x
    7: sum(x,s(y)) -> s(sum(x,y))
    8: le(0(),x) -> true()
    9: le(s(x),0()) -> false()
    10: le(s(x),s(y)) -> le(x,y)
    11: take(0(),cons(y,ys)) -> y
    12: take(s(x),cons(y,ys)) -> take(x,ys)
    13: addList(x,y) -> if(le(0(),min(len(x),len(y))),0(),x,y,nil())
    14: if(false(),c,x,y,z) -> z
    15: if(true(),c,xs,ys,z) -> if(le(s(c),min(len(xs),len(ys))),s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))
Number of strict rules: 15
Direct POLO(bPol) ... failed.
Uncurrying le
1: min(0(),y) -> 0()
2: min(s(x),0()) -> 0()
3: min(s(x),s(y)) -> min(x,y)
4: len(nil()) -> 0()
5: len(cons(x,xs)) -> s(len(xs))
6: sum(x,0()) -> x
7: sum(x,s(y)) -> s(sum(x,y))
8: le^1_0(x) -> true()
9: le^1_s(x,0()) -> false()
10: le^1_s(x,s(y)) -> le(x,y)
11: take(0(),cons(y,ys)) -> y
12: take(s(x),cons(y,ys)) -> take(x,ys)
13: addList(x,y) -> if(le^1_0(min(len(x),len(y))),0(),x,y,nil())
14: if(false(),c,x,y,z) -> z
15: if(true(),c,xs,ys,z) -> if(le^1_s(c,min(len(xs),len(ys))),s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))
16: le(0(),_1) ->= le^1_0(_1)
17: le(s(_1),_2) ->= le^1_s(_1,_2)
Number of strict rules: 15
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #addList(x,y) -> #if(le^1_0(min(len(x),len(y))),0(),x,y,nil())
   #2: #addList(x,y) -> #le^1_0(min(len(x),len(y)))
   #3: #addList(x,y) -> #min(len(x),len(y))
   #4: #addList(x,y) -> #len(x)
   #5: #addList(x,y) -> #len(y)
   #6: #take(s(x),cons(y,ys)) -> #take(x,ys)
   #7: #sum(x,s(y)) -> #sum(x,y)
   #8: #le^1_s(x,s(y)) -> #le(x,y)
   #9: #len(cons(x,xs)) -> #len(xs)
   #10: #le(s(_1),_2) ->? #le^1_s(_1,_2)
   #11: #le(0(),_1) ->? #le^1_0(_1)
   #12: #min(s(x),s(y)) -> #min(x,y)
   #13: #if(true(),c,xs,ys,z) -> #if(le^1_s(c,min(len(xs),len(ys))),s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))
   #14: #if(true(),c,xs,ys,z) -> #le^1_s(c,min(len(xs),len(ys)))
   #15: #if(true(),c,xs,ys,z) -> #min(len(xs),len(ys))
   #16: #if(true(),c,xs,ys,z) -> #len(xs)
   #17: #if(true(),c,xs,ys,z) -> #len(ys)
   #18: #if(true(),c,xs,ys,z) -> #sum(take(c,xs),take(c,ys))
   #19: #if(true(),c,xs,ys,z) -> #take(c,xs)
   #20: #if(true(),c,xs,ys,z) -> #take(c,ys)
Number of SCCs: 5, DPs: 6
  SCC { #9 }
POLO(Sum)... succeeded.
      #le^1_s	w: 0
      le	w: 0
      le^1_s	w: 0
      #len	w: x1
      s 	w: 0
      #le	w: 0
      #take	w: 0
      #le^1_0	w: 0
      take	w: 0
      false	w: 0
      #min	w: 0
      addList	w: 0
      true	w: 0
      sum	w: 0
      0 	w: 0
      if	w: 0
      nil	w: 0
      min	w: 0
      cons	w: x2 + 1
      le^1_0	w: 0
      #if	w: 0
      #sum	w: 0
      #addList	w: 0
      len	w: 0
    USABLE RULES: { }
    Removed DPs: #9
Number of SCCs: 4, DPs: 5
  SCC { #7 }
POLO(Sum)... succeeded.
      #le^1_s	w: 0
      le	w: 0
      le^1_s	w: 0
      #len	w: 0
      s 	w: x1 + 1
      #le	w: 0
      #take	w: 0
      #le^1_0	w: 0
      take	w: 0
      false	w: 0
      #min	w: 0
      addList	w: 0
      true	w: 0
      sum	w: 0
      0 	w: 0
      if	w: 0
      nil	w: 0
      min	w: 0
      cons	w: 1
      le^1_0	w: 0
      #if	w: 0
      #sum	w: x2
      #addList	w: 0
      len	w: 0
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 3, DPs: 4
  SCC { #12 }
POLO(Sum)... succeeded.
      #le^1_s	w: 0
      le	w: 0
      le^1_s	w: 0
      #len	w: 0
      s 	w: x1 + 1
      #le	w: 0
      #take	w: 0
      #le^1_0	w: 0
      take	w: 0
      false	w: 0
      #min	w: x2
      addList	w: 0
      true	w: 0
      sum	w: 0
      0 	w: 0
      if	w: 0
      nil	w: 0
      min	w: 0
      cons	w: 1
      le^1_0	w: 0
      #if	w: 0
      #sum	w: 0
      #addList	w: 0
      len	w: 0
    USABLE RULES: { }
    Removed DPs: #12
Number of SCCs: 2, DPs: 3
  SCC { #6 }
POLO(Sum)... succeeded.
      #le^1_s	w: 0
      le	w: 0
      le^1_s	w: 0
      #len	w: 0
      s 	w: 1
      #le	w: 0
      #take	w: x2
      #le^1_0	w: 0
      take	w: 0
      false	w: 0
      #min	w: 0
      addList	w: 0
      true	w: 0
      sum	w: 0
      0 	w: 0
      if	w: 0
      nil	w: 0
      min	w: 0
      cons	w: x2 + 1
      le^1_0	w: 0
      #if	w: 0
      #sum	w: 0
      #addList	w: 0
      len	w: 0
    USABLE RULES: { }
    Removed DPs: #6
Number of SCCs: 1, DPs: 2
  SCC { #8 #10 }
POLO(Sum)... succeeded.
      #le^1_s	w: x2
      le	w: 0
      le^1_s	w: 0
      #len	w: 0
      s 	w: x1 + 2
      #le	w: x2 + 1
      #take	w: 0
      #le^1_0	w: 0
      take	w: 0
      false	w: 0
      #min	w: 0
      addList	w: 0
      true	w: 0
      sum	w: 0
      0 	w: 0
      if	w: 0
      nil	w: 0
      min	w: 0
      cons	w: 1
      le^1_0	w: 0
      #if	w: 0
      #sum	w: 0
      #addList	w: 0
      len	w: 0
    USABLE RULES: { }
    Removed DPs: #8 #10
Number of SCCs: 0, DPs: 0