/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(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(minus(),x),0()) -> x
    4: app(app(minus(),app(s(),x)),app(s(),y)) -> app(app(minus(),app(p(),app(s(),x))),app(p(),app(s(),y)))
    5: app(p(),app(s(),x)) -> x
    6: app(app(div(),0()),app(s(),y)) -> 0()
    7: app(app(div(),app(s(),x)),app(s(),y)) -> app(s(),app(app(div(),app(app(minus(),x),y)),app(s(),y)))
Number of strict rules: 7
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_minus(x,0()) -> x
4: app^2_minus(app^1_s(x),app^1_s(y)) -> app^2_minus(app^1_p(app^1_s(x)),app^1_p(app^1_s(y)))
5: app^1_p(app^1_s(x)) -> x
6: app^2_div(0(),app^1_s(y)) -> 0()
7: app^2_div(app^1_s(x),app^1_s(y)) -> app^1_s(app^2_div(app^2_minus(x,y),app^1_s(y)))
8: app(p(),_1) ->= app^1_p(_1)
9: app(cons(),_1) ->= app^1_cons(_1)
10: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
11: app(div(),_1) ->= app^1_div(_1)
12: app(app^1_div(_1),_2) ->= app^2_div(_1,_2)
13: app(s(),_1) ->= app^1_s(_1)
14: app(minus(),_1) ->= app^1_minus(_1)
15: app(app^1_minus(_1),_2) ->= app^2_minus(_1,_2)
16: app(map(),_1) ->= app^1_map(_1)
17: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
Number of strict rules: 7
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(app^1_div(_1),_2) ->? #app^2_div(_1,_2)
   #4: #app^2_div(app^1_s(x),app^1_s(y)) -> #app^2_div(app^2_minus(x,y),app^1_s(y))
   #5: #app^2_div(app^1_s(x),app^1_s(y)) -> #app^2_minus(x,y)
   #6: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
   #7: #app(p(),_1) ->? #app^1_p(_1)
   #8: #app(app^1_minus(_1),_2) ->? #app^2_minus(_1,_2)
   #9: #app^2_minus(app^1_s(x),app^1_s(y)) -> #app^2_minus(app^1_p(app^1_s(x)),app^1_p(app^1_s(y)))
   #10: #app^2_minus(app^1_s(x),app^1_s(y)) -> #app^1_p(app^1_s(x))
   #11: #app^2_minus(app^1_s(x),app^1_s(y)) -> #app^1_p(app^1_s(y))
Number of SCCs: 3, DPs: 5
  SCC { #4 }
POLO(Sum)... succeeded.
      app^1_div	w: 0
      #app^2_minus	w: 0
      s 	w: 0
      app^1_cons	w: 0
      #app^2_map	w: 0
      #app^1_p	w: 0
      minus	w: 0
      div	w: 0
      app^1_p	w: x1
      p 	w: 0
      0 	w: 1
      nil	w: 0
      #app	w: 0
      #app^2_div	w: x1
      app^2_minus	w: x1 + 1
      map	w: 0
      app^2_div	w: 0
      cons	w: 0
      app^1_minus	w: 0
      app^1_map	w: 0
      app^2_cons	w: 0
      app^1_s	w: x1 + 2
      app^2_map	w: 0
      app	w: 0
    USABLE RULES: { 3..5 }
    Removed DPs: #4
Number of SCCs: 2, DPs: 4
  SCC { #9 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      app^1_div	w: 0
      #app^2_minus	w: max(x1 - 1, 0)
      s 	w: 0
      app^1_cons	w: max(x1 - 1, 0)
      #app^2_map	w: 0
      #app^1_p	w: 0
      minus	w: 0
      div	w: 0
      app^1_p	w: max(x1 - 2, 0)
      p 	w: 0
      0 	w: 0
      nil	w: 0
      #app	w: 0
      #app^2_div	w: max(x2 - 1, 0)
      app^2_minus	w: max(x1 - 1, 0)
      map	w: 0
      app^2_div	w: max(x1 - 1, 0)
      cons	w: 0
      app^1_minus	w: max(x1 - 1, 0)
      app^1_map	w: max(x1 - 1, 0)
      app^2_cons	w: 0
      app^1_s	w: max(x1 + 2, 0)
      app^2_map	w: max(x1 - 1, 0)
      app	w: max(x1 - 1, 0)
    USABLE RULES: { 5 }
    Removed DPs: #9
Number of SCCs: 1, DPs: 3
  SCC { #1 #2 #6 }
POLO(Sum)... succeeded.
      app^1_div	w: 0
      #app^2_minus	w: 0
      s 	w: 0
      app^1_cons	w: 0
      #app^2_map	w: x2
      #app^1_p	w: 0
      minus	w: 0
      div	w: 0
      app^1_p	w: 0
      p 	w: 0
      0 	w: 0
      nil	w: 0
      #app	w: x2 + 1
      #app^2_div	w: 0
      app^2_minus	w: x1 + x2 + 1
      map	w: 0
      app^2_div	w: 0
      cons	w: 0
      app^1_minus	w: 0
      app^1_map	w: 1
      app^2_cons	w: x1 + x2 + 2
      app^1_s	w: 2
      app^2_map	w: 0
      app	w: 0
    USABLE RULES: { 3 }
    Removed DPs: #1 #2 #6
Number of SCCs: 0, DPs: 0