/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(plus(),0()),y) -> y
    2: app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
    3: app(app(sumwith(),f),nil()) -> nil()
    4: app(app(sumwith(),f),app(app(cons(),x),xs)) -> app(app(plus(),app(f,x)),app(app(sumwith(),f),xs))
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying app
1: app^2_plus(0(),y) -> y
2: app^2_plus(app^1_s(x),y) -> app^1_s(app^2_plus(x,y))
3: app^2_sumwith(f,nil()) -> nil()
4: app^2_sumwith(f,app^2_cons(x,xs)) -> app^2_plus(app(f,x),app^2_sumwith(f,xs))
5: app(plus(),_1) ->= app^1_plus(_1)
6: app(app^1_plus(_1),_2) ->= app^2_plus(_1,_2)
7: app(cons(),_1) ->= app^1_cons(_1)
8: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
9: app(s(),_1) ->= app^1_s(_1)
10: app(sumwith(),_1) ->= app^1_sumwith(_1)
11: app(app^1_sumwith(_1),_2) ->= app^2_sumwith(_1,_2)
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #app^2_plus(app^1_s(x),y) -> #app^2_plus(x,y)
   #2: #app(app^1_plus(_1),_2) ->? #app^2_plus(_1,_2)
   #3: #app(app^1_sumwith(_1),_2) ->? #app^2_sumwith(_1,_2)
   #4: #app^2_sumwith(f,app^2_cons(x,xs)) -> #app^2_plus(app(f,x),app^2_sumwith(f,xs))
   #5: #app^2_sumwith(f,app^2_cons(x,xs)) -> #app(f,x)
   #6: #app^2_sumwith(f,app^2_cons(x,xs)) -> #app^2_sumwith(f,xs)
Number of SCCs: 2, DPs: 4
  SCC { #1 }
POLO(Sum)... succeeded.
      s 	w: 0
      app^1_cons	w: 0
      app^1_plus	w: 0
      app^1_sumwith	w: 0
      #app^2_plus	w: x1
      app^2_plus	w: 0
      0 	w: 0
      sumwith	w: 0
      nil	w: 0
      #app	w: 0
      app^2_sumwith	w: 0
      plus	w: 0
      #app^2_sumwith	w: 0
      cons	w: 0
      app^2_cons	w: 0
      app^1_s	w: x1 + 1
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 3
  SCC { #3 #5 #6 }
POLO(Sum)... succeeded.
      s 	w: 0
      app^1_cons	w: 0
      app^1_plus	w: 0
      app^1_sumwith	w: x1 + 2
      #app^2_plus	w: 0
      app^2_plus	w: 0
      0 	w: 0
      sumwith	w: 0
      nil	w: 0
      #app	w: x1
      app^2_sumwith	w: 0
      plus	w: 0
      #app^2_sumwith	w: x1 + 1
      cons	w: 0
      app^2_cons	w: 1
      app^1_s	w: 1
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #3 #5
Number of SCCs: 1, DPs: 1
  SCC { #6 }
POLO(Sum)... succeeded.
      s 	w: 0
      app^1_cons	w: 0
      app^1_plus	w: 0
      app^1_sumwith	w: 2
      #app^2_plus	w: 0
      app^2_plus	w: 0
      0 	w: 0
      sumwith	w: 0
      nil	w: 0
      #app	w: 0
      app^2_sumwith	w: 0
      plus	w: 0
      #app^2_sumwith	w: x2 + 1
      cons	w: 0
      app^2_cons	w: x2 + 1
      app^1_s	w: 1
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #6
Number of SCCs: 0, DPs: 0