/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(and(),true()),true()) -> true()
    2: app(app(and(),x),false()) -> false()
    3: app(app(and(),false()),y) -> false()
    4: app(app(or(),true()),y) -> true()
    5: app(app(or(),x),true()) -> true()
    6: app(app(or(),false()),false()) -> false()
    7: app(app(forall(),p),nil()) -> true()
    8: app(app(forall(),p),app(app(cons(),x),xs)) -> app(app(and(),app(p,x)),app(app(forall(),p),xs))
    9: app(app(forsome(),p),nil()) -> false()
    10: app(app(forsome(),p),app(app(cons(),x),xs)) -> app(app(or(),app(p,x)),app(app(forsome(),p),xs))
Number of strict rules: 10
Direct POLO(bPol) ... failed.
Uncurrying app
1: app^2_and(true(),true()) -> true()
2: app^2_and(x,false()) -> false()
3: app^2_and(false(),y) -> false()
4: app^2_or(true(),y) -> true()
5: app^2_or(x,true()) -> true()
6: app^2_or(false(),false()) -> false()
7: app^2_forall(p,nil()) -> true()
8: app^2_forall(p,app^2_cons(x,xs)) -> app^2_and(app(p,x),app^2_forall(p,xs))
9: app^2_forsome(p,nil()) -> false()
10: app^2_forsome(p,app^2_cons(x,xs)) -> app^2_or(app(p,x),app^2_forsome(p,xs))
11: app(cons(),_1) ->= app^1_cons(_1)
12: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
13: app(or(),_1) ->= app^1_or(_1)
14: app(app^1_or(_1),_2) ->= app^2_or(_1,_2)
15: app(and(),_1) ->= app^1_and(_1)
16: app(app^1_and(_1),_2) ->= app^2_and(_1,_2)
17: app(forsome(),_1) ->= app^1_forsome(_1)
18: app(app^1_forsome(_1),_2) ->= app^2_forsome(_1,_2)
19: app(forall(),_1) ->= app^1_forall(_1)
20: app(app^1_forall(_1),_2) ->= app^2_forall(_1,_2)
Number of strict rules: 10
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #app(app^1_or(_1),_2) ->? #app^2_or(_1,_2)
   #2: #app(app^1_forall(_1),_2) ->? #app^2_forall(_1,_2)
   #3: #app^2_forsome(p,app^2_cons(x,xs)) -> #app^2_or(app(p,x),app^2_forsome(p,xs))
   #4: #app^2_forsome(p,app^2_cons(x,xs)) -> #app(p,x)
   #5: #app^2_forsome(p,app^2_cons(x,xs)) -> #app^2_forsome(p,xs)
   #6: #app(app^1_and(_1),_2) ->? #app^2_and(_1,_2)
   #7: #app^2_forall(p,app^2_cons(x,xs)) -> #app^2_and(app(p,x),app^2_forall(p,xs))
   #8: #app^2_forall(p,app^2_cons(x,xs)) -> #app(p,x)
   #9: #app^2_forall(p,app^2_cons(x,xs)) -> #app^2_forall(p,xs)
   #10: #app(app^1_forsome(_1),_2) ->? #app^2_forsome(_1,_2)
Number of SCCs: 1, DPs: 6
  SCC { #2 #4 #5 #8..10 }
POLO(Sum)... succeeded.
      app^1_cons	w: 0
      and	w: 0
      app^1_forsome	w: x1 + 1
      false	w: 0
      #app^2_and	w: 0
      app^2_or	w: 0
      true	w: 0
      #app^2_or	w: 0
      forsome	w: 0
      forall	w: 0
      app^1_forall	w: x1 + 1
      #app^2_forall	w: x1 + x2
      nil	w: 0
      or	w: 0
      #app	w: x1 + x2
      app^1_and	w: 0
      app^2_and	w: 0
      #app^2_forsome	w: x1 + x2
      cons	w: 0
      app^1_or	w: 0
      app^2_forsome	w: 0
      app^2_cons	w: x1 + x2 + 1
      app^2_forall	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #2 #4 #5 #8..10
Number of SCCs: 0, DPs: 0