/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(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 poly ... failed.
Freezing 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 poly ... 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 }
Sum... succeeded.
  app❆2_forall(x1,x2)		w: (0)
  app❆1_and(x1)		w: (0)
  and()		w: (0)
  false()		w: (0)
  app❆2_and(x1,x2)		w: (0)
  app❆1_forall(x1)		w: (1)
  #app❆2_forall(x1,x2)		w: (x2)
  true()		w: (0)
  app❆1_or(x1)		w: (0)
  app❆1_forsome(x1)		w: (1)
  forsome()		w: (0)
  #app❆2_or(x1,x2)		w: (0)
  forall()		w: (0)
  #app❆2_and(x1,x2)		w: (0)
  #app❆2_forsome(x1,x2)		w: (x2)
  app❆2_or(x1,x2)		w: (0)
  nil()		w: (0)
  or()		w: (0)
  #app(x1,x2)		w: (1 + x2)
  app❆2_forsome(x1,x2)		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (40 + x2 + x1)
  app❆1_cons(x1)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #2 #4 #5 #8..10
Number of SCCs: 0, DPs: 0