/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(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))
Number of strict rules: 2
Direct poly ... failed.
Freezing 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(cons(),_1) ->= app❆1_cons(_1)
4: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
5: app(map(),_1) ->= app❆1_map(_1)
6: app(app❆1_map(_1),_2) ->= app❆2_map(_1,_2)
Number of strict rules: 2
Direct poly ... 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_map(_1),_2) ->? #app❆2_map(_1,_2)
Number of SCCs: 1, DPs: 3
	SCC { #1..3 }
Sum... succeeded.
  #app❆2_map(x1,x2)		w: (1 + x1)
  app❆1_map(x1)		w: (2 + x1)
  app❆2_map(x1,x2)		w: (0)
  nil()		w: (0)
  #app(x1,x2)		w: (x1)
  map()		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (1)
  app❆1_cons(x1)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1 #3
Number of SCCs: 1, DPs: 1
	SCC { #2 }
Sum... succeeded.
  #app❆2_map(x1,x2)		w: (1 + x2)
  app❆1_map(x1)		w: (2)
  app❆2_map(x1,x2)		w: (0)
  nil()		w: (0)
  #app(x1,x2)		w: (0)
  map()		w: (0)
  cons()		w: (0)
  app❆2_cons(x1,x2)		w: (1 + x2)
  app❆1_cons(x1)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0