/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(nil(),k) -> k
    2: app(l,nil()) -> l
    3: app(cons(x,l),k) -> cons(x,app(l,k))
    4: sum(cons(x,nil())) -> cons(x,nil())
    5: sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
    6: a(h(),h(),x) -> s(x)
    7: a(x,s(y),h()) -> a(x,y,s(h()))
    8: a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
    9: a(s(x),h(),z) -> a(x,z,z)
Number of strict rules: 9
Direct poly ... failed.
Freezing sum
1: app(nil(),k) -> k
2: app(l,nil()) -> l
3: app(cons(x,l),k) -> cons(x,app(l,k))
4: sum❆1_cons(x,nil()) -> cons(x,nil())
5: sum❆1_cons(x,cons(y,l)) -> sum❆1_cons(a(x,y,h()),l)
6: a(h(),h(),x) -> s(x)
7: a(x,s(y),h()) -> a(x,y,s(h()))
8: a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
9: a(s(x),h(),z) -> a(x,z,z)
10: sum(cons(_1,_2)) ->= sum❆1_cons(_1,_2)
Number of strict rules: 9
Direct poly ... failed.
Dependency Pairs:
   #1: #a(s(x),h(),z) -> #a(x,z,z)
   #2: #a(x,s(y),h()) -> #a(x,y,s(h()))
   #3: #sum(cons(_1,_2)) ->? #sum❆1_cons(_1,_2)
   #4: #sum❆1_cons(x,cons(y,l)) -> #sum❆1_cons(a(x,y,h()),l)
   #5: #sum❆1_cons(x,cons(y,l)) -> #a(x,y,h())
   #6: #app(cons(x,l),k) -> #app(l,k)
   #7: #a(x,s(y),s(z)) -> #a(x,y,a(x,s(y),z))
   #8: #a(x,s(y),s(z)) -> #a(x,s(y),z)
Number of SCCs: 3, DPs: 6
	SCC { #6 }
Sum... succeeded.
  h()		w: (0)
  a(x1,x2,x3)		w: (0)
  s(x1)		w: (0)
  sum❆1_cons(x1,x2)		w: (0)
  #sum❆1_cons(x1,x2)		w: (0)
  sum(x1)		w: (0)
  nil()		w: (0)
  #app(x1,x2)		w: (x1)
  cons(x1,x2)		w: (1 + x2)
  #a(x1,x2,x3)		w: (0)
  #sum(x1)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #6
Number of SCCs: 2, DPs: 5
	SCC { #4 }
Sum... succeeded.
  h()		w: (1)
  a(x1,x2,x3)		w: (1 + x2 + x1)
  s(x1)		w: (7723 + x1)
  sum❆1_cons(x1,x2)		w: (0)
  #sum❆1_cons(x1,x2)		w: (21238 + x2)
  sum(x1)		w: (0)
  nil()		w: (0)
  #app(x1,x2)		w: (0)
  cons(x1,x2)		w: (1 + x2 + x1)
  #a(x1,x2,x3)		w: (0)
  #sum(x1)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #4
Number of SCCs: 1, DPs: 4
	SCC { #1 #2 #7 #8 }
Sum... succeeded.
  h()		w: (1)
  a(x1,x2,x3)		w: (1 + x2 + x1)
  s(x1)		w: (7723 + x1)
  sum❆1_cons(x1,x2)		w: (0)
  #sum❆1_cons(x1,x2)		w: (21238)
  sum(x1)		w: (0)
  nil()		w: (0)
  #app(x1,x2)		w: (0)
  cons(x1,x2)		w: (1)
  #a(x1,x2,x3)		w: (x1)
  #sum(x1)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 3
	SCC { #2 #7 #8 }
Sum... succeeded.
  h()		w: (1143)
  a(x1,x2,x3)		w: (x2 + x1)
  s(x1)		w: (2287 + x1)
  sum❆1_cons(x1,x2)		w: (0)
  #sum❆1_cons(x1,x2)		w: (21238)
  sum(x1)		w: (0)
  nil()		w: (0)
  #app(x1,x2)		w: (0)
  cons(x1,x2)		w: (1)
  #a(x1,x2,x3)		w: (28100 + x2 + x1)
  #sum(x1)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #2 #7
Number of SCCs: 1, DPs: 1
	SCC { #8 }
Sum... Max... succeeded.
  h()		w: (0)
  a(x1,x2,x3)		w: (0)
  s(x1)		w: (1 + x1)
  sum❆1_cons(x1,x2)		w: (0)
  #sum❆1_cons(x1,x2)		w: (0)
  sum(x1)		w: (0)
  nil()		w: (0)
  #app(x1,x2)		w: (0)
  cons(x1,x2)		w: (0)
  #a(x1,x2,x3)		w: (max{1 + x3, 0})
  #sum(x1)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 0, DPs: 0