/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: 0(\#()) -> \#()
    2: +(x,\#()) -> x
    3: +(\#(),x) -> x
    4: +(0(x),0(y)) -> 0(+(x,y))
    5: +(0(x),1(y)) -> 1(+(x,y))
    6: +(1(x),0(y)) -> 1(+(x,y))
    7: +(1(x),1(y)) -> 0(+(+(x,y),1(\#())))
    8: +(+(x,y),z) -> +(x,+(y,z))
    9: *(\#(),x) -> \#()
    10: *(0(x),y) -> 0(*(x,y))
    11: *(1(x),y) -> +(0(*(x,y)),y)
    12: *(*(x,y),z) -> *(x,*(y,z))
    13: *(x,+(y,z)) -> +(*(x,y),*(x,z))
    14: app(nil(),l) -> l
    15: app(cons(x,l1),l2) -> cons(x,app(l1,l2))
    16: sum(nil()) -> 0(\#())
    17: sum(cons(x,l)) -> +(x,sum(l))
    18: sum(app(l1,l2)) -> +(sum(l1),sum(l2))
    19: prod(nil()) -> 1(\#())
    20: prod(cons(x,l)) -> *(x,prod(l))
    21: prod(app(l1,l2)) -> *(prod(l1),prod(l2))
Number of strict rules: 21
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #+(1(x),0(y)) -> #+(x,y)
   #2: #*(x,+(y,z)) -> #+(*(x,y),*(x,z))
   #3: #*(x,+(y,z)) -> #*(x,y)
   #4: #*(x,+(y,z)) -> #*(x,z)
   #5: #*(1(x),y) -> #+(0(*(x,y)),y)
   #6: #*(1(x),y) -> #0(*(x,y))
   #7: #*(1(x),y) -> #*(x,y)
   #8: #*(*(x,y),z) -> #*(x,*(y,z))
   #9: #*(*(x,y),z) -> #*(y,z)
   #10: #prod(cons(x,l)) -> #*(x,prod(l))
   #11: #prod(cons(x,l)) -> #prod(l)
   #12: #+(1(x),1(y)) -> #0(+(+(x,y),1(\#())))
   #13: #+(1(x),1(y)) -> #+(+(x,y),1(\#()))
   #14: #+(1(x),1(y)) -> #+(x,y)
   #15: #*(0(x),y) -> #0(*(x,y))
   #16: #*(0(x),y) -> #*(x,y)
   #17: #+(0(x),1(y)) -> #+(x,y)
   #18: #sum(cons(x,l)) -> #+(x,sum(l))
   #19: #sum(cons(x,l)) -> #sum(l)
   #20: #prod(app(l1,l2)) -> #*(prod(l1),prod(l2))
   #21: #prod(app(l1,l2)) -> #prod(l1)
   #22: #prod(app(l1,l2)) -> #prod(l2)
   #23: #sum(nil()) -> #0(\#())
   #24: #+(+(x,y),z) -> #+(x,+(y,z))
   #25: #+(+(x,y),z) -> #+(y,z)
   #26: #app(cons(x,l1),l2) -> #app(l1,l2)
   #27: #+(0(x),0(y)) -> #0(+(x,y))
   #28: #+(0(x),0(y)) -> #+(x,y)
   #29: #sum(app(l1,l2)) -> #+(sum(l1),sum(l2))
   #30: #sum(app(l1,l2)) -> #sum(l1)
   #31: #sum(app(l1,l2)) -> #sum(l2)
Number of SCCs: 5, DPs: 20
	SCC { #26 }
Sum... succeeded.
  #0(x1)		w: (0)
  1(x1)		w: (0)
  prod(x1)		w: (0)
  #prod(x1)		w: (0)
  #*(x1,x2)		w: (0)
  \#()		w: (0)
  sum(x1)		w: (0)
  0(x1)		w: (0)
  nil()		w: (0)
  #app(x1,x2)		w: (x1)
  cons(x1,x2)		w: (1 + x2)
  +(x1,x2)		w: (0)
  #sum(x1)		w: (0)
  #+(x1,x2)		w: (0)
  *(x1,x2)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #26
Number of SCCs: 4, DPs: 19
	SCC { #19 #30 #31 }
Sum... succeeded.
  #0(x1)		w: (0)
  1(x1)		w: (0)
  prod(x1)		w: (0)
  #prod(x1)		w: (0)
  #*(x1,x2)		w: (0)
  \#()		w: (0)
  sum(x1)		w: (0)
  0(x1)		w: (0)
  nil()		w: (0)
  #app(x1,x2)		w: (0)
  cons(x1,x2)		w: (1 + x2)
  +(x1,x2)		w: (0)
  #sum(x1)		w: (x1)
  #+(x1,x2)		w: (0)
  *(x1,x2)		w: (0)
  app(x1,x2)		w: (1 + x2 + x1)
    USABLE RULES: { }
    Removed DPs: #19 #30 #31
Number of SCCs: 3, DPs: 16
	SCC { #11 #21 #22 }
Sum... succeeded.
  #0(x1)		w: (0)
  1(x1)		w: (0)
  prod(x1)		w: (0)
  #prod(x1)		w: (x1)
  #*(x1,x2)		w: (0)
  \#()		w: (0)
  sum(x1)		w: (0)
  0(x1)		w: (0)
  nil()		w: (0)
  #app(x1,x2)		w: (0)
  cons(x1,x2)		w: (1 + x2)
  +(x1,x2)		w: (0)
  #sum(x1)		w: (0)
  #+(x1,x2)		w: (0)
  *(x1,x2)		w: (0)
  app(x1,x2)		w: (1 + x2 + x1)
    USABLE RULES: { }
    Removed DPs: #11 #21 #22
Number of SCCs: 2, DPs: 13
	SCC { #3 #4 #7..9 #16 }
Sum... succeeded.
  #0(x1)		w: (0)
  1(x1)		w: (2 + x1)
  prod(x1)		w: (0)
  #prod(x1)		w: (0)
  #*(x1,x2)		w: (x1)
  \#()		w: (2438)
  sum(x1)		w: (0)
  0(x1)		w: (1 + x1)
  nil()		w: (0)
  #app(x1,x2)		w: (0)
  cons(x1,x2)		w: (1)
  +(x1,x2)		w: (4 + x2)
  #sum(x1)		w: (0)
  #+(x1,x2)		w: (0)
  *(x1,x2)		w: (1 + x2 + x1)
  app(x1,x2)		w: (1)
    USABLE RULES: { }
    Removed DPs: #7..9 #16
Number of SCCs: 2, DPs: 9
	SCC { #3 #4 }
Sum... Max... succeeded.
  #0(x1)		w: (0)
  1(x1)		w: (0)
  prod(x1)		w: (0)
  #prod(x1)		w: (0)
  #*(x1,x2)		w: (max{1 + x2, 0})
  \#()		w: (0)
  sum(x1)		w: (0)
  0(x1)		w: (0)
  nil()		w: (0)
  #app(x1,x2)		w: (0)
  cons(x1,x2)		w: (0)
  +(x1,x2)		w: (max{7720 + x2, 1 + x1})
  #sum(x1)		w: (0)
  #+(x1,x2)		w: (0)
  *(x1,x2)		w: (0)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #3 #4
Number of SCCs: 1, DPs: 7
	SCC { #1 #13 #14 #17 #24 #25 #28 }
Sum... succeeded.
  #0(x1)		w: (0)
  1(x1)		w: (14684 + x1)
  prod(x1)		w: (0)
  #prod(x1)		w: (0)
  #*(x1,x2)		w: (0)
  \#()		w: (14682)
  sum(x1)		w: (0)
  0(x1)		w: (1 + x1)
  nil()		w: (0)
  #app(x1,x2)		w: (0)
  cons(x1,x2)		w: (1)
  +(x1,x2)		w: (1 + x2 + x1)
  #sum(x1)		w: (0)
  #+(x1,x2)		w: (x2 + x1)
  *(x1,x2)		w: (1 + x2)
  app(x1,x2)		w: (1)
    USABLE RULES: { 1..8 }
    Removed DPs: #1 #13 #14 #17 #25 #28
Number of SCCs: 1, DPs: 1
	SCC { #24 }
Sum... succeeded.
  #0(x1)		w: (0)
  1(x1)		w: (14684 + x1)
  prod(x1)		w: (0)
  #prod(x1)		w: (0)
  #*(x1,x2)		w: (0)
  \#()		w: (14682)
  sum(x1)		w: (0)
  0(x1)		w: (1 + x1)
  nil()		w: (0)
  #app(x1,x2)		w: (0)
  cons(x1,x2)		w: (1)
  +(x1,x2)		w: (1 + x2 + x1)
  #sum(x1)		w: (0)
  #+(x1,x2)		w: (18457 + x1)
  *(x1,x2)		w: (1 + x2)
  app(x1,x2)		w: (1)
    USABLE RULES: { 1..8 }
    Removed DPs: #24
Number of SCCs: 0, DPs: 0