/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: plus(x,0()) -> x
    2: plus(0(),y) -> y
    3: plus(s(x),y) -> s(plus(x,y))
    4: times(0(),y) -> 0()
    5: times(s(0()),y) -> y
    6: times(s(x),y) -> plus(y,times(x,y))
    7: div(0(),y) -> 0()
    8: div(x,y) -> quot(x,y,y)
    9: quot(0(),s(y),z) -> 0()
    10: quot(s(x),s(y),z) -> quot(x,y,z)
    11: quot(x,0(),s(z)) -> s(div(x,s(z)))
    12: div(div(x,y),z) -> div(x,times(y,z))
Number of strict rules: 12
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #times(s(x),y) -> #plus(y,times(x,y))
   #2: #times(s(x),y) -> #times(x,y)
   #3: #quot(x,0(),s(z)) -> #div(x,s(z))
   #4: #div(div(x,y),z) -> #div(x,times(y,z))
   #5: #div(div(x,y),z) -> #times(y,z)
   #6: #quot(s(x),s(y),z) -> #quot(x,y,z)
   #7: #plus(s(x),y) -> #plus(x,y)
   #8: #div(x,y) -> #quot(x,y,y)
Number of SCCs: 3, DPs: 6
	SCC { #2 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  #plus(x1,x2)		w: (0)
  div(x1,x2)		w: (0)
  #times(x1,x2)		w: (x1)
  0()		w: (0)
  quot(x1,x2,x3)		w: (0)
  times(x1,x2)		w: (0)
  plus(x1,x2)		w: (0)
  #quot(x1,x2,x3)		w: (0)
    USABLE RULES: { }
    Removed DPs: #2
Number of SCCs: 2, DPs: 5
	SCC { #7 }
Sum... succeeded.
  #div(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  #plus(x1,x2)		w: (x1)
  div(x1,x2)		w: (0)
  #times(x1,x2)		w: (0)
  0()		w: (0)
  quot(x1,x2,x3)		w: (0)
  times(x1,x2)		w: (0)
  plus(x1,x2)		w: (0)
  #quot(x1,x2,x3)		w: (0)
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 1, DPs: 4
	SCC { #3 #4 #6 #8 }
Sum... succeeded.
  #div(x1,x2)		w: (7719 + x1)
  s(x1)		w: (21239 + x1)
  #plus(x1,x2)		w: (0)
  div(x1,x2)		w: (1 + x2 + x1)
  #times(x1,x2)		w: (0)
  0()		w: (1)
  quot(x1,x2,x3)		w: (0)
  times(x1,x2)		w: (1 + x2 + x1)
  plus(x1,x2)		w: (21240 + x2 + x1)
  #quot(x1,x2,x3)		w: (7719 + x1)
    USABLE RULES: { 1 2 }
    Removed DPs: #4 #6
Number of SCCs: 1, DPs: 2
	SCC { #3 #8 }
Sum... Max... succeeded.
  #div(x1,x2)		w: (max{2036 + x2, 0})
  s(x1)		w: (5722)
  #plus(x1,x2)		w: (0)
  div(x1,x2)		w: (0)
  #times(x1,x2)		w: (0)
  0()		w: (5723)
  quot(x1,x2,x3)		w: (0)
  times(x1,x2)		w: (0)
  plus(x1,x2)		w: (0)
  #quot(x1,x2,x3)		w: (max{2036 + x3, 2036 + x2, 0})
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0