/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: leq(0(),y) -> true()
    2: leq(s(x),0()) -> false()
    3: leq(s(x),s(y)) -> leq(x,y)
    4: if(true(),x,y) -> x
    5: if(false(),x,y) -> y
    6: -(x,0()) -> x
    7: -(s(x),s(y)) -> -(x,y)
    8: mod(0(),y) -> 0()
    9: mod(s(x),0()) -> 0()
    10: mod(s(x),s(y)) -> if(leq(y,x),mod(-(s(x),s(y)),s(y)),s(x))
Number of strict rules: 10
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #-(s(x),s(y)) -> #-(x,y)
   #2: #mod(s(x),s(y)) -> #if(leq(y,x),mod(-(s(x),s(y)),s(y)),s(x))
   #3: #mod(s(x),s(y)) -> #leq(y,x)
   #4: #mod(s(x),s(y)) -> #mod(-(s(x),s(y)),s(y))
   #5: #mod(s(x),s(y)) -> #-(s(x),s(y))
   #6: #leq(s(x),s(y)) -> #leq(x,y)
Number of SCCs: 3, DPs: 3
	SCC { #6 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  mod(x1,x2)		w: (0)
  false()		w: (0)
  leq(x1,x2)		w: (0)
  true()		w: (0)
  #leq(x1,x2)		w: (x2 + x1)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  -(x1,x2)		w: (0)
  #mod(x1,x2)		w: (0)
  #-(x1,x2)		w: (0)
  #if(x1,x2,x3)		w: (0)
    USABLE RULES: { }
    Removed DPs: #6
Number of SCCs: 2, DPs: 2
	SCC { #1 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  mod(x1,x2)		w: (0)
  false()		w: (0)
  leq(x1,x2)		w: (0)
  true()		w: (0)
  #leq(x1,x2)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  -(x1,x2)		w: (0)
  #mod(x1,x2)		w: (0)
  #-(x1,x2)		w: (x2)
  #if(x1,x2,x3)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 1
	SCC { #4 }
Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... 2D-Mat... sum_sum_int,sum_neg... succeeded.
  s(x1)		w: (max{0, 3 + x1_1}, -3)
  mod(x1,x2)		w: (0, 0)
  false()		w: (0, 0)
  leq(x1,x2)		w: (0, 0)
  true()		w: (0, 0)
  #leq(x1,x2)		w: (0, 0)
  0()		w: (1, -1)
  if(x1,x2,x3)		w: (0, 0)
  -(x1,x2)		w: (max{0, 1 + x2_2 + x1_1}, 0)
  #mod(x1,x2)		w: (max{0, 1 + x1_1}, x2_2)
  #-(x1,x2)		w: (0, 0)
  #if(x1,x2,x3)		w: (0, 0)
    USABLE RULES: { 6 7 }
    Removed DPs: #4
Number of SCCs: 0, DPs: 0