/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: le(0(),y) -> true()
    2: le(s(x),0()) -> false()
    3: le(s(x),s(y)) -> le(x,y)
    4: pred(s(x)) -> x
    5: minus(x,0()) -> x
    6: minus(x,s(y)) -> pred(minus(x,y))
    7: mod(0(),y) -> 0()
    8: mod(s(x),0()) -> 0()
    9: mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
    10: if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
    11: if_mod(false(),s(x),s(y)) -> s(x)
Number of strict rules: 11
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #minus(x,s(y)) -> #pred(minus(x,y))
   #2: #minus(x,s(y)) -> #minus(x,y)
   #3: #mod(s(x),s(y)) -> #if_mod(le(y,x),s(x),s(y))
   #4: #mod(s(x),s(y)) -> #le(y,x)
   #5: #if_mod(true(),s(x),s(y)) -> #mod(minus(x,y),s(y))
   #6: #if_mod(true(),s(x),s(y)) -> #minus(x,y)
   #7: #le(s(x),s(y)) -> #le(x,y)
Number of SCCs: 3, DPs: 4
	SCC { #2 }
Sum... succeeded.
  le(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  #le(x1,x2)		w: (0)
  minus(x1,x2)		w: (0)
  mod(x1,x2)		w: (0)
  false()		w: (0)
  true()		w: (0)
  pred(x1)		w: (0)
  if_mod(x1,x2,x3)		w: (0)
  0()		w: (0)
  #minus(x1,x2)		w: (x2)
  #mod(x1,x2)		w: (0)
  #if_mod(x1,x2,x3)		w: (0)
  #pred(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #2
Number of SCCs: 2, DPs: 3
	SCC { #7 }
Sum... succeeded.
  le(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  #le(x1,x2)		w: (x2)
  minus(x1,x2)		w: (0)
  mod(x1,x2)		w: (0)
  false()		w: (0)
  true()		w: (0)
  pred(x1)		w: (0)
  if_mod(x1,x2,x3)		w: (0)
  0()		w: (0)
  #minus(x1,x2)		w: (0)
  #mod(x1,x2)		w: (0)
  #if_mod(x1,x2,x3)		w: (0)
  #pred(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 1, DPs: 2
	SCC { #3 #5 }
Sum... succeeded.
  le(x1,x2)		w: (4 + x2)
  s(x1)		w: (3 + x1)
  #le(x1,x2)		w: (0)
  minus(x1,x2)		w: (1 + x1)
  mod(x1,x2)		w: (0)
  false()		w: (6)
  true()		w: (5)
  pred(x1)		w: (x1)
  if_mod(x1,x2,x3)		w: (0)
  0()		w: (1)
  #minus(x1,x2)		w: (0)
  #mod(x1,x2)		w: (35234 + x1)
  #if_mod(x1,x2,x3)		w: (35233 + x2)
  #pred(x1)		w: (0)
    USABLE RULES: { 4..6 }
    Removed DPs: #3 #5
Number of SCCs: 0, DPs: 0