/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(),y) -> y
    2: +(s(x),y) -> s(+(x,y))
    3: +(p(x),y) -> p(+(x,y))
    4: minus(0()) -> 0()
    5: minus(s(x)) -> p(minus(x))
    6: minus(p(x)) -> s(minus(x))
    7: *(0(),y) -> 0()
    8: *(s(x),y) -> +(*(x,y),y)
    9: *(p(x),y) -> +(*(x,y),minus(y))
Number of strict rules: 9
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #+(s(x),y) -> #+(x,y)
   #2: #minus(p(x)) -> #minus(x)
   #3: #*(p(x),y) -> #+(*(x,y),minus(y))
   #4: #*(p(x),y) -> #*(x,y)
   #5: #*(p(x),y) -> #minus(y)
   #6: #minus(s(x)) -> #minus(x)
   #7: #+(p(x),y) -> #+(x,y)
   #8: #*(s(x),y) -> #+(*(x,y),y)
   #9: #*(s(x),y) -> #*(x,y)
Number of SCCs: 3, DPs: 6
	SCC { #2 #6 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  minus(x1)		w: (0)
  #*(x1,x2)		w: (0)
  p(x1)		w: (1 + x1)
  0()		w: (0)
  #minus(x1)		w: (x1)
  +(x1,x2)		w: (0)
  #+(x1,x2)		w: (0)
  *(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #2 #6
Number of SCCs: 2, DPs: 4
	SCC { #4 #9 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  minus(x1)		w: (0)
  #*(x1,x2)		w: (x1)
  p(x1)		w: (1 + x1)
  0()		w: (0)
  #minus(x1)		w: (0)
  +(x1,x2)		w: (0)
  #+(x1,x2)		w: (0)
  *(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #4 #9
Number of SCCs: 1, DPs: 2
	SCC { #1 #7 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  minus(x1)		w: (0)
  #*(x1,x2)		w: (0)
  p(x1)		w: (1 + x1)
  0()		w: (0)
  #minus(x1)		w: (0)
  +(x1,x2)		w: (0)
  #+(x1,x2)		w: (x1)
  *(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1 #7
Number of SCCs: 0, DPs: 0