/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: p(0()) -> 0()
    2: p(s(x)) -> x
    3: le(0(),y) -> true()
    4: le(s(x),0()) -> false()
    5: le(s(x),s(y)) -> le(x,y)
    6: minus(x,0()) -> x
    7: minus(x,s(y)) -> if(le(x,s(y)),0(),p(minus(x,p(s(y)))))
    8: if(true(),x,y) -> x
    9: if(false(),x,y) -> y
Number of strict rules: 9
Direct poly ... failed.
Freezing p
1: p❆1_0() -> 0()
2: p❆1_s(x) -> x
3: le(0(),y) -> true()
4: le(s(x),0()) -> false()
5: le(s(x),s(y)) -> le(x,y)
6: minus(x,0()) -> x
7: minus(x,s(y)) -> if(le(x,s(y)),0(),p(minus(x,p❆1_s(y))))
8: if(true(),x,y) -> x
9: if(false(),x,y) -> y
10: p(0()) ->= p❆1_0()
11: p(s(_1)) ->= p❆1_s(_1)
Number of strict rules: 9
Direct poly ... failed.
Dependency Pairs:
   #1: #p(s(_1)) ->? #p❆1_s(_1)
   #2: #minus(x,s(y)) -> #if(le(x,s(y)),0(),p(minus(x,p❆1_s(y))))
   #3: #minus(x,s(y)) -> #le(x,s(y))
   #4: #minus(x,s(y)) -> #p(minus(x,p❆1_s(y)))
   #5: #minus(x,s(y)) -> #minus(x,p❆1_s(y))
   #6: #minus(x,s(y)) -> #p❆1_s(y)
   #7: #p(0()) ->? #p❆1_0()
   #8: #le(s(x),s(y)) -> #le(x,y)
Number of SCCs: 2, DPs: 2
	SCC { #5 }
Sum... succeeded.
  le(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  #le(x1,x2)		w: (0)
  minus(x1,x2)		w: (0)
  p❆1_s(x1)		w: (x1)
  #p❆1_0()		w: (0)
  false()		w: (0)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  true()		w: (0)
  p(x1)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  p❆1_0()		w: (0)
  #minus(x1,x2)		w: (x2)
  #if(x1,x2,x3)		w: (0)
    USABLE RULES: { 2 }
    Removed DPs: #5
Number of SCCs: 1, DPs: 1
	SCC { #8 }
Sum... succeeded.
  le(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  #le(x1,x2)		w: (x2 + x1)
  minus(x1,x2)		w: (0)
  p❆1_s(x1)		w: (x1)
  #p❆1_0()		w: (0)
  false()		w: (0)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  true()		w: (0)
  p(x1)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  p❆1_0()		w: (0)
  #minus(x1,x2)		w: (x2)
  #if(x1,x2,x3)		w: (0)
    USABLE RULES: { 2 }
    Removed DPs: #8
Number of SCCs: 0, DPs: 0