/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES
Input TRS:
    1: perfectp(0()) -> false()
    2: perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
    3: f(0(),y,0(),u) -> true()
    4: f(0(),y,s(z),u) -> false()
    5: f(s(x),0(),z,u) -> f(x,u,minus(z,s(x)),u)
    6: f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
Number of strict rules: 6
Direct poly ... failed.
Freezing f
1: perfectp(0()) -> false()
2: perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
3: f❆1_0(y,0(),u) -> true()
4: f❆1_0(y,s(z),u) -> false()
5: f❆1_s(x,0(),z,u) -> f(x,u,minus(z,s(x)),u)
6: f❆1_s(x,s(y),z,u) -> if(le(x,y),f❆1_s(x,minus(y,x),z,u),f(x,u,z,u))
7: f(0(),_3,_4,_5) ->= f❆1_0(_3,_4,_5)
8: f(s(_1),_4,_5,_6) ->= f❆1_s(_1,_4,_5,_6)
Number of strict rules: 6
Direct poly ... failed.
Dependency Pairs:
   #1: #perfectp(s(x)) -> #f(x,s(0()),s(x),s(x))
   #2: #f❆1_s(x,s(y),z,u) -> #f❆1_s(x,minus(y,x),z,u)
   #3: #f❆1_s(x,s(y),z,u) -> #f(x,u,z,u)
   #4: #f(0(),_3,_4,_5) ->? #f❆1_0(_3,_4,_5)
   #5: #f❆1_s(x,0(),z,u) -> #f(x,u,minus(z,s(x)),u)
   #6: #f(s(_1),_4,_5,_6) ->? #f❆1_s(_1,_4,_5,_6)
Number of SCCs: 1, DPs: 3
	SCC { #3 #5 #6 }
Sum... succeeded.
  #f❆1_s(x1,x2,x3,x4)		w: (1 + x4 + x1)
  le(x1,x2)		w: (0)
  s(x1)		w: (40 + x1)
  minus(x1,x2)		w: (x2)
  #perfectp(x1)		w: (0)
  false()		w: (0)
  true()		w: (0)
  f❆1_s(x1,x2,x3,x4)		w: (0)
  f(x1,x2,x3,x4)		w: (0)
  0()		w: (1)
  if(x1,x2,x3)		w: (0)
  #f❆1_0(x1,x2,x3)		w: (0)
  #f(x1,x2,x3,x4)		w: (x4 + x1)
  perfectp(x1)		w: (0)
  f❆1_0(x1,x2,x3)		w: (0)
    USABLE RULES: { }
    Removed DPs: #3 #5 #6
Number of SCCs: 0, DPs: 0