/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: -(x,0()) -> x
    2: -(s(x),s(y)) -> -(x,y)
    3: <=(0(),y) -> true()
    4: <=(s(x),0()) -> false()
    5: <=(s(x),s(y)) -> <=(x,y)
    6: if(true(),x,y) -> x
    7: if(false(),x,y) -> y
    8: perfectp(0()) -> false()
    9: perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
    10: f(0(),y,0(),u) -> true()
    11: f(0(),y,s(z),u) -> false()
    12: f(s(x),0(),z,u) -> f(x,u,-(z,s(x)),u)
    13: f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u))
Number of strict rules: 13
Direct poly ... failed.
Freezing f
1: -(x,0()) -> x
2: -(s(x),s(y)) -> -(x,y)
3: <=(0(),y) -> true()
4: <=(s(x),0()) -> false()
5: <=(s(x),s(y)) -> <=(x,y)
6: if(true(),x,y) -> x
7: if(false(),x,y) -> y
8: perfectp(0()) -> false()
9: perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
10: f❆1_0(y,0(),u) -> true()
11: f❆1_0(y,s(z),u) -> false()
12: f❆1_s(x,0(),z,u) -> f(x,u,-(z,s(x)),u)
13: f❆1_s(x,s(y),z,u) -> if(<=(x,y),f❆1_s(x,-(y,x),z,u),f(x,u,z,u))
14: f(0(),_3,_4,_5) ->= f❆1_0(_3,_4,_5)
15: f(s(_1),_4,_5,_6) ->= f❆1_s(_1,_4,_5,_6)
Number of strict rules: 13
Direct poly ... failed.
Dependency Pairs:
   #1: #-(s(x),s(y)) -> #-(x,y)
   #2: #f❆1_s(x,s(y),z,u) -> #if(<=(x,y),f❆1_s(x,-(y,x),z,u),f(x,u,z,u))
   #3: #f❆1_s(x,s(y),z,u) -> #<=(x,y)
   #4: #f❆1_s(x,s(y),z,u) -> #f❆1_s(x,-(y,x),z,u)
   #5: #f❆1_s(x,s(y),z,u) -> #-(y,x)
   #6: #f❆1_s(x,s(y),z,u) -> #f(x,u,z,u)
   #7: #perfectp(s(x)) -> #f(x,s(0()),s(x),s(x))
   #8: #f❆1_s(x,0(),z,u) -> #f(x,u,-(z,s(x)),u)
   #9: #f❆1_s(x,0(),z,u) -> #-(z,s(x))
   #10: #f(0(),_3,_4,_5) ->? #f❆1_0(_3,_4,_5)
   #11: #<=(s(x),s(y)) -> #<=(x,y)
   #12: #f(s(_1),_4,_5,_6) ->? #f❆1_s(_1,_4,_5,_6)
Number of SCCs: 3, DPs: 6
	SCC { #11 }
Sum... succeeded.
  #f❆1_s(x1,x2,x3,x4)		w: (0)
  s(x1)		w: (1 + x1)
  <=(x1,x2)		w: (0)
  #perfectp(x1)		w: (0)
  false()		w: (0)
  #<=(x1,x2)		w: (x2)
  true()		w: (0)
  f❆1_s(x1,x2,x3,x4)		w: (0)
  f(x1,x2,x3,x4)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  -(x1,x2)		w: (0)
  #f❆1_0(x1,x2,x3)		w: (0)
  #f(x1,x2,x3,x4)		w: (0)
  #-(x1,x2)		w: (0)
  #if(x1,x2,x3)		w: (0)
  perfectp(x1)		w: (0)
  f❆1_0(x1,x2,x3)		w: (0)
    USABLE RULES: { }
    Removed DPs: #11
Number of SCCs: 2, DPs: 5
	SCC { #1 }
Sum... succeeded.
  #f❆1_s(x1,x2,x3,x4)		w: (0)
  s(x1)		w: (1 + x1)
  <=(x1,x2)		w: (0)
  #perfectp(x1)		w: (0)
  false()		w: (0)
  #<=(x1,x2)		w: (0)
  true()		w: (0)
  f❆1_s(x1,x2,x3,x4)		w: (0)
  f(x1,x2,x3,x4)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  -(x1,x2)		w: (0)
  #f❆1_0(x1,x2,x3)		w: (0)
  #f(x1,x2,x3,x4)		w: (0)
  #-(x1,x2)		w: (x2)
  #if(x1,x2,x3)		w: (0)
  perfectp(x1)		w: (0)
  f❆1_0(x1,x2,x3)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 4
	SCC { #4 #6 #8 #12 }
Sum... succeeded.
  #f❆1_s(x1,x2,x3,x4)		w: (1 + x4 + x1)
  s(x1)		w: (7721 + x1)
  <=(x1,x2)		w: (0)
  #perfectp(x1)		w: (0)
  false()		w: (0)
  #<=(x1,x2)		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)
  -(x1,x2)		w: (x2 + x1)
  #f❆1_0(x1,x2,x3)		w: (0)
  #f(x1,x2,x3,x4)		w: (x4 + x1)
  #-(x1,x2)		w: (0)
  #if(x1,x2,x3)		w: (0)
  perfectp(x1)		w: (0)
  f❆1_0(x1,x2,x3)		w: (0)
    USABLE RULES: { }
    Removed DPs: #6 #8 #12
Number of SCCs: 1, DPs: 1
	SCC { #4 }
Sum... succeeded.
  #f❆1_s(x1,x2,x3,x4)		w: (1 + x2)
  s(x1)		w: (7721 + x1)
  <=(x1,x2)		w: (0)
  #perfectp(x1)		w: (0)
  false()		w: (0)
  #<=(x1,x2)		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)
  -(x1,x2)		w: (x1)
  #f❆1_0(x1,x2,x3)		w: (0)
  #f(x1,x2,x3,x4)		w: (0)
  #-(x1,x2)		w: (0)
  #if(x1,x2,x3)		w: (0)
  perfectp(x1)		w: (0)
  f❆1_0(x1,x2,x3)		w: (0)
    USABLE RULES: { 1 2 }
    Removed DPs: #4
Number of SCCs: 0, DPs: 0