/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: check(0()) -> zero()
    2: check(s(0())) -> odd()
    3: check(s(s(0()))) -> even()
    4: check(s(s(s(x)))) -> check(s(x))
    5: half(0()) -> 0()
    6: half(s(0())) -> 0()
    7: half(s(s(x))) -> s(half(x))
    8: plus(0(),y) -> y
    9: plus(s(x),y) -> s(plus(x,y))
    10: times(x,y) -> timesIter(x,y,0())
    11: timesIter(x,y,z) -> if(check(x),x,y,z,plus(z,y))
    12: p(s(x)) -> x
    13: p(0()) -> 0()
    14: if(zero(),x,y,z,u) -> z
    15: if(odd(),x,y,z,u) -> timesIter(p(x),y,u)
    16: if(even(),x,y,z,u) -> plus(timesIter(half(x),y,half(z)),timesIter(half(x),y,half(s(z))))
Number of strict rules: 16
Direct POLO(bPol) ... failed.
Uncurrying half check
1: check^1_0() -> zero()
2: check^1_s(0()) -> odd()
3: check^1_s(s(0())) -> even()
4: check^1_s(s(s(x))) -> check^1_s(x)
5: half^1_0() -> 0()
6: half^1_s(0()) -> 0()
7: half^1_s(s(x)) -> s(half(x))
8: plus(0(),y) -> y
9: plus(s(x),y) -> s(plus(x,y))
10: times(x,y) -> timesIter(x,y,0())
11: timesIter(x,y,z) -> if(check(x),x,y,z,plus(z,y))
12: p(s(x)) -> x
13: p(0()) -> 0()
14: if(zero(),x,y,z,u) -> z
15: if(odd(),x,y,z,u) -> timesIter(p(x),y,u)
16: if(even(),x,y,z,u) -> plus(timesIter(half(x),y,half(z)),timesIter(half(x),y,half^1_s(z)))
17: check(0()) ->= check^1_0()
18: check(s(_1)) ->= check^1_s(_1)
19: half(0()) ->= half^1_0()
20: half(s(_1)) ->= half^1_s(_1)
Number of strict rules: 16
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #plus(s(x),y) -> #plus(x,y)
   #2: #timesIter(x,y,z) -> #if(check(x),x,y,z,plus(z,y))
   #3: #timesIter(x,y,z) -> #check(x)
   #4: #timesIter(x,y,z) -> #plus(z,y)
   #5: #half(s(_1)) ->? #half^1_s(_1)
   #6: #half^1_s(s(x)) -> #half(x)
   #7: #times(x,y) -> #timesIter(x,y,0())
   #8: #check(0()) ->? #check^1_0()
   #9: #half(0()) ->? #half^1_0()
   #10: #if(even(),x,y,z,u) -> #plus(timesIter(half(x),y,half(z)),timesIter(half(x),y,half^1_s(z)))
   #11: #if(even(),x,y,z,u) -> #timesIter(half(x),y,half(z))
   #12: #if(even(),x,y,z,u) -> #half(x)
   #13: #if(even(),x,y,z,u) -> #half(z)
   #14: #if(even(),x,y,z,u) -> #timesIter(half(x),y,half^1_s(z))
   #15: #if(even(),x,y,z,u) -> #half(x)
   #16: #if(even(),x,y,z,u) -> #half^1_s(z)
   #17: #if(odd(),x,y,z,u) -> #timesIter(p(x),y,u)
   #18: #if(odd(),x,y,z,u) -> #p(x)
   #19: #check^1_s(s(s(x))) -> #check^1_s(x)
   #20: #check(s(_1)) ->? #check^1_s(_1)
Number of SCCs: 4, DPs: 8
  SCC { #19 }
POLO(Sum)... succeeded.
      zero	w: 0
      timesIter	w: 0
      s 	w: x1 + 1
      check^1_0	w: 0
      #timesIter	w: 0
      even	w: 0
      #plus	w: 0
      #check	w: 0
      #half	w: 0
      #p 	w: 0
      half^1_s	w: 0
      half	w: 0
      #check^1_0	w: 0
      check	w: 0
      p 	w: 0
      #times	w: 0
      0 	w: 0
      if	w: 0
      times	w: 0
      #half^1_s	w: 0
      half^1_0	w: 0
      plus	w: 0
      odd	w: 0
      #check^1_s	w: x1
      #if	w: 0
      #half^1_0	w: 0
      check^1_s	w: 0
    USABLE RULES: { }
    Removed DPs: #19
Number of SCCs: 3, DPs: 7
  SCC { #1 }
POLO(Sum)... succeeded.
      zero	w: 0
      timesIter	w: 0
      s 	w: x1 + 1
      check^1_0	w: 0
      #timesIter	w: 0
      even	w: 0
      #plus	w: x1
      #check	w: 0
      #half	w: 0
      #p 	w: 0
      half^1_s	w: 0
      half	w: 0
      #check^1_0	w: 0
      check	w: 0
      p 	w: 0
      #times	w: 0
      0 	w: 0
      if	w: 0
      times	w: 0
      #half^1_s	w: 0
      half^1_0	w: 0
      plus	w: 0
      odd	w: 0
      #check^1_s	w: 0
      #if	w: 0
      #half^1_0	w: 0
      check^1_s	w: 0
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 6
  SCC { #5 #6 }
POLO(Sum)... succeeded.
      zero	w: 0
      timesIter	w: 0
      s 	w: x1 + 1
      check^1_0	w: 0
      #timesIter	w: 0
      even	w: 0
      #plus	w: 0
      #check	w: 0
      #half	w: x1
      #p 	w: 0
      half^1_s	w: 0
      half	w: 0
      #check^1_0	w: 0
      check	w: 0
      p 	w: 0
      #times	w: 0
      0 	w: 0
      if	w: 0
      times	w: 0
      #half^1_s	w: x1
      half^1_0	w: 0
      plus	w: 0
      odd	w: 0
      #check^1_s	w: 0
      #if	w: 0
      #half^1_0	w: 0
      check^1_s	w: 0
    USABLE RULES: { }
    Removed DPs: #5 #6
Number of SCCs: 1, DPs: 4
  SCC { #2 #11 #14 #17 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      zero	w: 0
      timesIter	w: 0
      s 	w: max(x1 + 7, 0)
      check^1_0	w: 0
      #timesIter	w: max(x1 + 3, 0)
      even	w: 3
      #plus	w: 0
      #check	w: 0
      #half	w: max(x1 - 1, 0)
      #p 	w: max(x1 - 1, 0)
      half^1_s	w: max(x1 + 2, 0)
      half	w: max(x1 - 4, 0)
      #check^1_0	w: 0
      check	w: max(x1 - 1, 0)
      p 	w: max(x1 - 4, 0)
      #times	w: max(x2 - 1, 0)
      0 	w: 0
      if	w: max(x3 - 1, 0)
      times	w: max(x2 - 1, 0)
      #half^1_s	w: 0
      half^1_0	w: 0
      plus	w: max(x1 - 5, x2 - 1, 0)
      odd	w: 2
      #check^1_s	w: 0
      #if	w: max(x1 + 2, x2 + 1, 0)
      #half^1_0	w: 0
      check^1_s	w: max(x1 + 2, 0)
    USABLE RULES: { 1..7 12 13 17..20 }
    Removed DPs: #2 #11 #14 #17
Number of SCCs: 0, DPs: 0