/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES
Input TRS:
    1: times(x,0()) -> 0()
    2: times(x,s(y)) -> plus(times(x,y),x)
    3: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
    4: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
    5: plus(zero(),y) -> y
    6: plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y))))
    7: id(x) -> x
    8: if(true(),x,y) -> x
    9: if(false(),x,y) -> y
    10: not(x) -> if(x,false(),true())
    11: gt(s(x),zero()) -> true()
    12: gt(zero(),y) -> false()
    13: gt(s(x),s(y)) -> gt(x,y)
Number of strict rules: 13
Direct POLO(bPol) ... failed.
Uncurrying gt
1: times(x,0()) -> 0()
2: times(x,s(y)) -> plus(times(x,y),x)
3: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
4: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
5: plus(zero(),y) -> y
6: plus(id(x),s(y)) -> s(plus(x,if(gt^1_s(y,y),y,s(y))))
7: id(x) -> x
8: if(true(),x,y) -> x
9: if(false(),x,y) -> y
10: not(x) -> if(x,false(),true())
11: gt^1_s(x,zero()) -> true()
12: gt^1_zero(y) -> false()
13: gt^1_s(x,s(y)) -> gt(x,y)
14: gt(zero(),_1) ->= gt^1_zero(_1)
15: gt(s(_1),_2) ->= gt^1_s(_1,_2)
Number of strict rules: 13
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #times(x,s(y)) -> #plus(times(x,y),x)
   #2: #times(x,s(y)) -> #times(x,y)
   #3: #plus(id(x),s(y)) -> #plus(x,if(gt^1_s(y,y),y,s(y)))
   #4: #plus(id(x),s(y)) -> #if(gt^1_s(y,y),y,s(y))
   #5: #plus(id(x),s(y)) -> #gt^1_s(y,y)
   #6: #gt^1_s(x,s(y)) -> #gt(x,y)
   #7: #gt(zero(),_1) ->? #gt^1_zero(_1)
   #8: #not(x) -> #if(x,false(),true())
   #9: #plus(s(x),s(y)) -> #plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
   #10: #plus(s(x),s(y)) -> #if(gt(x,y),x,y)
   #11: #plus(s(x),s(y)) -> #gt(x,y)
   #12: #plus(s(x),s(y)) -> #if(not(gt(x,y)),id(x),id(y))
   #13: #plus(s(x),s(y)) -> #not(gt(x,y))
   #14: #plus(s(x),s(y)) -> #gt(x,y)
   #15: #plus(s(x),s(y)) -> #id(x)
   #16: #plus(s(x),s(y)) -> #id(y)
   #17: #gt(s(_1),_2) ->? #gt^1_s(_1,_2)
   #18: #plus(s(x),x) -> #plus(if(gt(x,x),id(x),id(x)),s(x))
   #19: #plus(s(x),x) -> #if(gt(x,x),id(x),id(x))
   #20: #plus(s(x),x) -> #gt(x,x)
   #21: #plus(s(x),x) -> #id(x)
   #22: #plus(s(x),x) -> #id(x)
Number of SCCs: 3, DPs: 6
  SCC { #2 }
POLO(Sum)... succeeded.
      zero	w: 0
      s 	w: x1 + 1
      gt	w: 0
      #gt^1_zero	w: 0
      #plus	w: 0
      false	w: 0
      #id	w: 0
      gt^1_zero	w: 0
      true	w: 0
      #not	w: 0
      #times	w: x2
      0 	w: 0
      if	w: 0
      times	w: 0
      #gt	w: 0
      plus	w: 0
      gt^1_s	w: 0
      #if	w: 0
      id	w: 0
      #gt^1_s	w: 0
      not	w: 0
    USABLE RULES: { }
    Removed DPs: #2
Number of SCCs: 2, DPs: 5
  SCC { #6 #17 }
POLO(Sum)... succeeded.
      zero	w: 0
      s 	w: x1 + 2
      gt	w: 0
      #gt^1_zero	w: 0
      #plus	w: 0
      false	w: 0
      #id	w: 0
      gt^1_zero	w: 0
      true	w: 0
      #not	w: 0
      #times	w: 0
      0 	w: 0
      if	w: 0
      times	w: 0
      #gt	w: x2 + 1
      plus	w: 0
      gt^1_s	w: 0
      #if	w: 0
      id	w: 0
      #gt^1_s	w: x2
      not	w: 0
    USABLE RULES: { }
    Removed DPs: #6 #17
Number of SCCs: 1, DPs: 3
  SCC { #3 #9 #18 }
POLO(Sum)... POLO(max)... succeeded.
      zero	w: 4
      s 	w: x1 + 10
      gt	w: max(x1 + 1, x2 + 4)
      #gt^1_zero	w: 0
      #plus	w: max(x1 + 3, x2 + 1)
      false	w: 0
      #id	w: 0
      gt^1_zero	w: 5
      true	w: 4
      #not	w: 0
      #times	w: 0
      0 	w: 0
      if	w: max(x1 + 1, x2 + 4, x3)
      times	w: 0
      #gt	w: 0
      plus	w: 0
      gt^1_s	w: max(x1 + 3, x2 + 1)
      #if	w: 0
      id	w: x1 + 1
      #gt^1_s	w: 0
      not	w: x1 + 4
    USABLE RULES: { 7..15 }
    Removed DPs: #9 #18
Number of SCCs: 1, DPs: 1
  SCC { #3 }
POLO(Sum)... succeeded.
      zero	w: 1
      s 	w: 1
      gt	w: 1
      #gt^1_zero	w: 0
      #plus	w: x1
      false	w: 1
      #id	w: 0
      gt^1_zero	w: 1
      true	w: 1
      #not	w: 0
      #times	w: 0
      0 	w: 0
      if	w: x2 + x3
      times	w: 0
      #gt	w: 1
      plus	w: 0
      gt^1_s	w: 1
      #if	w: 0
      id	w: x1 + 1
      #gt^1_s	w: 0
      not	w: 2
    USABLE RULES: { 7..15 }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0