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


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


YES
Input TRS:
    1: active(f(X)) -> mark(if(X,c(),f(true())))
    2: active(if(true(),X,Y)) -> mark(X)
    3: active(if(false(),X,Y)) -> mark(Y)
    4: active(f(X)) -> f(active(X))
    5: active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
    6: active(if(X1,X2,X3)) -> if(X1,active(X2),X3)
    7: f(mark(X)) -> mark(f(X))
    8: if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
    9: if(X1,mark(X2),X3) -> mark(if(X1,X2,X3))
    10: proper(f(X)) -> f(proper(X))
    11: proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
    12: proper(c()) -> ok(c())
    13: proper(true()) -> ok(true())
    14: proper(false()) -> ok(false())
    15: f(ok(X)) -> ok(f(X))
    16: if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
    17: top(mark(X)) -> top(proper(X))
    18: top(ok(X)) -> top(active(X))
Number of strict rules: 18
Direct POLO(bPol) ... removes: 3
      top	w: 2 * x1
      false	w: 1
      c 	w: 0
      true	w: 0
      f 	w: x1 + 1
      proper	w: x1
      ok	w: x1
      if	w: x1 + x2 + x3
      mark	w: x1
      active	w: x1
Number of strict rules: 17
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #active(if(X1,X2,X3)) -> #if(X1,active(X2),X3)
   #2: #active(if(X1,X2,X3)) -> #active(X2)
   #3: #if(X1,mark(X2),X3) -> #if(X1,X2,X3)
   #4: #proper(if(X1,X2,X3)) -> #if(proper(X1),proper(X2),proper(X3))
   #5: #proper(if(X1,X2,X3)) -> #proper(X1)
   #6: #proper(if(X1,X2,X3)) -> #proper(X2)
   #7: #proper(if(X1,X2,X3)) -> #proper(X3)
   #8: #f(mark(X)) -> #f(X)
   #9: #proper(f(X)) -> #f(proper(X))
   #10: #proper(f(X)) -> #proper(X)
   #11: #active(if(X1,X2,X3)) -> #if(active(X1),X2,X3)
   #12: #active(if(X1,X2,X3)) -> #active(X1)
   #13: #top(mark(X)) -> #top(proper(X))
   #14: #top(mark(X)) -> #proper(X)
   #15: #if(ok(X1),ok(X2),ok(X3)) -> #if(X1,X2,X3)
   #16: #active(f(X)) -> #if(X,c(),f(true()))
   #17: #active(f(X)) -> #f(true())
   #18: #if(mark(X1),X2,X3) -> #if(X1,X2,X3)
   #19: #f(ok(X)) -> #f(X)
   #20: #active(f(X)) -> #f(active(X))
   #21: #active(f(X)) -> #active(X)
   #22: #top(ok(X)) -> #top(active(X))
   #23: #top(ok(X)) -> #active(X)
Number of SCCs: 5, DPs: 14
  SCC { #8 #19 }
POLO(Sum)... succeeded.
      top	w: 0
      false	w: 0
      #top	w: 0
      c 	w: 0
      true	w: 0
      f 	w: 0
      proper	w: 0
      ok	w: x1 + 1
      if	w: 0
      mark	w: x1 + 1
      #f 	w: x1
      #proper	w: 0
      active	w: 0
      #if	w: 0
      #active	w: 0
    USABLE RULES: { }
    Removed DPs: #8 #19
Number of SCCs: 4, DPs: 12
  SCC { #13 #22 }
POLO(Sum)... succeeded.
      top	w: 0
      false	w: 1
      #top	w: x1
      c 	w: 1
      true	w: 1
      f 	w: x1 + 3
      proper	w: x1
      ok	w: x1
      if	w: x1 + x2 + 1
      mark	w: x1 + 1
      #f 	w: 0
      #proper	w: 0
      active	w: x1
      #if	w: 0
      #active	w: 0
    USABLE RULES: { 1 2 4..16 }
    Removed DPs: #13
Number of SCCs: 4, DPs: 11
  SCC { #22 }
POLO(Sum)... succeeded.
      top	w: 0
      false	w: 1
      #top	w: x1
      c 	w: 1
      true	w: 1
      f 	w: x1
      proper	w: x1 + 2
      ok	w: x1 + 2
      if	w: x1 + 1
      mark	w: 1
      #f 	w: 0
      #proper	w: 0
      active	w: x1 + 1
      #if	w: 0
      #active	w: 0
    USABLE RULES: { 1 2 4..16 }
    Removed DPs: #22
Number of SCCs: 3, DPs: 10
  SCC { #2 #12 #21 }
POLO(Sum)... succeeded.
      top	w: 0
      false	w: 1
      #top	w: 0
      c 	w: 1
      true	w: 1
      f 	w: x1 + 1
      proper	w: x1 + 1
      ok	w: x1 + 1
      if	w: x1 + x2 + 1
      mark	w: 1
      #f 	w: 0
      #proper	w: 0
      active	w: x1 + 1
      #if	w: 0
      #active	w: x1
    USABLE RULES: { 1 2 4..9 12..16 }
    Removed DPs: #2 #12 #21
Number of SCCs: 2, DPs: 7
  SCC { #5..7 #10 }
POLO(Sum)... succeeded.
      top	w: 0
      false	w: 1
      #top	w: 0
      c 	w: 1
      true	w: 1
      f 	w: x1 + 1
      proper	w: x1 + 1
      ok	w: x1 + 1
      if	w: x1 + x2 + x3 + 1
      mark	w: 1
      #f 	w: 0
      #proper	w: x1
      active	w: x1 + 1
      #if	w: 0
      #active	w: 0
    USABLE RULES: { 1 2 4..9 12..16 }
    Removed DPs: #5..7 #10
Number of SCCs: 1, DPs: 3
  SCC { #3 #15 #18 }
POLO(Sum)... succeeded.
      top	w: 0
      false	w: 1
      #top	w: 0
      c 	w: 1
      true	w: 1
      f 	w: x1 + 1
      proper	w: x1 + 1
      ok	w: x1 + 1
      if	w: x1 + x2 + x3 + 1
      mark	w: 1
      #f 	w: 0
      #proper	w: 0
      active	w: x1 + 1
      #if	w: x3
      #active	w: 0
    USABLE RULES: { 1 2 4..9 12..16 }
    Removed DPs: #15
Number of SCCs: 1, DPs: 2
  SCC { #3 #18 }
POLO(Sum)... succeeded.
      top	w: 0
      false	w: 1
      #top	w: 0
      c 	w: 1
      true	w: 1
      f 	w: x1 + 1
      proper	w: x1 + 1
      ok	w: x1 + 1
      if	w: x1 + x2 + x3 + 1
      mark	w: x1 + 2
      #f 	w: 0
      #proper	w: 0
      active	w: x1 + 5
      #if	w: x1 + x2
      #active	w: 0
    USABLE RULES: { 1 2 4..9 12..16 }
    Removed DPs: #3 #18
Number of SCCs: 0, DPs: 0