/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:
    AC symbols: plus
    1: f(plus(x,y)) -> plus(f(x),y)
    2: plus(g(x),y) -> g(plus(x,y))
    3: plus(f(a()),g(b())) -> plus(f(b()),g(a()))
    4: h(a(),b()) -> h(b(),a())
    5: h(a(),g(g(a()))) -> h(g(a()),f(a()))
    6: h(g(a()),a()) -> h(a(),g(b()))
    7: h(g(a()),b()) -> h(a(),g(a()))
Number of strict rules: 7
Direct POLO(bPol) ... removes: 5
      a 	w: 1
      h 	w: x1 + x2
      b 	w: 1
      f 	w: x1
      plus	w: x1 + x2 + 1
      g 	w: x1 + 4
Number of strict rules: 6
Direct POLO(bPol) ... removes: 1
      a 	w: 1
      h 	w: x1 + x2
      b 	w: 1
      f 	w: 2 * x1
      plus	w: x1 + x2 + 1
      g 	w: x1 + 4
Number of strict rules: 5
Direct POLO(bPol) ... removes: 4 3 7 6
      a 	w: 2
      h 	w: 2 * x1 + x2
      b 	w: 1
      f 	w: 2 * x1
      plus	w: x1 + x2 + 1
      g 	w: x1 + 2
Number of strict rules: 1
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #plus(g(x),y) -> #plus(x,y)
   #2: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
   #3: #plus(x,plus(y,z)) ->= #plus(x,y)
Number of SCCs: 1, DPs: 3
  SCC { #1..3 }
POLO(Sum)... succeeded.
      a 	w: 0
      h 	w: 0
      b 	w: 0
      #plus	w: x1 + x2
      f 	w: 0
      plus	w: x1 + x2 + 1
      g 	w: x1 + 1
    USABLE RULES: { 2 8 }
    Removed DPs: #1 #3
Number of SCCs: 1, DPs: 1
  SCC { #2 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
   #4: #plus(plus(g(x),y),_1) -> #plus(g(plus(x,y)),_1)
   #5: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
   #6: #plus(x,plus(y,z)) ->= #plus(x,y)
Number of SCCs: 1, DPs: 3
  SCC { #4..6 }
POLO(Sum)... succeeded.
      a 	w: 0
      h 	w: 0
      b 	w: 0
      #plus	w: x1 + x2
      f 	w: 0
      plus	w: x1 + x2 + 1
      g 	w: x1 + 1
    USABLE RULES: { 2 8 }
    Removed DPs: #6
Number of SCCs: 1, DPs: 2
  SCC { #4 #5 }
POLO(Sum)... succeeded.
      a 	w: 0
      h 	w: 0
      b 	w: 0
      #plus	w: x1 + x2
      f 	w: 0
      plus	w: x1 + x2 + 1
      g 	w: 1
    USABLE RULES: { 2 8 }
    Removed DPs: #4
Number of SCCs: 1, DPs: 1
  SCC { #5 }
only weak rules.
Number of SCCs: 0, DPs: 0