/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: f(c(s(x),y)) -> f(c(x,s(y)))
    2: f(c(s(x),s(y))) -> g(c(x,y))
    3: g(c(x,s(y))) -> g(c(s(x),y))
    4: g(c(s(x),s(y))) -> f(c(x,y))
    5: rand(x) ->= x
    6: rand(x) ->= rand(s(x))
Number of strict rules: 4
Direct POLO(bPol) ... removes: 5
      s 	w: x1
      c 	w: x1 + x2 + 1
      f 	w: x1
      rand	w: x1 + 1
      g 	w: x1
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying f g
1: f^1_c(s(x),y) -> f^1_c(x,s(y))
2: f^1_c(s(x),s(y)) -> g^1_c(x,y)
3: g^1_c(x,s(y)) -> g^1_c(s(x),y)
4: g^1_c(s(x),s(y)) -> f^1_c(x,y)
6: rand(x) ->= rand(s(x))
7: g(c(_1,_2)) ->= g^1_c(_1,_2)
8: f(c(_1,_2)) ->= f^1_c(_1,_2)
Number of strict rules: 4
Direct POLO(bPol) ... removes: 8 7
      s 	w: x1
      g^1_c	w: x1 + 2 * x2
      c 	w: x1 + 2 * x2 + 1
      f 	w: x1 + 1
      rand	w: x1
      f^1_c	w: x1 + 2 * x2
      g 	w: 2 * x1
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #f^1_c(s(x),s(y)) -> #g^1_c(x,y)
   #2: #g^1_c(x,s(y)) -> #g^1_c(s(x),y)
   #3: #f^1_c(s(x),y) -> #f^1_c(x,s(y))
   #4: #g^1_c(s(x),s(y)) -> #f^1_c(x,y)
Number of SCCs: 1, DPs: 4
  SCC { #1..4 }
POLO(Sum)... succeeded.
      s 	w: x1 + 2
      g^1_c	w: x1 + x2
      c 	w: 0
      #g^1_c	w: x1 + x2
      f 	w: 0
      rand	w: 0
      #f^1_c	w: x1 + x2
      f^1_c	w: x1 + x2
      g 	w: 0
    Removed DPs: #1 #4
Number of SCCs: 2, DPs: 2
  SCC { #3 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      g^1_c	w: x1 + x2
      c 	w: 0
      #g^1_c	w: 0
      f 	w: 0
      rand	w: 0
      #f^1_c	w: x1
      f^1_c	w: x1 + x2
      g 	w: 0
    Removed DPs: #3
Number of SCCs: 1, DPs: 1
  SCC { #2 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      g^1_c	w: x1 + x2
      c 	w: 0
      #g^1_c	w: x2
      f 	w: 0
      rand	w: 0
      #f^1_c	w: 0
      f^1_c	w: x1 + x2
      g 	w: 0
    Removed DPs: #2
Number of SCCs: 0, DPs: 0