/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(a(),g(y)) -> g(g(y))
    2: f(g(x),a()) -> f(x,g(a()))
    3: f(g(x),g(y)) -> h(g(y),x,g(y))
    4: h(g(x),y,z) -> f(y,h(x,y,z))
    5: h(a(),y,z) -> z
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Uncurrying h
1: f(a(),g(y)) -> g(g(y))
2: f(g(x),a()) -> f(x,g(a()))
3: f(g(x),g(y)) -> h^1_g(y,x,g(y))
4: h^1_g(x,y,z) -> f(y,h(x,y,z))
5: h^1_a(y,z) -> z
6: h(a(),_2,_3) ->= h^1_a(_2,_3)
7: h(g(_1),_3,_4) ->= h^1_g(_1,_3,_4)
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #f(g(x),a()) -> #f(x,g(a()))
   #2: #h(a(),_2,_3) ->? #h^1_a(_2,_3)
   #3: #h(g(_1),_3,_4) ->? #h^1_g(_1,_3,_4)
   #4: #f(g(x),g(y)) -> #h^1_g(y,x,g(y))
   #5: #h^1_g(x,y,z) -> #f(y,h(x,y,z))
   #6: #h^1_g(x,y,z) -> #h(x,y,z)
Number of SCCs: 1, DPs: 5
  SCC { #1 #3..6 }
POLO(Sum)... succeeded.
      a 	w: 1
      h 	w: x1 + 1
      #h^1_a	w: 0
      h^1_a	w: x1 + x2 + 3
      h^1_g	w: x3 + 7
      #h^1_g	w: x2 + 1
      f 	w: x1 + 8
      #h 	w: x2 + 1
      #f 	w: x1
      g 	w: x1 + 5
    USABLE RULES: { }
    Removed DPs: #1 #4 #5
Number of SCCs: 1, DPs: 2
  SCC { #3 #6 }
POLO(Sum)... succeeded.
      a 	w: 1
      h 	w: x1 + 1
      #h^1_a	w: 0
      h^1_a	w: x1 + x2 + 3
      h^1_g	w: x3 + 7
      #h^1_g	w: x1 + 2
      f 	w: x1 + 8
      #h 	w: x1 + 1
      #f 	w: 0
      g 	w: x1 + 5
    USABLE RULES: { }
    Removed DPs: #3 #6
Number of SCCs: 0, DPs: 0