/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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 poly ... failed.
Freezing 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 poly ... 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 }
Sum... succeeded.
  a()		w: (1)
  h(x1,x2,x3)		w: (21239 + x1)
  h❆1_a(x1,x2)		w: (21241 + x1)
  f(x1,x2)		w: (42480 + x1)
  #h(x1,x2,x3)		w: (7720 + x2)
  #h❆1_g(x1,x2,x3)		w: (7720 + x2)
  #f(x1,x2)		w: (7719 + x1)
  h❆1_g(x1,x2,x3)		w: (42481 + x3 + x2 + x1)
  g(x1)		w: (21241 + x1)
  #h❆1_a(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1 #4 #5
Number of SCCs: 1, DPs: 2
	SCC { #3 #6 }
Sum... succeeded.
  a()		w: (1)
  h(x1,x2,x3)		w: (32286 + x1)
  h❆1_a(x1,x2)		w: (32288 + x1)
  f(x1,x2)		w: (2 + x1)
  #h(x1,x2,x3)		w: (7720 + x1)
  #h❆1_g(x1,x2,x3)		w: (7721 + x1)
  #f(x1,x2)		w: (7719)
  h❆1_g(x1,x2,x3)		w: (32289 + x3 + x2 + x1)
  g(x1)		w: (2 + x1)
  #h❆1_a(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #3 #6
Number of SCCs: 0, DPs: 0