/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: app(app(F(),app(app(F(),f),x)),x) -> app(app(F(),app(G(),app(app(F(),f),x))),app(f,x))
Number of strict rules: 1
Direct poly ... failed.
Freezing app
1: app❆2_F(app❆2_F(f,x),x) -> app❆2_F(app❆1_G(app❆2_F(f,x)),app(f,x))
2: app(G(),_1) ->= app❆1_G(_1)
3: app(F(),_1) ->= app❆1_F(_1)
4: app(app❆1_F(_1),_2) ->= app❆2_F(_1,_2)
Number of strict rules: 1
Direct poly ... failed.
Dependency Pairs:
   #1: #app❆2_F(app❆2_F(f,x),x) -> #app❆2_F(app❆1_G(app❆2_F(f,x)),app(f,x))
   #2: #app❆2_F(app❆2_F(f,x),x) -> #app(f,x)
   #3: #app(app❆1_F(_1),_2) ->? #app❆2_F(_1,_2)
Number of SCCs: 1, DPs: 2
	SCC { #2 #3 }
Sum... succeeded.
  G()		w: (0)
  F()		w: (0)
  app❆2_F(x1,x2)		w: (41 + x2 + x1)
  app❆1_F(x1)		w: (1 + x1)
  #app(x1,x2)		w: (41 + x1)
  app❆1_G(x1)		w: (0)
  #app❆2_F(x1,x2)		w: (1 + x1)
  app(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #2 #3
Number of SCCs: 0, DPs: 0