/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
Input TRS:
    1: f(a(),x) -> f(b(),f(c(),x))
    2: f(a(),f(b(),x)) -> f(b(),f(a(),x))
    3: f(d(),f(c(),x)) -> f(d(),f(a(),x))
    4: f(a(),f(c(),x)) -> f(c(),f(a(),x))
Number of strict rules: 4
Direct poly ... failed.
Freezing f
1: f❆1_a(x) -> f❆1_b(f❆1_c(x))
2: f❆1_a(f❆1_b(x)) -> f❆1_b(f❆1_a(x))
3: f❆1_d(f❆1_c(x)) -> f❆1_d(f❆1_a(x))
4: f❆1_a(f❆1_c(x)) -> f❆1_c(f❆1_a(x))
5: f(a(),_1) ->= f❆1_a(_1)
6: f(d(),_1) ->= f❆1_d(_1)
7: f(c(),_1) ->= f❆1_c(_1)
8: f(b(),_1) ->= f❆1_b(_1)
Number of strict rules: 4
Direct poly ... removes: 8 5 7 6
  a()		w: (1)
  d()		w: (1)
  b()		w: (20538)
  c()		w: (1)
  f❆1_c(x1)		w: (1 + x1)
  f(x1,x2)		w: (x2 + 2 * x1)
  f❆1_b(x1)		w: (x1)
  f❆1_d(x1)		w: (1 + x1)
  f❆1_a(x1)		w: (1 + x1)
Number of strict rules: 4
Direct poly ... failed.
Dependency Pairs:
   #1: #f❆1_a(f❆1_b(x)) -> #f❆1_a(x)
   #2: #f❆1_d(f❆1_c(x)) -> #f❆1_d(f❆1_a(x))
   #3: #f❆1_d(f❆1_c(x)) -> #f❆1_a(x)
   #4: #f❆1_a(f❆1_c(x)) -> #f❆1_a(x)
Number of SCCs: 2, DPs: 3
	SCC { #2 }
Sum... succeeded.
  a()		w: (0)
  d()		w: (0)
  b()		w: (0)
  c()		w: (0)
  #f❆1_d(x1)		w: (x1)
  f❆1_c(x1)		w: (2 + x1)
  f(x1,x2)		w: (0)
  #f❆1_a(x1)		w: (0)
  f❆1_b(x1)		w: (1)
  f❆1_d(x1)		w: (0)
  f❆1_a(x1)		w: (1 + x1)
    USABLE RULES: { 1 2 4 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 2
	SCC { #1 #4 }
Sum... succeeded.
  a()		w: (0)
  d()		w: (0)
  b()		w: (0)
  c()		w: (0)
  #f❆1_d(x1)		w: (x1)
  f❆1_c(x1)		w: (1 + x1)
  f(x1,x2)		w: (0)
  #f❆1_a(x1)		w: (x1)
  f❆1_b(x1)		w: (2438 + x1)
  f❆1_d(x1)		w: (0)
  f❆1_a(x1)		w: (2439 + x1)
    USABLE RULES: { 1 2 4 }
    Removed DPs: #1 #4
Number of SCCs: 0, DPs: 0