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


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


YES
Input TRS:
    1: f(a(),a()) -> f(a(),b())
    2: f(a(),b()) -> f(s(a()),c())
    3: f(s(X),c()) -> f(X,c())
    4: f(c(),c()) -> f(a(),a())
Number of strict rules: 4
Direct poly ... failed.
Freezing f
1: f❆1_a(a()) -> f❆1_a(b())
2: f❆1_a(b()) -> f❆1_s(a(),c())
3: f❆1_s(X,c()) -> f(X,c())
4: f❆1_c(c()) -> f❆1_a(a())
5: f(a(),_1) ->= f❆1_a(_1)
6: f(s(_1),_2) ->= f❆1_s(_1,_2)
7: f(c(),_1) ->= f❆1_c(_1)
Number of strict rules: 4
Direct poly ... removes: 6
  a()		w: (1)
  s(x1)		w: (1 + x1)
  b()		w: (1)
  c()		w: (1)
  f❆1_s(x1,x2)		w: (11688 + x2 + x1)
  f❆1_c(x1)		w: (11689 + x1)
  f(x1,x2)		w: (11688 + x2 + x1)
  f❆1_a(x1)		w: (11689 + x1)
Number of strict rules: 4
Direct poly ... failed.
Dependency Pairs:
   #1: #f❆1_a(b()) -> #f❆1_s(a(),c())
   #2: #f(c(),_1) ->? #f❆1_c(_1)
   #3: #f(a(),_1) ->? #f❆1_a(_1)
   #4: #f❆1_s(X,c()) -> #f(X,c())
   #5: #f❆1_a(a()) -> #f❆1_a(b())
   #6: #f❆1_c(c()) -> #f❆1_a(a())
Number of SCCs: 1, DPs: 6
	SCC { #1..6 }
Sum... succeeded.
  a()		w: (2)
  #f❆1_s(x1,x2)		w: (30213)
  s(x1)		w: (0)
  b()		w: (2)
  c()		w: (1)
  f❆1_s(x1,x2)		w: (0)
  f❆1_c(x1)		w: (0)
  f(x1,x2)		w: (0)
  #f❆1_c(x1)		w: (30212 + x1)
  #f❆1_a(x1)		w: (30211 + x1)
  #f(x1,x2)		w: (30212 + x2)
  f❆1_a(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 5
	SCC { #1 #2 #4..6 }
Sum... succeeded.
  a()		w: (2)
  #f❆1_s(x1,x2)		w: (1 + x2 + x1)
  s(x1)		w: (0)
  b()		w: (1)
  c()		w: (7)
  f❆1_s(x1,x2)		w: (0)
  f❆1_c(x1)		w: (0)
  f(x1,x2)		w: (0)
  #f❆1_c(x1)		w: (6 + x1)
  #f❆1_a(x1)		w: (10 + x1)
  #f(x1,x2)		w: (x2 + x1)
  f❆1_a(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1 #2 #4..6
Number of SCCs: 0, DPs: 0