/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: and(true(),y) -> y
    2: and(false(),y) -> false()
    3: eq(nil(),nil()) -> true()
    4: eq(cons(t,l),nil()) -> false()
    5: eq(nil(),cons(t,l)) -> false()
    6: eq(cons(t,l),cons(t',l')) -> and(eq(t,t'),eq(l,l'))
    7: eq(var(l),var(l')) -> eq(l,l')
    8: eq(var(l),apply(t,s)) -> false()
    9: eq(var(l),lambda(x,t)) -> false()
    10: eq(apply(t,s),var(l)) -> false()
    11: eq(apply(t,s),apply(t',s')) -> and(eq(t,t'),eq(s,s'))
    12: eq(apply(t,s),lambda(x,t)) -> false()
    13: eq(lambda(x,t),var(l)) -> false()
    14: eq(lambda(x,t),apply(t,s)) -> false()
    15: eq(lambda(x,t),lambda(x',t')) -> and(eq(x,x'),eq(t,t'))
    16: if(true(),var(k),var(l')) -> var(k)
    17: if(false(),var(k),var(l')) -> var(l')
    18: ren(var(l),var(k),var(l')) -> if(eq(l,l'),var(k),var(l'))
    19: ren(x,y,apply(t,s)) -> apply(ren(x,y,t),ren(x,y,s))
    20: ren(x,y,lambda(z,t)) -> lambda(var(cons(x,cons(y,cons(lambda(z,t),nil())))),ren(x,y,ren(z,var(cons(x,cons(y,cons(lambda(z,t),nil())))),t)))
Number of strict rules: 20
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #eq(cons(t,l),cons(t',l')) -> #and(eq(t,t'),eq(l,l'))
   #2: #eq(cons(t,l),cons(t',l')) -> #eq(t,t')
   #3: #eq(cons(t,l),cons(t',l')) -> #eq(l,l')
   #4: #eq(apply(t,s),apply(t',s')) -> #and(eq(t,t'),eq(s,s'))
   #5: #eq(apply(t,s),apply(t',s')) -> #eq(t,t')
   #6: #eq(apply(t,s),apply(t',s')) -> #eq(s,s')
   #7: #ren(x,y,lambda(z,t)) -> #ren(x,y,ren(z,var(cons(x,cons(y,cons(lambda(z,t),nil())))),t))
   #8: #ren(x,y,lambda(z,t)) -> #ren(z,var(cons(x,cons(y,cons(lambda(z,t),nil())))),t)
   #9: #eq(var(l),var(l')) -> #eq(l,l')
   #10: #ren(x,y,apply(t,s)) -> #ren(x,y,t)
   #11: #ren(x,y,apply(t,s)) -> #ren(x,y,s)
   #12: #eq(lambda(x,t),lambda(x',t')) -> #and(eq(x,x'),eq(t,t'))
   #13: #eq(lambda(x,t),lambda(x',t')) -> #eq(x,x')
   #14: #eq(lambda(x,t),lambda(x',t')) -> #eq(t,t')
   #15: #ren(var(l),var(k),var(l')) -> #if(eq(l,l'),var(k),var(l'))
   #16: #ren(var(l),var(k),var(l')) -> #eq(l,l')
Number of SCCs: 2, DPs: 11
	SCC { #7 #8 #10 #11 }
Sum... succeeded.
  apply(x1,x2)		w: (8366 + x2 + x1)
  ren(x1,x2,x3)		w: (x3)
  and(x1,x2)		w: (32285 + x2 + x1)
  eq(x1,x2)		w: (1)
  lambda(x1,x2)		w: (10452 + x2)
  false()		w: (2)
  true()		w: (2)
  #eq(x1,x2)		w: (0)
  if(x1,x2,x3)		w: (1)
  nil()		w: (1)
  #ren(x1,x2,x3)		w: (30612 + x3 + x2)
  cons(x1,x2)		w: (1 + x2 + x1)
  #if(x1,x2,x3)		w: (0)
  var(x1)		w: (1)
  #and(x1,x2)		w: (0)
    USABLE RULES: { 16..20 }
    Removed DPs: #7 #8 #10 #11
Number of SCCs: 1, DPs: 7
	SCC { #2 #3 #5 #6 #9 #13 #14 }
Sum... succeeded.
  apply(x1,x2)		w: (14681 + x2 + x1)
  ren(x1,x2,x3)		w: (x3)
  and(x1,x2)		w: (31892 + x1)
  eq(x1,x2)		w: (1)
  lambda(x1,x2)		w: (x2 + x1)
  false()		w: (2)
  true()		w: (2)
  #eq(x1,x2)		w: (20976 + x2)
  if(x1,x2,x3)		w: (x2)
  nil()		w: (0)
  #ren(x1,x2,x3)		w: (30612)
  cons(x1,x2)		w: (x2 + x1)
  #if(x1,x2,x3)		w: (0)
  var(x1)		w: (x1)
  #and(x1,x2)		w: (0)
    USABLE RULES: { 16 }
    Removed DPs: #5 #6
Number of SCCs: 1, DPs: 5
	SCC { #2 #3 #9 #13 #14 }
Sum... succeeded.
  apply(x1,x2)		w: (1 + x2)
  ren(x1,x2,x3)		w: (9726)
  and(x1,x2)		w: (2)
  eq(x1,x2)		w: (x2)
  lambda(x1,x2)		w: (x2 + x1)
  false()		w: (2)
  true()		w: (2)
  #eq(x1,x2)		w: (20975 + x1)
  if(x1,x2,x3)		w: (9725 + x3)
  nil()		w: (0)
  #ren(x1,x2,x3)		w: (30612)
  cons(x1,x2)		w: (x2 + x1)
  #if(x1,x2,x3)		w: (0)
  var(x1)		w: (1 + x1)
  #and(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #9
Number of SCCs: 1, DPs: 4
	SCC { #2 #3 #13 #14 }
Sum... succeeded.
  apply(x1,x2)		w: (x2)
  ren(x1,x2,x3)		w: (7182)
  and(x1,x2)		w: (1)
  eq(x1,x2)		w: (0)
  lambda(x1,x2)		w: (21238 + x2 + x1)
  false()		w: (1)
  true()		w: (1)
  #eq(x1,x2)		w: (23611 + x1)
  if(x1,x2,x3)		w: (9726 + x3)
  nil()		w: (0)
  #ren(x1,x2,x3)		w: (30612)
  cons(x1,x2)		w: (1 + x2 + x1)
  #if(x1,x2,x3)		w: (0)
  var(x1)		w: (1 + x1)
  #and(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #2 #3 #13 #14
Number of SCCs: 0, DPs: 0