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


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


YES
Input TRS:
    1: and(false(),false()) -> false()
    2: and(true(),false()) -> false()
    3: and(false(),true()) -> false()
    4: and(true(),true()) -> true()
    5: eq(nil(),nil()) -> true()
    6: eq(cons(T,L),nil()) -> false()
    7: eq(nil(),cons(T,L)) -> false()
    8: eq(cons(T,L),cons(Tp,Lp)) -> and(eq(T,Tp),eq(L,Lp))
    9: eq(var(L),var(Lp)) -> eq(L,Lp)
    10: eq(var(L),apply(T,S)) -> false()
    11: eq(var(L),lambda(X,T)) -> false()
    12: eq(apply(T,S),var(L)) -> false()
    13: eq(apply(T,S),apply(Tp,Sp)) -> and(eq(T,Tp),eq(S,Sp))
    14: eq(apply(T,S),lambda(X,Tp)) -> false()
    15: eq(lambda(X,T),var(L)) -> false()
    16: eq(lambda(X,T),apply(Tp,Sp)) -> false()
    17: eq(lambda(X,T),lambda(Xp,Tp)) -> and(eq(T,Tp),eq(X,Xp))
    18: if(true(),var(K),var(L)) -> var(K)
    19: if(false(),var(K),var(L)) -> var(L)
    20: ren(var(L),var(K),var(Lp)) -> if(eq(L,Lp),var(K),var(Lp))
    21: ren(X,Y,apply(T,S)) -> apply(ren(X,Y,T),ren(X,Y,S))
    22: 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: 22
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #eq(apply(T,S),apply(Tp,Sp)) -> #and(eq(T,Tp),eq(S,Sp))
   #2: #eq(apply(T,S),apply(Tp,Sp)) -> #eq(T,Tp)
   #3: #eq(apply(T,S),apply(Tp,Sp)) -> #eq(S,Sp)
   #4: #eq(var(L),var(Lp)) -> #eq(L,Lp)
   #5: #ren(var(L),var(K),var(Lp)) -> #if(eq(L,Lp),var(K),var(Lp))
   #6: #ren(var(L),var(K),var(Lp)) -> #eq(L,Lp)
   #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(lambda(X,T),lambda(Xp,Tp)) -> #and(eq(T,Tp),eq(X,Xp))
   #10: #eq(lambda(X,T),lambda(Xp,Tp)) -> #eq(T,Tp)
   #11: #eq(lambda(X,T),lambda(Xp,Tp)) -> #eq(X,Xp)
   #12: #ren(X,Y,apply(T,S)) -> #ren(X,Y,T)
   #13: #ren(X,Y,apply(T,S)) -> #ren(X,Y,S)
   #14: #eq(cons(T,L),cons(Tp,Lp)) -> #and(eq(T,Tp),eq(L,Lp))
   #15: #eq(cons(T,L),cons(Tp,Lp)) -> #eq(T,Tp)
   #16: #eq(cons(T,L),cons(Tp,Lp)) -> #eq(L,Lp)
Number of SCCs: 2, DPs: 11
	SCC { #7 #8 #12 #13 }
Sum... succeeded.
  apply(x1,x2)		w: (28101 + x2 + x1)
  ren(x1,x2,x3)		w: (x3)
  and(x1,x2)		w: (1)
  eq(x1,x2)		w: (0)
  lambda(x1,x2)		w: (30613 + x2 + x1)
  false()		w: (1)
  true()		w: (1)
  #eq(x1,x2)		w: (0)
  if(x1,x2,x3)		w: (0)
  nil()		w: (1143)
  #ren(x1,x2,x3)		w: (281 + x3 + x2)
  cons(x1,x2)		w: (5854 + x2 + x1)
  #if(x1,x2,x3)		w: (0)
  var(x1)		w: (0)
  #and(x1,x2)		w: (0)
    USABLE RULES: { 18..22 }
    Removed DPs: #7 #8 #12 #13
Number of SCCs: 1, DPs: 7
	SCC { #2..4 #10 #11 #15 #16 }
Sum... succeeded.
  apply(x1,x2)		w: (1 + x2 + x1)
  ren(x1,x2,x3)		w: (0)
  and(x1,x2)		w: (2)
  eq(x1,x2)		w: (x1)
  lambda(x1,x2)		w: (1 + x2 + x1)
  false()		w: (2)
  true()		w: (2)
  #eq(x1,x2)		w: (32278 + x2 + x1)
  if(x1,x2,x3)		w: (9725 + x3)
  nil()		w: (1)
  #ren(x1,x2,x3)		w: (281)
  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..4 #10 #11 #15 #16
Number of SCCs: 0, DPs: 0