/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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NO

Problem:
 app(app(app(if(),true()),xs),ys) -> xs
 app(app(app(if(),false()),xs),ys) -> ys
 app(app(lt(),app(s(),x)),app(s(),y)) -> app(app(lt(),x),y)
 app(app(lt(),0()),app(s(),y)) -> true()
 app(app(lt(),y),0()) -> false()
 app(app(eq(),x),x) -> true()
 app(app(eq(),app(s(),x)),0()) -> false()
 app(app(eq(),0()),app(s(),x)) -> false()
 app(app(merge(),xs),nil()) -> xs
 app(app(merge(),nil()),ys) -> ys
 app(app(merge(),app(app(cons(),x),xs)),app(app(cons(),y),ys)) ->
 app(app(app(if(),app(app(lt(),x),y)),app(app(cons(),x),app(app(merge(),xs),app(app(cons(),y),ys)))),
     app(app(app(if(),app(app(eq(),x),y)),app(app(cons(),x),app(app(merge(),xs),ys))),
         app(app(cons(),y),app(app(merge(),app(app(cons(),x),xs)),ys))))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(mult(),0()),x) -> 0()
 app(app(mult(),app(s(),x)),y) -> app(app(plus(),y),app(app(mult(),x),y))
 app(app(plus(),0()),x) -> 0()
 app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
 list1() -> app(app(map(),app(mult(),app(s(),app(s(),0())))),hamming())
 list2() -> app(app(map(),app(mult(),app(s(),app(s(),app(s(),0()))))),hamming())
 list3() -> app(app(map(),app(mult(),app(s(),app(s(),app(s(),app(s(),app(s(),0()))))))),hamming())
 hamming() ->
 app(app(cons(),app(s(),0())),app(app(merge(),list1()),app(app(merge(),list2()),list3())))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   list3 ==> list30/0
   list2 ==> list20/0
   hamming ==> hamming0/0
   list1 ==> list10/0
   plus ==> plus0/0 plus1/1 plus2/2
   mult ==> mult0/0 mult1/1 mult2/2
   map ==> map0/0 map1/1 map2/2
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   merge ==> merge0/0 merge1/1 merge2/2
   eq ==> eq0/0 eq1/1 eq2/2
   0 ==> 00/0
   s ==> s0/0 s1/1
   lt ==> lt0/0 lt1/1 lt2/2
   false ==> false0/0
   true ==> true0/0
   if ==> if0/0 if1/1 if2/2 if3/3
   
  uncurry-rules:
   app(if2(x5,x6),x7) -> if3(x5,x6,x7)
   app(if1(x5),x6) -> if2(x5,x6)
   app(if0(),x5) -> if1(x5)
   app(lt1(x11),x12) -> lt2(x11,x12)
   app(lt0(),x11) -> lt1(x11)
   app(s0(),x14) -> s1(x14)
   app(eq1(x17),x18) -> eq2(x17,x18)
   app(eq0(),x17) -> eq1(x17)
   app(merge1(x20),x21) -> merge2(x20,x21)
   app(merge0(),x20) -> merge1(x20)
   app(cons1(x24),x25) -> cons2(x24,x25)
   app(cons0(),x24) -> cons1(x24)
   app(map1(x27),x28) -> map2(x27,x28)
   app(map0(),x27) -> map1(x27)
   app(mult1(x30),x31) -> mult2(x30,x31)
   app(mult0(),x30) -> mult1(x30)
   app(plus1(x33),x34) -> plus2(x33,x34)
   app(plus0(),x33) -> plus1(x33)
  eta-rules:
   
  problem:
   if3(true0(),xs,ys) -> xs
   if3(false0(),xs,ys) -> ys
   lt2(s1(x),s1(y)) -> lt2(x,y)
   lt2(00(),s1(y)) -> true0()
   lt2(y,00()) -> false0()
   eq2(x,x) -> true0()
   eq2(s1(x),00()) -> false0()
   eq2(00(),s1(x)) -> false0()
   merge2(xs,nil0()) -> xs
   merge2(nil0(),ys) -> ys
   merge2(cons2(x,xs),cons2(y,ys)) ->
   if3(lt2(x,y),cons2(x,merge2(xs,cons2(y,ys))),if3(eq2(x,y),cons2(x,merge2(xs,ys)),
                                                    cons2(y,merge2(cons2(x,xs),ys))))
   map2(f,nil0()) -> nil0()
   map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
   mult2(00(),x) -> 00()
   mult2(s1(x),y) -> plus2(y,mult2(x,y))
   plus2(00(),x) -> 00()
   plus2(s1(x),y) -> s1(plus2(x,y))
   list10() -> map2(mult1(s1(s1(00()))),hamming0())
   list20() -> map2(mult1(s1(s1(s1(00())))),hamming0())
   list30() -> map2(mult1(s1(s1(s1(s1(s1(00())))))),hamming0())
   hamming0() -> cons2(s1(00()),merge2(list10(),merge2(list20(),list30())))
   app(if2(x5,x6),x7) -> if3(x5,x6,x7)
   app(if1(x5),x6) -> if2(x5,x6)
   app(if0(),x5) -> if1(x5)
   app(lt1(x11),x12) -> lt2(x11,x12)
   app(lt0(),x11) -> lt1(x11)
   app(s0(),x14) -> s1(x14)
   app(eq1(x17),x18) -> eq2(x17,x18)
   app(eq0(),x17) -> eq1(x17)
   app(merge1(x20),x21) -> merge2(x20,x21)
   app(merge0(),x20) -> merge1(x20)
   app(cons1(x24),x25) -> cons2(x24,x25)
   app(cons0(),x24) -> cons1(x24)
   app(map1(x27),x28) -> map2(x27,x28)
   app(map0(),x27) -> map1(x27)
   app(mult1(x30),x31) -> mult2(x30,x31)
   app(mult0(),x30) -> mult1(x30)
   app(plus1(x33),x34) -> plus2(x33,x34)
   app(plus0(),x33) -> plus1(x33)
  Unfolding Processor:
   loop length: 2
   terms:
    list10()
    map2(mult1(s1(s1(00()))),hamming0())
   context: map2(mult1(s1(s1(00()))),cons2(s1(00()),merge2([],merge2(list20(),list30()))))
   substitution:
    
   Qed