MAYBE

Problem:
 app(nil(),k) -> k
 app(l,nil()) -> l
 app(cons(x,l),k) -> cons(x,app(l,k))
 sum(cons(x,nil())) -> cons(x,nil())
 sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
 a(h(),h(),x) -> s(x)
 a(x,s(y),h()) -> a(x,y,s(h()))
 a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
 a(s(x),h(),z) -> a(x,z,z)

Proof:
 DP Processor:
  DPs:
   app#(cons(x,l),k) -> app#(l,k)
   sum#(cons(x,cons(y,l))) -> a#(x,y,h())
   sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h()),l))
   a#(x,s(y),h()) -> a#(x,y,s(h()))
   a#(x,s(y),s(z)) -> a#(x,s(y),z)
   a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z))
   a#(s(x),h(),z) -> a#(x,z,z)
  TRS:
   app(nil(),k) -> k
   app(l,nil()) -> l
   app(cons(x,l),k) -> cons(x,app(l,k))
   sum(cons(x,nil())) -> cons(x,nil())
   sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
   a(h(),h(),x) -> s(x)
   a(x,s(y),h()) -> a(x,y,s(h()))
   a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
   a(s(x),h(),z) -> a(x,z,z)
  Usable Rule Processor:
   DPs:
    app#(cons(x,l),k) -> app#(l,k)
    sum#(cons(x,cons(y,l))) -> a#(x,y,h())
    sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h()),l))
    a#(x,s(y),h()) -> a#(x,y,s(h()))
    a#(x,s(y),s(z)) -> a#(x,s(y),z)
    a#(x,s(y),s(z)) -> a#(x,y,a(x,s(y),z))
    a#(s(x),h(),z) -> a#(x,z,z)
   TRS:
    a(h(),h(),x) -> s(x)
    a(x,s(y),h()) -> a(x,y,s(h()))
    a(s(x),h(),z) -> a(x,z,z)
    a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
   Open