MAYBE

Problem:
 circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
 circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
 circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
 circ(circ(s,t),u) -> circ(s,circ(t,u))
 circ(s,id()) -> s
 circ(id(),s) -> s
 circ(cons(lift(),s),circ(cons(lift(),t),u)) -> circ(cons(lift(),circ(s,t)),u)
 subst(a,id()) -> a
 msubst(a,id()) -> a
 msubst(msubst(a,s),t) -> msubst(a,circ(s,t))

Proof:
 DP Processor:
  DPs:
   circ#(cons(a,s),t) -> circ#(s,t)
   circ#(cons(a,s),t) -> msubst#(a,t)
   circ#(cons(lift(),s),cons(a,t)) -> circ#(s,t)
   circ#(cons(lift(),s),cons(lift(),t)) -> circ#(s,t)
   circ#(circ(s,t),u) -> circ#(t,u)
   circ#(circ(s,t),u) -> circ#(s,circ(t,u))
   circ#(cons(lift(),s),circ(cons(lift(),t),u)) -> circ#(s,t)
   circ#(cons(lift(),s),circ(cons(lift(),t),u)) -> circ#(cons(lift(),circ(s,t)),u)
   msubst#(msubst(a,s),t) -> circ#(s,t)
   msubst#(msubst(a,s),t) -> msubst#(a,circ(s,t))
  TRS:
   circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
   circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
   circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
   circ(circ(s,t),u) -> circ(s,circ(t,u))
   circ(s,id()) -> s
   circ(id(),s) -> s
   circ(cons(lift(),s),circ(cons(lift(),t),u)) -> circ(cons(lift(),circ(s,t)),u)
   subst(a,id()) -> a
   msubst(a,id()) -> a
   msubst(msubst(a,s),t) -> msubst(a,circ(s,t))
  Usable Rule Processor:
   DPs:
    circ#(cons(a,s),t) -> circ#(s,t)
    circ#(cons(a,s),t) -> msubst#(a,t)
    circ#(cons(lift(),s),cons(a,t)) -> circ#(s,t)
    circ#(cons(lift(),s),cons(lift(),t)) -> circ#(s,t)
    circ#(circ(s,t),u) -> circ#(t,u)
    circ#(circ(s,t),u) -> circ#(s,circ(t,u))
    circ#(cons(lift(),s),circ(cons(lift(),t),u)) -> circ#(s,t)
    circ#(cons(lift(),s),circ(cons(lift(),t),u)) -> circ#(cons(lift(),circ(s,t)),u)
    msubst#(msubst(a,s),t) -> circ#(s,t)
    msubst#(msubst(a,s),t) -> msubst#(a,circ(s,t))
   TRS:
    circ(cons(a,s),t) -> cons(msubst(a,t),circ(s,t))
    circ(cons(lift(),s),cons(a,t)) -> cons(a,circ(s,t))
    circ(cons(lift(),s),cons(lift(),t)) -> cons(lift(),circ(s,t))
    circ(circ(s,t),u) -> circ(s,circ(t,u))
    circ(s,id()) -> s
    circ(id(),s) -> s
    circ(cons(lift(),s),circ(cons(lift(),t),u)) -> circ(cons(lift(),circ(s,t)),u)
    msubst(a,id()) -> a
    msubst(msubst(a,s),t) -> msubst(a,circ(s,t))
   Open