MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { active(zeros()) -> mark(cons(0(), zeros()))
  , active(cons(X1, X2)) -> cons(active(X1), X2)
  , active(U11(X1, X2)) -> U11(active(X1), X2)
  , active(U11(tt(), L)) -> mark(s(length(L)))
  , active(s(X)) -> s(active(X))
  , active(length(X)) -> length(active(X))
  , active(length(cons(N, L))) ->
    mark(U11(and(isNatList(L), isNat(N)), L))
  , active(length(nil())) -> mark(0())
  , active(U21(X)) -> U21(active(X))
  , active(U21(tt())) -> mark(nil())
  , active(U31(X1, X2, X3, X4)) -> U31(active(X1), X2, X3, X4)
  , active(U31(tt(), IL, M, N)) -> mark(cons(N, take(M, IL)))
  , active(take(X1, X2)) -> take(X1, active(X2))
  , active(take(X1, X2)) -> take(active(X1), X2)
  , active(take(0(), IL)) -> mark(U21(isNatIList(IL)))
  , active(take(s(M), cons(N, IL))) ->
    mark(U31(and(isNatIList(IL), and(isNat(M), isNat(N))), IL, M, N))
  , active(and(X1, X2)) -> and(active(X1), X2)
  , active(and(tt(), X)) -> mark(X)
  , active(isNat(0())) -> mark(tt())
  , active(isNat(s(V1))) -> mark(isNat(V1))
  , active(isNat(length(V1))) -> mark(isNatList(V1))
  , active(isNatList(cons(V1, V2))) ->
    mark(and(isNat(V1), isNatList(V2)))
  , active(isNatList(nil())) -> mark(tt())
  , active(isNatList(take(V1, V2))) ->
    mark(and(isNat(V1), isNatIList(V2)))
  , active(isNatIList(V)) -> mark(isNatList(V))
  , active(isNatIList(zeros())) -> mark(tt())
  , active(isNatIList(cons(V1, V2))) ->
    mark(and(isNat(V1), isNatIList(V2)))
  , cons(mark(X1), X2) -> mark(cons(X1, X2))
  , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  , U11(mark(X1), X2) -> mark(U11(X1, X2))
  , U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
  , s(mark(X)) -> mark(s(X))
  , s(ok(X)) -> ok(s(X))
  , length(mark(X)) -> mark(length(X))
  , length(ok(X)) -> ok(length(X))
  , U21(mark(X)) -> mark(U21(X))
  , U21(ok(X)) -> ok(U21(X))
  , U31(mark(X1), X2, X3, X4) -> mark(U31(X1, X2, X3, X4))
  , U31(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U31(X1, X2, X3, X4))
  , take(X1, mark(X2)) -> mark(take(X1, X2))
  , take(mark(X1), X2) -> mark(take(X1, X2))
  , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
  , and(mark(X1), X2) -> mark(and(X1, X2))
  , and(ok(X1), ok(X2)) -> ok(and(X1, X2))
  , isNat(ok(X)) -> ok(isNat(X))
  , isNatList(ok(X)) -> ok(isNatList(X))
  , isNatIList(ok(X)) -> ok(isNatIList(X))
  , proper(zeros()) -> ok(zeros())
  , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  , proper(0()) -> ok(0())
  , proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
  , proper(tt()) -> ok(tt())
  , proper(s(X)) -> s(proper(X))
  , proper(length(X)) -> length(proper(X))
  , proper(U21(X)) -> U21(proper(X))
  , proper(nil()) -> ok(nil())
  , proper(U31(X1, X2, X3, X4)) ->
    U31(proper(X1), proper(X2), proper(X3), proper(X4))
  , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
  , proper(and(X1, X2)) -> and(proper(X1), proper(X2))
  , proper(isNat(X)) -> isNat(proper(X))
  , proper(isNatList(X)) -> isNatList(proper(X))
  , proper(isNatIList(X)) -> isNatIList(proper(X))
  , top(mark(X)) -> top(proper(X))
  , top(ok(X)) -> top(active(X)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
   
   Empty strict component of the problem is NOT empty.

2) 'Best' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'WithProblem (timeout of 60 seconds)' failed due to the
      following reason:
      
      Computation stopped due to timeout after 60.0 seconds.
   
   2) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
         failed due to the following reason:
         
         Computation stopped due to timeout after 30.0 seconds.
      
      2) 'Best' failed due to the following reason:
         
         None of the processors succeeded.
         
         Details of failed attempt(s):
         -----------------------------
         1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
            following reason:
            
            The input cannot be shown compatible
         
         2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
            to the following reason:
            
            The input cannot be shown compatible
         
      
      3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
         due to the following reason:
         
         None of the processors succeeded.
         
         Details of failed attempt(s):
         -----------------------------
         1) 'Bounds with minimal-enrichment and initial automaton 'match''
            failed due to the following reason:
            
            match-boundness of the problem could not be verified.
         
         2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
            failed due to the following reason:
            
            match-boundness of the problem could not be verified.
         
      
   


Arrrr..