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(), V1)) -> mark(U12(isNatIListKind(V1), V1))
  , active(U12(X1, X2)) -> U12(active(X1), X2)
  , active(U12(tt(), V1)) -> mark(U13(isNatList(V1)))
  , active(isNatIListKind(zeros())) -> mark(tt())
  , active(isNatIListKind(cons(V1, V2))) ->
    mark(U51(isNatKind(V1), V2))
  , active(isNatIListKind(nil())) -> mark(tt())
  , active(U13(X)) -> U13(active(X))
  , active(U13(tt())) -> mark(tt())
  , active(isNatList(cons(V1, V2))) ->
    mark(U81(isNatKind(V1), V1, V2))
  , active(isNatList(nil())) -> mark(tt())
  , active(U21(X1, X2)) -> U21(active(X1), X2)
  , active(U21(tt(), V1)) -> mark(U22(isNatKind(V1), V1))
  , active(U22(X1, X2)) -> U22(active(X1), X2)
  , active(U22(tt(), V1)) -> mark(U23(isNat(V1)))
  , active(isNatKind(0())) -> mark(tt())
  , active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
  , active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
  , active(U23(X)) -> U23(active(X))
  , active(U23(tt())) -> mark(tt())
  , active(isNat(0())) -> mark(tt())
  , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
  , active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1), V1))
  , active(U31(X1, X2)) -> U31(active(X1), X2)
  , active(U31(tt(), V)) -> mark(U32(isNatIListKind(V), V))
  , active(U32(X1, X2)) -> U32(active(X1), X2)
  , active(U32(tt(), V)) -> mark(U33(isNatList(V)))
  , active(U33(X)) -> U33(active(X))
  , active(U33(tt())) -> mark(tt())
  , active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
  , active(U41(tt(), V1, V2)) -> mark(U42(isNatKind(V1), V1, V2))
  , active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3)
  , active(U42(tt(), V1, V2)) ->
    mark(U43(isNatIListKind(V2), V1, V2))
  , active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3)
  , active(U43(tt(), V1, V2)) ->
    mark(U44(isNatIListKind(V2), V1, V2))
  , active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3)
  , active(U44(tt(), V1, V2)) -> mark(U45(isNat(V1), V2))
  , active(U45(X1, X2)) -> U45(active(X1), X2)
  , active(U45(tt(), V2)) -> mark(U46(isNatIList(V2)))
  , active(U46(X)) -> U46(active(X))
  , active(U46(tt())) -> mark(tt())
  , active(isNatIList(V)) -> mark(U31(isNatIListKind(V), V))
  , active(isNatIList(zeros())) -> mark(tt())
  , active(isNatIList(cons(V1, V2))) ->
    mark(U41(isNatKind(V1), V1, V2))
  , active(U51(X1, X2)) -> U51(active(X1), X2)
  , active(U51(tt(), V2)) -> mark(U52(isNatIListKind(V2)))
  , active(U52(X)) -> U52(active(X))
  , active(U52(tt())) -> mark(tt())
  , active(U61(X)) -> U61(active(X))
  , active(U61(tt())) -> mark(tt())
  , active(U71(X)) -> U71(active(X))
  , active(U71(tt())) -> mark(tt())
  , active(U81(X1, X2, X3)) -> U81(active(X1), X2, X3)
  , active(U81(tt(), V1, V2)) -> mark(U82(isNatKind(V1), V1, V2))
  , active(U82(X1, X2, X3)) -> U82(active(X1), X2, X3)
  , active(U82(tt(), V1, V2)) ->
    mark(U83(isNatIListKind(V2), V1, V2))
  , active(U83(X1, X2, X3)) -> U83(active(X1), X2, X3)
  , active(U83(tt(), V1, V2)) ->
    mark(U84(isNatIListKind(V2), V1, V2))
  , active(U84(X1, X2, X3)) -> U84(active(X1), X2, X3)
  , active(U84(tt(), V1, V2)) -> mark(U85(isNat(V1), V2))
  , active(U85(X1, X2)) -> U85(active(X1), X2)
  , active(U85(tt(), V2)) -> mark(U86(isNatList(V2)))
  , active(U86(X)) -> U86(active(X))
  , active(U86(tt())) -> mark(tt())
  , active(U91(X1, X2, X3)) -> U91(active(X1), X2, X3)
  , active(U91(tt(), L, N)) -> mark(U92(isNatIListKind(L), L, N))
  , active(U92(X1, X2, X3)) -> U92(active(X1), X2, X3)
  , active(U92(tt(), L, N)) -> mark(U93(isNat(N), L, N))
  , active(U93(X1, X2, X3)) -> U93(active(X1), X2, X3)
  , active(U93(tt(), L, N)) -> mark(U94(isNatKind(N), L))
  , active(U94(X1, X2)) -> U94(active(X1), X2)
  , active(U94(tt(), L)) -> mark(s(length(L)))
  , active(s(X)) -> s(active(X))
  , active(length(X)) -> length(active(X))
  , active(length(cons(N, L))) -> mark(U91(isNatList(L), L, N))
  , active(length(nil())) -> mark(0())
  , 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))
  , U12(mark(X1), X2) -> mark(U12(X1, X2))
  , U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
  , isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
  , U13(mark(X)) -> mark(U13(X))
  , U13(ok(X)) -> ok(U13(X))
  , isNatList(ok(X)) -> ok(isNatList(X))
  , U21(mark(X1), X2) -> mark(U21(X1, X2))
  , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2))
  , U22(mark(X1), X2) -> mark(U22(X1, X2))
  , U22(ok(X1), ok(X2)) -> ok(U22(X1, X2))
  , isNatKind(ok(X)) -> ok(isNatKind(X))
  , U23(mark(X)) -> mark(U23(X))
  , U23(ok(X)) -> ok(U23(X))
  , isNat(ok(X)) -> ok(isNat(X))
  , U31(mark(X1), X2) -> mark(U31(X1, X2))
  , U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
  , U32(mark(X1), X2) -> mark(U32(X1, X2))
  , U32(ok(X1), ok(X2)) -> ok(U32(X1, X2))
  , U33(mark(X)) -> mark(U33(X))
  , U33(ok(X)) -> ok(U33(X))
  , U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
  , U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3))
  , U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3))
  , U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3))
  , U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3))
  , U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3))
  , U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3))
  , U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3))
  , U45(mark(X1), X2) -> mark(U45(X1, X2))
  , U45(ok(X1), ok(X2)) -> ok(U45(X1, X2))
  , U46(mark(X)) -> mark(U46(X))
  , U46(ok(X)) -> ok(U46(X))
  , isNatIList(ok(X)) -> ok(isNatIList(X))
  , U51(mark(X1), X2) -> mark(U51(X1, X2))
  , U51(ok(X1), ok(X2)) -> ok(U51(X1, X2))
  , U52(mark(X)) -> mark(U52(X))
  , U52(ok(X)) -> ok(U52(X))
  , U61(mark(X)) -> mark(U61(X))
  , U61(ok(X)) -> ok(U61(X))
  , U71(mark(X)) -> mark(U71(X))
  , U71(ok(X)) -> ok(U71(X))
  , U81(mark(X1), X2, X3) -> mark(U81(X1, X2, X3))
  , U81(ok(X1), ok(X2), ok(X3)) -> ok(U81(X1, X2, X3))
  , U82(mark(X1), X2, X3) -> mark(U82(X1, X2, X3))
  , U82(ok(X1), ok(X2), ok(X3)) -> ok(U82(X1, X2, X3))
  , U83(mark(X1), X2, X3) -> mark(U83(X1, X2, X3))
  , U83(ok(X1), ok(X2), ok(X3)) -> ok(U83(X1, X2, X3))
  , U84(mark(X1), X2, X3) -> mark(U84(X1, X2, X3))
  , U84(ok(X1), ok(X2), ok(X3)) -> ok(U84(X1, X2, X3))
  , U85(mark(X1), X2) -> mark(U85(X1, X2))
  , U85(ok(X1), ok(X2)) -> ok(U85(X1, X2))
  , U86(mark(X)) -> mark(U86(X))
  , U86(ok(X)) -> ok(U86(X))
  , U91(mark(X1), X2, X3) -> mark(U91(X1, X2, X3))
  , U91(ok(X1), ok(X2), ok(X3)) -> ok(U91(X1, X2, X3))
  , U92(mark(X1), X2, X3) -> mark(U92(X1, X2, X3))
  , U92(ok(X1), ok(X2), ok(X3)) -> ok(U92(X1, X2, X3))
  , U93(mark(X1), X2, X3) -> mark(U93(X1, X2, X3))
  , U93(ok(X1), ok(X2), ok(X3)) -> ok(U93(X1, X2, X3))
  , U94(mark(X1), X2) -> mark(U94(X1, X2))
  , U94(ok(X1), ok(X2)) -> ok(U94(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))
  , 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(U12(X1, X2)) -> U12(proper(X1), proper(X2))
  , proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
  , proper(U13(X)) -> U13(proper(X))
  , proper(isNatList(X)) -> isNatList(proper(X))
  , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2))
  , proper(U22(X1, X2)) -> U22(proper(X1), proper(X2))
  , proper(isNatKind(X)) -> isNatKind(proper(X))
  , proper(U23(X)) -> U23(proper(X))
  , proper(isNat(X)) -> isNat(proper(X))
  , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
  , proper(U32(X1, X2)) -> U32(proper(X1), proper(X2))
  , proper(U33(X)) -> U33(proper(X))
  , proper(U41(X1, X2, X3)) ->
    U41(proper(X1), proper(X2), proper(X3))
  , proper(U42(X1, X2, X3)) ->
    U42(proper(X1), proper(X2), proper(X3))
  , proper(U43(X1, X2, X3)) ->
    U43(proper(X1), proper(X2), proper(X3))
  , proper(U44(X1, X2, X3)) ->
    U44(proper(X1), proper(X2), proper(X3))
  , proper(U45(X1, X2)) -> U45(proper(X1), proper(X2))
  , proper(U46(X)) -> U46(proper(X))
  , proper(isNatIList(X)) -> isNatIList(proper(X))
  , proper(U51(X1, X2)) -> U51(proper(X1), proper(X2))
  , proper(U52(X)) -> U52(proper(X))
  , proper(U61(X)) -> U61(proper(X))
  , proper(U71(X)) -> U71(proper(X))
  , proper(U81(X1, X2, X3)) ->
    U81(proper(X1), proper(X2), proper(X3))
  , proper(U82(X1, X2, X3)) ->
    U82(proper(X1), proper(X2), proper(X3))
  , proper(U83(X1, X2, X3)) ->
    U83(proper(X1), proper(X2), proper(X3))
  , proper(U84(X1, X2, X3)) ->
    U84(proper(X1), proper(X2), proper(X3))
  , proper(U85(X1, X2)) -> U85(proper(X1), proper(X2))
  , proper(U86(X)) -> U86(proper(X))
  , proper(U91(X1, X2, X3)) ->
    U91(proper(X1), proper(X2), proper(X3))
  , proper(U92(X1, X2, X3)) ->
    U92(proper(X1), proper(X2), proper(X3))
  , proper(U93(X1, X2, X3)) ->
    U93(proper(X1), proper(X2), proper(X3))
  , proper(U94(X1, X2)) -> U94(proper(X1), proper(X2))
  , proper(s(X)) -> s(proper(X))
  , proper(length(X)) -> length(proper(X))
  , proper(nil()) -> ok(nil())
  , 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) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
            to the following reason:
            
            The input cannot be shown compatible
         
         2) 'bsearch-popstar (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..