MAYBE

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

Strict Trs:
  { active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
  , active(U11(tt(), V1, V2)) -> mark(U12(isNat(V1), V2))
  , active(U12(X1, X2)) -> U12(active(X1), X2)
  , active(U12(tt(), V2)) -> mark(U13(isNat(V2)))
  , active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
  , active(isNat(plus(V1, V2))) ->
    mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2))
  , active(isNat(0())) -> mark(tt())
  , active(U13(X)) -> U13(active(X))
  , active(U13(tt())) -> mark(tt())
  , active(U21(X1, X2)) -> U21(active(X1), X2)
  , active(U21(tt(), V1)) -> mark(U22(isNat(V1)))
  , active(U22(X)) -> U22(active(X))
  , active(U22(tt())) -> mark(tt())
  , active(U31(X1, X2)) -> U31(active(X1), X2)
  , active(U31(tt(), N)) -> mark(N)
  , active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
  , active(U41(tt(), M, N)) -> mark(s(plus(N, M)))
  , active(s(X)) -> s(active(X))
  , active(plus(X1, X2)) -> plus(X1, active(X2))
  , active(plus(X1, X2)) -> plus(active(X1), X2)
  , active(plus(N, s(M))) ->
    mark(U41(and(and(isNat(M), isNatKind(M)),
                 and(isNat(N), isNatKind(N))),
             M,
             N))
  , active(plus(N, 0())) -> mark(U31(and(isNat(N), isNatKind(N)), N))
  , active(and(X1, X2)) -> and(active(X1), X2)
  , active(and(tt(), X)) -> mark(X)
  , active(isNatKind(s(V1))) -> mark(isNatKind(V1))
  , active(isNatKind(plus(V1, V2))) ->
    mark(and(isNatKind(V1), isNatKind(V2)))
  , active(isNatKind(0())) -> mark(tt())
  , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3))
  , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3))
  , U12(mark(X1), X2) -> mark(U12(X1, X2))
  , U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
  , isNat(ok(X)) -> ok(isNat(X))
  , U13(mark(X)) -> mark(U13(X))
  , U13(ok(X)) -> ok(U13(X))
  , U21(mark(X1), X2) -> mark(U21(X1, X2))
  , U21(ok(X1), ok(X2)) -> ok(U21(X1, X2))
  , U22(mark(X)) -> mark(U22(X))
  , U22(ok(X)) -> ok(U22(X))
  , U31(mark(X1), X2) -> mark(U31(X1, X2))
  , U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
  , U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
  , U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3))
  , s(mark(X)) -> mark(s(X))
  , s(ok(X)) -> ok(s(X))
  , plus(X1, mark(X2)) -> mark(plus(X1, X2))
  , plus(mark(X1), X2) -> mark(plus(X1, X2))
  , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
  , and(mark(X1), X2) -> mark(and(X1, X2))
  , and(ok(X1), ok(X2)) -> ok(and(X1, X2))
  , isNatKind(ok(X)) -> ok(isNatKind(X))
  , proper(U11(X1, X2, X3)) ->
    U11(proper(X1), proper(X2), proper(X3))
  , proper(tt()) -> ok(tt())
  , proper(U12(X1, X2)) -> U12(proper(X1), proper(X2))
  , proper(isNat(X)) -> isNat(proper(X))
  , proper(U13(X)) -> U13(proper(X))
  , proper(U21(X1, X2)) -> U21(proper(X1), proper(X2))
  , proper(U22(X)) -> U22(proper(X))
  , proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
  , proper(U41(X1, X2, X3)) ->
    U41(proper(X1), proper(X2), proper(X3))
  , proper(s(X)) -> s(proper(X))
  , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
  , proper(and(X1, X2)) -> and(proper(X1), proper(X2))
  , proper(0()) -> ok(0())
  , proper(isNatKind(X)) -> isNatKind(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) '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 perSymbol-enrichment and initial automaton 'match''
            failed due to the following reason:
            
            match-boundness of the problem could not be verified.
         
         2) 'Bounds with minimal-enrichment and initial automaton 'match''
            failed due to the following reason:
            
            match-boundness of the problem could not be verified.
         
      
   


Arrrr..