MAYBE

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

Strict Trs:
  { U11(tt(), V1, V2) ->
    U12(isNatKind(activate(V1)), activate(V1), activate(V2))
  , U12(tt(), V1, V2) ->
    U13(isNatKind(activate(V2)), activate(V1), activate(V2))
  , isNatKind(n__0()) -> tt()
  , isNatKind(n__plus(V1, V2)) ->
    U31(isNatKind(activate(V1)), activate(V2))
  , isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
  , activate(X) -> X
  , activate(n__0()) -> 0()
  , activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2))
  , activate(n__s(X)) -> s(activate(X))
  , U13(tt(), V1, V2) ->
    U14(isNatKind(activate(V2)), activate(V1), activate(V2))
  , U14(tt(), V1, V2) -> U15(isNat(activate(V1)), activate(V2))
  , U15(tt(), V2) -> U16(isNat(activate(V2)))
  , isNat(n__0()) -> tt()
  , isNat(n__plus(V1, V2)) ->
    U11(isNatKind(activate(V1)), activate(V1), activate(V2))
  , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1))
  , U16(tt()) -> tt()
  , U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1))
  , U22(tt(), V1) -> U23(isNat(activate(V1)))
  , U23(tt()) -> tt()
  , U31(tt(), V2) -> U32(isNatKind(activate(V2)))
  , U32(tt()) -> tt()
  , U41(tt()) -> tt()
  , U51(tt(), N) -> U52(isNatKind(activate(N)), activate(N))
  , U52(tt(), N) -> activate(N)
  , U61(tt(), M, N) ->
    U62(isNatKind(activate(M)), activate(M), activate(N))
  , U62(tt(), M, N) ->
    U63(isNat(activate(N)), activate(M), activate(N))
  , U63(tt(), M, N) ->
    U64(isNatKind(activate(N)), activate(M), activate(N))
  , U64(tt(), M, N) -> s(plus(activate(N), activate(M)))
  , s(X) -> n__s(X)
  , plus(X1, X2) -> n__plus(X1, X2)
  , plus(N, s(M)) -> U61(isNat(M), M, N)
  , plus(N, 0()) -> U51(isNat(N), N)
  , 0() -> n__0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Arguments of following rules are not normal-forms:

{ plus(N, s(M)) -> U61(isNat(M), M, N)
, plus(N, 0()) -> U51(isNat(N), N) }

All above mentioned rules can be savely removed.

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

Strict Trs:
  { U11(tt(), V1, V2) ->
    U12(isNatKind(activate(V1)), activate(V1), activate(V2))
  , U12(tt(), V1, V2) ->
    U13(isNatKind(activate(V2)), activate(V1), activate(V2))
  , isNatKind(n__0()) -> tt()
  , isNatKind(n__plus(V1, V2)) ->
    U31(isNatKind(activate(V1)), activate(V2))
  , isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
  , activate(X) -> X
  , activate(n__0()) -> 0()
  , activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2))
  , activate(n__s(X)) -> s(activate(X))
  , U13(tt(), V1, V2) ->
    U14(isNatKind(activate(V2)), activate(V1), activate(V2))
  , U14(tt(), V1, V2) -> U15(isNat(activate(V1)), activate(V2))
  , U15(tt(), V2) -> U16(isNat(activate(V2)))
  , isNat(n__0()) -> tt()
  , isNat(n__plus(V1, V2)) ->
    U11(isNatKind(activate(V1)), activate(V1), activate(V2))
  , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1))
  , U16(tt()) -> tt()
  , U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1))
  , U22(tt(), V1) -> U23(isNat(activate(V1)))
  , U23(tt()) -> tt()
  , U31(tt(), V2) -> U32(isNatKind(activate(V2)))
  , U32(tt()) -> tt()
  , U41(tt()) -> tt()
  , U51(tt(), N) -> U52(isNatKind(activate(N)), activate(N))
  , U52(tt(), N) -> activate(N)
  , U61(tt(), M, N) ->
    U62(isNatKind(activate(M)), activate(M), activate(N))
  , U62(tt(), M, N) ->
    U63(isNat(activate(N)), activate(M), activate(N))
  , U63(tt(), M, N) ->
    U64(isNatKind(activate(N)), activate(M), activate(N))
  , U64(tt(), M, N) -> s(plus(activate(N), activate(M)))
  , s(X) -> n__s(X)
  , plus(X1, X2) -> n__plus(X1, X2)
  , 0() -> n__0() }
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..