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:
  runtime complexity
Answer:
  MAYBE

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 processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
      2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
         to the following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
   
   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.
      
   

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { U11^#(tt(), V1, V2) ->
       c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , U12^#(tt(), V1, V2) ->
       c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , U13^#(tt(), V1, V2) ->
       c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , isNatKind^#(n__0()) -> c_3()
     , isNatKind^#(n__plus(V1, V2)) ->
       c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
     , isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
     , U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
     , U41^#(tt()) -> c_22()
     , activate^#(X) -> c_6(X)
     , activate^#(n__0()) -> c_7(0^#())
     , activate^#(n__plus(X1, X2)) ->
       c_8(plus^#(activate(X1), activate(X2)))
     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
     , 0^#() -> c_33()
     , plus^#(X1, X2) -> c_30(X1, X2)
     , plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
     , plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
     , s^#(X) -> c_29(X)
     , U14^#(tt(), V1, V2) ->
       c_11(U15^#(isNat(activate(V1)), activate(V2)))
     , U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
     , U16^#(tt()) -> c_16()
     , isNat^#(n__0()) -> c_13()
     , isNat^#(n__plus(V1, V2)) ->
       c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , isNat^#(n__s(V1)) ->
       c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
     , U21^#(tt(), V1) ->
       c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
     , U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
     , U23^#(tt()) -> c_19()
     , U32^#(tt()) -> c_21()
     , U51^#(tt(), N) ->
       c_23(U52^#(isNatKind(activate(N)), activate(N)))
     , U52^#(tt(), N) -> c_24(activate^#(N))
     , U61^#(tt(), M, N) ->
       c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
     , U62^#(tt(), M, N) ->
       c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
     , U63^#(tt(), M, N) ->
       c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
     , U64^#(tt(), M, N) -> c_28(s^#(plus(activate(N), activate(M)))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { U11^#(tt(), V1, V2) ->
       c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , U12^#(tt(), V1, V2) ->
       c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , U13^#(tt(), V1, V2) ->
       c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , isNatKind^#(n__0()) -> c_3()
     , isNatKind^#(n__plus(V1, V2)) ->
       c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
     , isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
     , U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
     , U41^#(tt()) -> c_22()
     , activate^#(X) -> c_6(X)
     , activate^#(n__0()) -> c_7(0^#())
     , activate^#(n__plus(X1, X2)) ->
       c_8(plus^#(activate(X1), activate(X2)))
     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
     , 0^#() -> c_33()
     , plus^#(X1, X2) -> c_30(X1, X2)
     , plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
     , plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
     , s^#(X) -> c_29(X)
     , U14^#(tt(), V1, V2) ->
       c_11(U15^#(isNat(activate(V1)), activate(V2)))
     , U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
     , U16^#(tt()) -> c_16()
     , isNat^#(n__0()) -> c_13()
     , isNat^#(n__plus(V1, V2)) ->
       c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , isNat^#(n__s(V1)) ->
       c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
     , U21^#(tt(), V1) ->
       c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
     , U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
     , U23^#(tt()) -> c_19()
     , U32^#(tt()) -> c_21()
     , U51^#(tt(), N) ->
       c_23(U52^#(isNatKind(activate(N)), activate(N)))
     , U52^#(tt(), N) -> c_24(activate^#(N))
     , U61^#(tt(), M, N) ->
       c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
     , U62^#(tt(), M, N) ->
       c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
     , U63^#(tt(), M, N) ->
       c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
     , U64^#(tt(), M, N) -> c_28(s^#(plus(activate(N), activate(M)))) }
   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:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {4,8,13,20,21,26,27} by
   applications of Pre({4,8,13,20,21,26,27}) = {6,7,9,10,14,17,19,25}.
   Here rules are labeled as follows:
   
     DPs:
       { 1: U11^#(tt(), V1, V2) ->
            c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 2: U12^#(tt(), V1, V2) ->
            c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 3: U13^#(tt(), V1, V2) ->
            c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 4: isNatKind^#(n__0()) -> c_3()
       , 5: isNatKind^#(n__plus(V1, V2)) ->
            c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
       , 6: isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
       , 7: U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
       , 8: U41^#(tt()) -> c_22()
       , 9: activate^#(X) -> c_6(X)
       , 10: activate^#(n__0()) -> c_7(0^#())
       , 11: activate^#(n__plus(X1, X2)) ->
             c_8(plus^#(activate(X1), activate(X2)))
       , 12: activate^#(n__s(X)) -> c_9(s^#(activate(X)))
       , 13: 0^#() -> c_33()
       , 14: plus^#(X1, X2) -> c_30(X1, X2)
       , 15: plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
       , 16: plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
       , 17: s^#(X) -> c_29(X)
       , 18: U14^#(tt(), V1, V2) ->
             c_11(U15^#(isNat(activate(V1)), activate(V2)))
       , 19: U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
       , 20: U16^#(tt()) -> c_16()
       , 21: isNat^#(n__0()) -> c_13()
       , 22: isNat^#(n__plus(V1, V2)) ->
             c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 23: isNat^#(n__s(V1)) ->
             c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
       , 24: U21^#(tt(), V1) ->
             c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
       , 25: U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
       , 26: U23^#(tt()) -> c_19()
       , 27: U32^#(tt()) -> c_21()
       , 28: U51^#(tt(), N) ->
             c_23(U52^#(isNatKind(activate(N)), activate(N)))
       , 29: U52^#(tt(), N) -> c_24(activate^#(N))
       , 30: U61^#(tt(), M, N) ->
             c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
       , 31: U62^#(tt(), M, N) ->
             c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
       , 32: U63^#(tt(), M, N) ->
             c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
       , 33: U64^#(tt(), M, N) ->
             c_28(s^#(plus(activate(N), activate(M)))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { U11^#(tt(), V1, V2) ->
       c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , U12^#(tt(), V1, V2) ->
       c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , U13^#(tt(), V1, V2) ->
       c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , isNatKind^#(n__plus(V1, V2)) ->
       c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
     , isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
     , U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
     , activate^#(X) -> c_6(X)
     , activate^#(n__0()) -> c_7(0^#())
     , activate^#(n__plus(X1, X2)) ->
       c_8(plus^#(activate(X1), activate(X2)))
     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
     , plus^#(X1, X2) -> c_30(X1, X2)
     , plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
     , plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
     , s^#(X) -> c_29(X)
     , U14^#(tt(), V1, V2) ->
       c_11(U15^#(isNat(activate(V1)), activate(V2)))
     , U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
     , isNat^#(n__plus(V1, V2)) ->
       c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , isNat^#(n__s(V1)) ->
       c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
     , U21^#(tt(), V1) ->
       c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
     , U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
     , U51^#(tt(), N) ->
       c_23(U52^#(isNatKind(activate(N)), activate(N)))
     , U52^#(tt(), N) -> c_24(activate^#(N))
     , U61^#(tt(), M, N) ->
       c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
     , U62^#(tt(), M, N) ->
       c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
     , U63^#(tt(), M, N) ->
       c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
     , U64^#(tt(), M, N) -> c_28(s^#(plus(activate(N), activate(M)))) }
   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() }
   Weak DPs:
     { isNatKind^#(n__0()) -> c_3()
     , U41^#(tt()) -> c_22()
     , 0^#() -> c_33()
     , U16^#(tt()) -> c_16()
     , isNat^#(n__0()) -> c_13()
     , U23^#(tt()) -> c_19()
     , U32^#(tt()) -> c_21() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {5,6,8,16,20} by
   applications of Pre({5,6,8,16,20}) = {4,7,11,14,15,19,22}. Here
   rules are labeled as follows:
   
     DPs:
       { 1: U11^#(tt(), V1, V2) ->
            c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 2: U12^#(tt(), V1, V2) ->
            c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 3: U13^#(tt(), V1, V2) ->
            c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 4: isNatKind^#(n__plus(V1, V2)) ->
            c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
       , 5: isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
       , 6: U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
       , 7: activate^#(X) -> c_6(X)
       , 8: activate^#(n__0()) -> c_7(0^#())
       , 9: activate^#(n__plus(X1, X2)) ->
            c_8(plus^#(activate(X1), activate(X2)))
       , 10: activate^#(n__s(X)) -> c_9(s^#(activate(X)))
       , 11: plus^#(X1, X2) -> c_30(X1, X2)
       , 12: plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
       , 13: plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
       , 14: s^#(X) -> c_29(X)
       , 15: U14^#(tt(), V1, V2) ->
             c_11(U15^#(isNat(activate(V1)), activate(V2)))
       , 16: U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
       , 17: isNat^#(n__plus(V1, V2)) ->
             c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 18: isNat^#(n__s(V1)) ->
             c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
       , 19: U21^#(tt(), V1) ->
             c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
       , 20: U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
       , 21: U51^#(tt(), N) ->
             c_23(U52^#(isNatKind(activate(N)), activate(N)))
       , 22: U52^#(tt(), N) -> c_24(activate^#(N))
       , 23: U61^#(tt(), M, N) ->
             c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
       , 24: U62^#(tt(), M, N) ->
             c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
       , 25: U63^#(tt(), M, N) ->
             c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
       , 26: U64^#(tt(), M, N) ->
             c_28(s^#(plus(activate(N), activate(M))))
       , 27: isNatKind^#(n__0()) -> c_3()
       , 28: U41^#(tt()) -> c_22()
       , 29: 0^#() -> c_33()
       , 30: U16^#(tt()) -> c_16()
       , 31: isNat^#(n__0()) -> c_13()
       , 32: U23^#(tt()) -> c_19()
       , 33: U32^#(tt()) -> c_21() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { U11^#(tt(), V1, V2) ->
       c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , U12^#(tt(), V1, V2) ->
       c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , U13^#(tt(), V1, V2) ->
       c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , isNatKind^#(n__plus(V1, V2)) ->
       c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
     , activate^#(X) -> c_6(X)
     , activate^#(n__plus(X1, X2)) ->
       c_8(plus^#(activate(X1), activate(X2)))
     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
     , plus^#(X1, X2) -> c_30(X1, X2)
     , plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
     , plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
     , s^#(X) -> c_29(X)
     , U14^#(tt(), V1, V2) ->
       c_11(U15^#(isNat(activate(V1)), activate(V2)))
     , isNat^#(n__plus(V1, V2)) ->
       c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , isNat^#(n__s(V1)) ->
       c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
     , U21^#(tt(), V1) ->
       c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
     , U51^#(tt(), N) ->
       c_23(U52^#(isNatKind(activate(N)), activate(N)))
     , U52^#(tt(), N) -> c_24(activate^#(N))
     , U61^#(tt(), M, N) ->
       c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
     , U62^#(tt(), M, N) ->
       c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
     , U63^#(tt(), M, N) ->
       c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
     , U64^#(tt(), M, N) -> c_28(s^#(plus(activate(N), activate(M)))) }
   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() }
   Weak DPs:
     { isNatKind^#(n__0()) -> c_3()
     , isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
     , U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
     , U41^#(tt()) -> c_22()
     , activate^#(n__0()) -> c_7(0^#())
     , 0^#() -> c_33()
     , U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
     , U16^#(tt()) -> c_16()
     , isNat^#(n__0()) -> c_13()
     , U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
     , U23^#(tt()) -> c_19()
     , U32^#(tt()) -> c_21() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {4,12,15} by applications
   of Pre({4,12,15}) = {3,5,8,11,14}. Here rules are labeled as
   follows:
   
     DPs:
       { 1: U11^#(tt(), V1, V2) ->
            c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 2: U12^#(tt(), V1, V2) ->
            c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 3: U13^#(tt(), V1, V2) ->
            c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 4: isNatKind^#(n__plus(V1, V2)) ->
            c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
       , 5: activate^#(X) -> c_6(X)
       , 6: activate^#(n__plus(X1, X2)) ->
            c_8(plus^#(activate(X1), activate(X2)))
       , 7: activate^#(n__s(X)) -> c_9(s^#(activate(X)))
       , 8: plus^#(X1, X2) -> c_30(X1, X2)
       , 9: plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
       , 10: plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
       , 11: s^#(X) -> c_29(X)
       , 12: U14^#(tt(), V1, V2) ->
             c_11(U15^#(isNat(activate(V1)), activate(V2)))
       , 13: isNat^#(n__plus(V1, V2)) ->
             c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 14: isNat^#(n__s(V1)) ->
             c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
       , 15: U21^#(tt(), V1) ->
             c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
       , 16: U51^#(tt(), N) ->
             c_23(U52^#(isNatKind(activate(N)), activate(N)))
       , 17: U52^#(tt(), N) -> c_24(activate^#(N))
       , 18: U61^#(tt(), M, N) ->
             c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
       , 19: U62^#(tt(), M, N) ->
             c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
       , 20: U63^#(tt(), M, N) ->
             c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
       , 21: U64^#(tt(), M, N) ->
             c_28(s^#(plus(activate(N), activate(M))))
       , 22: isNatKind^#(n__0()) -> c_3()
       , 23: isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
       , 24: U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
       , 25: U41^#(tt()) -> c_22()
       , 26: activate^#(n__0()) -> c_7(0^#())
       , 27: 0^#() -> c_33()
       , 28: U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
       , 29: U16^#(tt()) -> c_16()
       , 30: isNat^#(n__0()) -> c_13()
       , 31: U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
       , 32: U23^#(tt()) -> c_19()
       , 33: U32^#(tt()) -> c_21() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { U11^#(tt(), V1, V2) ->
       c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , U12^#(tt(), V1, V2) ->
       c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , U13^#(tt(), V1, V2) ->
       c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , activate^#(X) -> c_6(X)
     , activate^#(n__plus(X1, X2)) ->
       c_8(plus^#(activate(X1), activate(X2)))
     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
     , plus^#(X1, X2) -> c_30(X1, X2)
     , plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
     , plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
     , s^#(X) -> c_29(X)
     , isNat^#(n__plus(V1, V2)) ->
       c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , isNat^#(n__s(V1)) ->
       c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
     , U51^#(tt(), N) ->
       c_23(U52^#(isNatKind(activate(N)), activate(N)))
     , U52^#(tt(), N) -> c_24(activate^#(N))
     , U61^#(tt(), M, N) ->
       c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
     , U62^#(tt(), M, N) ->
       c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
     , U63^#(tt(), M, N) ->
       c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
     , U64^#(tt(), M, N) -> c_28(s^#(plus(activate(N), activate(M)))) }
   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() }
   Weak DPs:
     { isNatKind^#(n__0()) -> c_3()
     , isNatKind^#(n__plus(V1, V2)) ->
       c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
     , isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
     , U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
     , U41^#(tt()) -> c_22()
     , activate^#(n__0()) -> c_7(0^#())
     , 0^#() -> c_33()
     , U14^#(tt(), V1, V2) ->
       c_11(U15^#(isNat(activate(V1)), activate(V2)))
     , U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
     , U16^#(tt()) -> c_16()
     , isNat^#(n__0()) -> c_13()
     , U21^#(tt(), V1) ->
       c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
     , U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
     , U23^#(tt()) -> c_19()
     , U32^#(tt()) -> c_21() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3,12} by applications of
   Pre({3,12}) = {2,4,7,10}. Here rules are labeled as follows:
   
     DPs:
       { 1: U11^#(tt(), V1, V2) ->
            c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 2: U12^#(tt(), V1, V2) ->
            c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 3: U13^#(tt(), V1, V2) ->
            c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 4: activate^#(X) -> c_6(X)
       , 5: activate^#(n__plus(X1, X2)) ->
            c_8(plus^#(activate(X1), activate(X2)))
       , 6: activate^#(n__s(X)) -> c_9(s^#(activate(X)))
       , 7: plus^#(X1, X2) -> c_30(X1, X2)
       , 8: plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
       , 9: plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
       , 10: s^#(X) -> c_29(X)
       , 11: isNat^#(n__plus(V1, V2)) ->
             c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 12: isNat^#(n__s(V1)) ->
             c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
       , 13: U51^#(tt(), N) ->
             c_23(U52^#(isNatKind(activate(N)), activate(N)))
       , 14: U52^#(tt(), N) -> c_24(activate^#(N))
       , 15: U61^#(tt(), M, N) ->
             c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
       , 16: U62^#(tt(), M, N) ->
             c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
       , 17: U63^#(tt(), M, N) ->
             c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
       , 18: U64^#(tt(), M, N) ->
             c_28(s^#(plus(activate(N), activate(M))))
       , 19: isNatKind^#(n__0()) -> c_3()
       , 20: isNatKind^#(n__plus(V1, V2)) ->
             c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
       , 21: isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
       , 22: U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
       , 23: U41^#(tt()) -> c_22()
       , 24: activate^#(n__0()) -> c_7(0^#())
       , 25: 0^#() -> c_33()
       , 26: U14^#(tt(), V1, V2) ->
             c_11(U15^#(isNat(activate(V1)), activate(V2)))
       , 27: U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
       , 28: U16^#(tt()) -> c_16()
       , 29: isNat^#(n__0()) -> c_13()
       , 30: U21^#(tt(), V1) ->
             c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
       , 31: U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
       , 32: U23^#(tt()) -> c_19()
       , 33: U32^#(tt()) -> c_21() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { U11^#(tt(), V1, V2) ->
       c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , U12^#(tt(), V1, V2) ->
       c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , activate^#(X) -> c_6(X)
     , activate^#(n__plus(X1, X2)) ->
       c_8(plus^#(activate(X1), activate(X2)))
     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
     , plus^#(X1, X2) -> c_30(X1, X2)
     , plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
     , plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
     , s^#(X) -> c_29(X)
     , isNat^#(n__plus(V1, V2)) ->
       c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , U51^#(tt(), N) ->
       c_23(U52^#(isNatKind(activate(N)), activate(N)))
     , U52^#(tt(), N) -> c_24(activate^#(N))
     , U61^#(tt(), M, N) ->
       c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
     , U62^#(tt(), M, N) ->
       c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
     , U63^#(tt(), M, N) ->
       c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
     , U64^#(tt(), M, N) -> c_28(s^#(plus(activate(N), activate(M)))) }
   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() }
   Weak DPs:
     { U13^#(tt(), V1, V2) ->
       c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , isNatKind^#(n__0()) -> c_3()
     , isNatKind^#(n__plus(V1, V2)) ->
       c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
     , isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
     , U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
     , U41^#(tt()) -> c_22()
     , activate^#(n__0()) -> c_7(0^#())
     , 0^#() -> c_33()
     , U14^#(tt(), V1, V2) ->
       c_11(U15^#(isNat(activate(V1)), activate(V2)))
     , U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
     , U16^#(tt()) -> c_16()
     , isNat^#(n__0()) -> c_13()
     , isNat^#(n__s(V1)) ->
       c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
     , U21^#(tt(), V1) ->
       c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
     , U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
     , U23^#(tt()) -> c_19()
     , U32^#(tt()) -> c_21() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {2} by applications of
   Pre({2}) = {1,3,6,9}. Here rules are labeled as follows:
   
     DPs:
       { 1: U11^#(tt(), V1, V2) ->
            c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 2: U12^#(tt(), V1, V2) ->
            c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 3: activate^#(X) -> c_6(X)
       , 4: activate^#(n__plus(X1, X2)) ->
            c_8(plus^#(activate(X1), activate(X2)))
       , 5: activate^#(n__s(X)) -> c_9(s^#(activate(X)))
       , 6: plus^#(X1, X2) -> c_30(X1, X2)
       , 7: plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
       , 8: plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
       , 9: s^#(X) -> c_29(X)
       , 10: isNat^#(n__plus(V1, V2)) ->
             c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 11: U51^#(tt(), N) ->
             c_23(U52^#(isNatKind(activate(N)), activate(N)))
       , 12: U52^#(tt(), N) -> c_24(activate^#(N))
       , 13: U61^#(tt(), M, N) ->
             c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
       , 14: U62^#(tt(), M, N) ->
             c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
       , 15: U63^#(tt(), M, N) ->
             c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
       , 16: U64^#(tt(), M, N) ->
             c_28(s^#(plus(activate(N), activate(M))))
       , 17: U13^#(tt(), V1, V2) ->
             c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 18: isNatKind^#(n__0()) -> c_3()
       , 19: isNatKind^#(n__plus(V1, V2)) ->
             c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
       , 20: isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
       , 21: U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
       , 22: U41^#(tt()) -> c_22()
       , 23: activate^#(n__0()) -> c_7(0^#())
       , 24: 0^#() -> c_33()
       , 25: U14^#(tt(), V1, V2) ->
             c_11(U15^#(isNat(activate(V1)), activate(V2)))
       , 26: U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
       , 27: U16^#(tt()) -> c_16()
       , 28: isNat^#(n__0()) -> c_13()
       , 29: isNat^#(n__s(V1)) ->
             c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
       , 30: U21^#(tt(), V1) ->
             c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
       , 31: U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
       , 32: U23^#(tt()) -> c_19()
       , 33: U32^#(tt()) -> c_21() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { U11^#(tt(), V1, V2) ->
       c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , activate^#(X) -> c_6(X)
     , activate^#(n__plus(X1, X2)) ->
       c_8(plus^#(activate(X1), activate(X2)))
     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
     , plus^#(X1, X2) -> c_30(X1, X2)
     , plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
     , plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
     , s^#(X) -> c_29(X)
     , isNat^#(n__plus(V1, V2)) ->
       c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , U51^#(tt(), N) ->
       c_23(U52^#(isNatKind(activate(N)), activate(N)))
     , U52^#(tt(), N) -> c_24(activate^#(N))
     , U61^#(tt(), M, N) ->
       c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
     , U62^#(tt(), M, N) ->
       c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
     , U63^#(tt(), M, N) ->
       c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
     , U64^#(tt(), M, N) -> c_28(s^#(plus(activate(N), activate(M)))) }
   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() }
   Weak DPs:
     { U12^#(tt(), V1, V2) ->
       c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , U13^#(tt(), V1, V2) ->
       c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , isNatKind^#(n__0()) -> c_3()
     , isNatKind^#(n__plus(V1, V2)) ->
       c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
     , isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
     , U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
     , U41^#(tt()) -> c_22()
     , activate^#(n__0()) -> c_7(0^#())
     , 0^#() -> c_33()
     , U14^#(tt(), V1, V2) ->
       c_11(U15^#(isNat(activate(V1)), activate(V2)))
     , U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
     , U16^#(tt()) -> c_16()
     , isNat^#(n__0()) -> c_13()
     , isNat^#(n__s(V1)) ->
       c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
     , U21^#(tt(), V1) ->
       c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
     , U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
     , U23^#(tt()) -> c_19()
     , U32^#(tt()) -> c_21() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1} by applications of
   Pre({1}) = {2,5,8,9}. Here rules are labeled as follows:
   
     DPs:
       { 1: U11^#(tt(), V1, V2) ->
            c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 2: activate^#(X) -> c_6(X)
       , 3: activate^#(n__plus(X1, X2)) ->
            c_8(plus^#(activate(X1), activate(X2)))
       , 4: activate^#(n__s(X)) -> c_9(s^#(activate(X)))
       , 5: plus^#(X1, X2) -> c_30(X1, X2)
       , 6: plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
       , 7: plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
       , 8: s^#(X) -> c_29(X)
       , 9: isNat^#(n__plus(V1, V2)) ->
            c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 10: U51^#(tt(), N) ->
             c_23(U52^#(isNatKind(activate(N)), activate(N)))
       , 11: U52^#(tt(), N) -> c_24(activate^#(N))
       , 12: U61^#(tt(), M, N) ->
             c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
       , 13: U62^#(tt(), M, N) ->
             c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
       , 14: U63^#(tt(), M, N) ->
             c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
       , 15: U64^#(tt(), M, N) ->
             c_28(s^#(plus(activate(N), activate(M))))
       , 16: U12^#(tt(), V1, V2) ->
             c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 17: U13^#(tt(), V1, V2) ->
             c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 18: isNatKind^#(n__0()) -> c_3()
       , 19: isNatKind^#(n__plus(V1, V2)) ->
             c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
       , 20: isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
       , 21: U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
       , 22: U41^#(tt()) -> c_22()
       , 23: activate^#(n__0()) -> c_7(0^#())
       , 24: 0^#() -> c_33()
       , 25: U14^#(tt(), V1, V2) ->
             c_11(U15^#(isNat(activate(V1)), activate(V2)))
       , 26: U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
       , 27: U16^#(tt()) -> c_16()
       , 28: isNat^#(n__0()) -> c_13()
       , 29: isNat^#(n__s(V1)) ->
             c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
       , 30: U21^#(tt(), V1) ->
             c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
       , 31: U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
       , 32: U23^#(tt()) -> c_19()
       , 33: U32^#(tt()) -> c_21() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { activate^#(X) -> c_6(X)
     , activate^#(n__plus(X1, X2)) ->
       c_8(plus^#(activate(X1), activate(X2)))
     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
     , plus^#(X1, X2) -> c_30(X1, X2)
     , plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
     , plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
     , s^#(X) -> c_29(X)
     , isNat^#(n__plus(V1, V2)) ->
       c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , U51^#(tt(), N) ->
       c_23(U52^#(isNatKind(activate(N)), activate(N)))
     , U52^#(tt(), N) -> c_24(activate^#(N))
     , U61^#(tt(), M, N) ->
       c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
     , U62^#(tt(), M, N) ->
       c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
     , U63^#(tt(), M, N) ->
       c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
     , U64^#(tt(), M, N) -> c_28(s^#(plus(activate(N), activate(M)))) }
   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() }
   Weak DPs:
     { U11^#(tt(), V1, V2) ->
       c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , U12^#(tt(), V1, V2) ->
       c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , U13^#(tt(), V1, V2) ->
       c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , isNatKind^#(n__0()) -> c_3()
     , isNatKind^#(n__plus(V1, V2)) ->
       c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
     , isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
     , U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
     , U41^#(tt()) -> c_22()
     , activate^#(n__0()) -> c_7(0^#())
     , 0^#() -> c_33()
     , U14^#(tt(), V1, V2) ->
       c_11(U15^#(isNat(activate(V1)), activate(V2)))
     , U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
     , U16^#(tt()) -> c_16()
     , isNat^#(n__0()) -> c_13()
     , isNat^#(n__s(V1)) ->
       c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
     , U21^#(tt(), V1) ->
       c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
     , U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
     , U23^#(tt()) -> c_19()
     , U32^#(tt()) -> c_21() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {8} by applications of
   Pre({8}) = {1,4,7}. Here rules are labeled as follows:
   
     DPs:
       { 1: activate^#(X) -> c_6(X)
       , 2: activate^#(n__plus(X1, X2)) ->
            c_8(plus^#(activate(X1), activate(X2)))
       , 3: activate^#(n__s(X)) -> c_9(s^#(activate(X)))
       , 4: plus^#(X1, X2) -> c_30(X1, X2)
       , 5: plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
       , 6: plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
       , 7: s^#(X) -> c_29(X)
       , 8: isNat^#(n__plus(V1, V2)) ->
            c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 9: U51^#(tt(), N) ->
            c_23(U52^#(isNatKind(activate(N)), activate(N)))
       , 10: U52^#(tt(), N) -> c_24(activate^#(N))
       , 11: U61^#(tt(), M, N) ->
             c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
       , 12: U62^#(tt(), M, N) ->
             c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
       , 13: U63^#(tt(), M, N) ->
             c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
       , 14: U64^#(tt(), M, N) ->
             c_28(s^#(plus(activate(N), activate(M))))
       , 15: U11^#(tt(), V1, V2) ->
             c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
       , 16: U12^#(tt(), V1, V2) ->
             c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 17: U13^#(tt(), V1, V2) ->
             c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
       , 18: isNatKind^#(n__0()) -> c_3()
       , 19: isNatKind^#(n__plus(V1, V2)) ->
             c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
       , 20: isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
       , 21: U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
       , 22: U41^#(tt()) -> c_22()
       , 23: activate^#(n__0()) -> c_7(0^#())
       , 24: 0^#() -> c_33()
       , 25: U14^#(tt(), V1, V2) ->
             c_11(U15^#(isNat(activate(V1)), activate(V2)))
       , 26: U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
       , 27: U16^#(tt()) -> c_16()
       , 28: isNat^#(n__0()) -> c_13()
       , 29: isNat^#(n__s(V1)) ->
             c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
       , 30: U21^#(tt(), V1) ->
             c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
       , 31: U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
       , 32: U23^#(tt()) -> c_19()
       , 33: U32^#(tt()) -> c_21() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { activate^#(X) -> c_6(X)
     , activate^#(n__plus(X1, X2)) ->
       c_8(plus^#(activate(X1), activate(X2)))
     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
     , plus^#(X1, X2) -> c_30(X1, X2)
     , plus^#(N, s(M)) -> c_31(U61^#(isNat(M), M, N))
     , plus^#(N, 0()) -> c_32(U51^#(isNat(N), N))
     , s^#(X) -> c_29(X)
     , U51^#(tt(), N) ->
       c_23(U52^#(isNatKind(activate(N)), activate(N)))
     , U52^#(tt(), N) -> c_24(activate^#(N))
     , U61^#(tt(), M, N) ->
       c_25(U62^#(isNatKind(activate(M)), activate(M), activate(N)))
     , U62^#(tt(), M, N) ->
       c_26(U63^#(isNat(activate(N)), activate(M), activate(N)))
     , U63^#(tt(), M, N) ->
       c_27(U64^#(isNatKind(activate(N)), activate(M), activate(N)))
     , U64^#(tt(), M, N) -> c_28(s^#(plus(activate(N), activate(M)))) }
   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() }
   Weak DPs:
     { U11^#(tt(), V1, V2) ->
       c_1(U12^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , U12^#(tt(), V1, V2) ->
       c_2(U13^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , U13^#(tt(), V1, V2) ->
       c_10(U14^#(isNatKind(activate(V2)), activate(V1), activate(V2)))
     , isNatKind^#(n__0()) -> c_3()
     , isNatKind^#(n__plus(V1, V2)) ->
       c_4(U31^#(isNatKind(activate(V1)), activate(V2)))
     , isNatKind^#(n__s(V1)) -> c_5(U41^#(isNatKind(activate(V1))))
     , U31^#(tt(), V2) -> c_20(U32^#(isNatKind(activate(V2))))
     , U41^#(tt()) -> c_22()
     , activate^#(n__0()) -> c_7(0^#())
     , 0^#() -> c_33()
     , U14^#(tt(), V1, V2) ->
       c_11(U15^#(isNat(activate(V1)), activate(V2)))
     , U15^#(tt(), V2) -> c_12(U16^#(isNat(activate(V2))))
     , U16^#(tt()) -> c_16()
     , isNat^#(n__0()) -> c_13()
     , isNat^#(n__plus(V1, V2)) ->
       c_14(U11^#(isNatKind(activate(V1)), activate(V1), activate(V2)))
     , isNat^#(n__s(V1)) ->
       c_15(U21^#(isNatKind(activate(V1)), activate(V1)))
     , U21^#(tt(), V1) ->
       c_17(U22^#(isNatKind(activate(V1)), activate(V1)))
     , U22^#(tt(), V1) -> c_18(U23^#(isNat(activate(V1))))
     , U23^#(tt()) -> c_19()
     , U32^#(tt()) -> c_21() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..