MAYBE

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

Strict Trs:
  { a__U11(X1, X2, X3) -> U11(X1, X2, X3)
  , a__U11(tt(), V1, V2) -> a__U12(a__isNat(V1), V2)
  , a__U12(X1, X2) -> U12(X1, X2)
  , a__U12(tt(), V2) -> a__U13(a__isNat(V2))
  , a__isNat(X) -> isNat(X)
  , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
  , a__isNat(0()) -> tt()
  , a__isNat(plus(V1, V2)) ->
    a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2)
  , a__U13(X) -> U13(X)
  , a__U13(tt()) -> tt()
  , a__U21(X1, X2) -> U21(X1, X2)
  , a__U21(tt(), V1) -> a__U22(a__isNat(V1))
  , a__U22(X) -> U22(X)
  , a__U22(tt()) -> tt()
  , a__U31(X1, X2) -> U31(X1, X2)
  , a__U31(tt(), N) -> mark(N)
  , mark(tt()) -> tt()
  , mark(s(X)) -> s(mark(X))
  , mark(0()) -> 0()
  , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
  , mark(isNatKind(X)) -> a__isNatKind(X)
  , mark(and(X1, X2)) -> a__and(mark(X1), X2)
  , mark(isNat(X)) -> a__isNat(X)
  , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
  , mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
  , mark(U13(X)) -> a__U13(mark(X))
  , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
  , mark(U22(X)) -> a__U22(mark(X))
  , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
  , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
  , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
  , a__U41(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
  , a__plus(X1, X2) -> plus(X1, X2)
  , a__plus(N, s(M)) ->
    a__U41(a__and(a__and(a__isNat(M), isNatKind(M)),
                  and(isNat(N), isNatKind(N))),
           M,
           N)
  , a__plus(N, 0()) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N)
  , a__and(X1, X2) -> and(X1, X2)
  , a__and(tt(), X) -> mark(X)
  , a__isNatKind(X) -> isNatKind(X)
  , a__isNatKind(s(V1)) -> a__isNatKind(V1)
  , a__isNatKind(0()) -> tt()
  , a__isNatKind(plus(V1, V2)) ->
    a__and(a__isNatKind(V1), isNatKind(V2)) }
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:
     { a__U11^#(X1, X2, X3) -> c_1(X1, X2, X3)
     , a__U11^#(tt(), V1, V2) -> c_2(a__U12^#(a__isNat(V1), V2))
     , a__U12^#(X1, X2) -> c_3(X1, X2)
     , a__U12^#(tt(), V2) -> c_4(a__U13^#(a__isNat(V2)))
     , a__U13^#(X) -> c_9(X)
     , a__U13^#(tt()) -> c_10()
     , a__isNat^#(X) -> c_5(X)
     , a__isNat^#(s(V1)) -> c_6(a__U21^#(a__isNatKind(V1), V1))
     , a__isNat^#(0()) -> c_7()
     , a__isNat^#(plus(V1, V2)) ->
       c_8(a__U11^#(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2))
     , a__U21^#(X1, X2) -> c_11(X1, X2)
     , a__U21^#(tt(), V1) -> c_12(a__U22^#(a__isNat(V1)))
     , a__U22^#(X) -> c_13(X)
     , a__U22^#(tt()) -> c_14()
     , a__U31^#(X1, X2) -> c_15(X1, X2)
     , a__U31^#(tt(), N) -> c_16(mark^#(N))
     , mark^#(tt()) -> c_17()
     , mark^#(s(X)) -> c_18(mark^#(X))
     , mark^#(0()) -> c_19()
     , mark^#(plus(X1, X2)) -> c_20(a__plus^#(mark(X1), mark(X2)))
     , mark^#(isNatKind(X)) -> c_21(a__isNatKind^#(X))
     , mark^#(and(X1, X2)) -> c_22(a__and^#(mark(X1), X2))
     , mark^#(isNat(X)) -> c_23(a__isNat^#(X))
     , mark^#(U11(X1, X2, X3)) -> c_24(a__U11^#(mark(X1), X2, X3))
     , mark^#(U12(X1, X2)) -> c_25(a__U12^#(mark(X1), X2))
     , mark^#(U13(X)) -> c_26(a__U13^#(mark(X)))
     , mark^#(U21(X1, X2)) -> c_27(a__U21^#(mark(X1), X2))
     , mark^#(U22(X)) -> c_28(a__U22^#(mark(X)))
     , mark^#(U31(X1, X2)) -> c_29(a__U31^#(mark(X1), X2))
     , mark^#(U41(X1, X2, X3)) -> c_30(a__U41^#(mark(X1), X2, X3))
     , a__plus^#(X1, X2) -> c_33(X1, X2)
     , a__plus^#(N, s(M)) ->
       c_34(a__U41^#(a__and(a__and(a__isNat(M), isNatKind(M)),
                            and(isNat(N), isNatKind(N))),
                     M,
                     N))
     , a__plus^#(N, 0()) ->
       c_35(a__U31^#(a__and(a__isNat(N), isNatKind(N)), N))
     , a__isNatKind^#(X) -> c_38(X)
     , a__isNatKind^#(s(V1)) -> c_39(a__isNatKind^#(V1))
     , a__isNatKind^#(0()) -> c_40()
     , a__isNatKind^#(plus(V1, V2)) ->
       c_41(a__and^#(a__isNatKind(V1), isNatKind(V2)))
     , a__and^#(X1, X2) -> c_36(X1, X2)
     , a__and^#(tt(), X) -> c_37(mark^#(X))
     , a__U41^#(X1, X2, X3) -> c_31(X1, X2, X3)
     , a__U41^#(tt(), M, N) -> c_32(a__plus^#(mark(N), mark(M))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { a__U11^#(X1, X2, X3) -> c_1(X1, X2, X3)
     , a__U11^#(tt(), V1, V2) -> c_2(a__U12^#(a__isNat(V1), V2))
     , a__U12^#(X1, X2) -> c_3(X1, X2)
     , a__U12^#(tt(), V2) -> c_4(a__U13^#(a__isNat(V2)))
     , a__U13^#(X) -> c_9(X)
     , a__U13^#(tt()) -> c_10()
     , a__isNat^#(X) -> c_5(X)
     , a__isNat^#(s(V1)) -> c_6(a__U21^#(a__isNatKind(V1), V1))
     , a__isNat^#(0()) -> c_7()
     , a__isNat^#(plus(V1, V2)) ->
       c_8(a__U11^#(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2))
     , a__U21^#(X1, X2) -> c_11(X1, X2)
     , a__U21^#(tt(), V1) -> c_12(a__U22^#(a__isNat(V1)))
     , a__U22^#(X) -> c_13(X)
     , a__U22^#(tt()) -> c_14()
     , a__U31^#(X1, X2) -> c_15(X1, X2)
     , a__U31^#(tt(), N) -> c_16(mark^#(N))
     , mark^#(tt()) -> c_17()
     , mark^#(s(X)) -> c_18(mark^#(X))
     , mark^#(0()) -> c_19()
     , mark^#(plus(X1, X2)) -> c_20(a__plus^#(mark(X1), mark(X2)))
     , mark^#(isNatKind(X)) -> c_21(a__isNatKind^#(X))
     , mark^#(and(X1, X2)) -> c_22(a__and^#(mark(X1), X2))
     , mark^#(isNat(X)) -> c_23(a__isNat^#(X))
     , mark^#(U11(X1, X2, X3)) -> c_24(a__U11^#(mark(X1), X2, X3))
     , mark^#(U12(X1, X2)) -> c_25(a__U12^#(mark(X1), X2))
     , mark^#(U13(X)) -> c_26(a__U13^#(mark(X)))
     , mark^#(U21(X1, X2)) -> c_27(a__U21^#(mark(X1), X2))
     , mark^#(U22(X)) -> c_28(a__U22^#(mark(X)))
     , mark^#(U31(X1, X2)) -> c_29(a__U31^#(mark(X1), X2))
     , mark^#(U41(X1, X2, X3)) -> c_30(a__U41^#(mark(X1), X2, X3))
     , a__plus^#(X1, X2) -> c_33(X1, X2)
     , a__plus^#(N, s(M)) ->
       c_34(a__U41^#(a__and(a__and(a__isNat(M), isNatKind(M)),
                            and(isNat(N), isNatKind(N))),
                     M,
                     N))
     , a__plus^#(N, 0()) ->
       c_35(a__U31^#(a__and(a__isNat(N), isNatKind(N)), N))
     , a__isNatKind^#(X) -> c_38(X)
     , a__isNatKind^#(s(V1)) -> c_39(a__isNatKind^#(V1))
     , a__isNatKind^#(0()) -> c_40()
     , a__isNatKind^#(plus(V1, V2)) ->
       c_41(a__and^#(a__isNatKind(V1), isNatKind(V2)))
     , a__and^#(X1, X2) -> c_36(X1, X2)
     , a__and^#(tt(), X) -> c_37(mark^#(X))
     , a__U41^#(X1, X2, X3) -> c_31(X1, X2, X3)
     , a__U41^#(tt(), M, N) -> c_32(a__plus^#(mark(N), mark(M))) }
   Strict Trs:
     { a__U11(X1, X2, X3) -> U11(X1, X2, X3)
     , a__U11(tt(), V1, V2) -> a__U12(a__isNat(V1), V2)
     , a__U12(X1, X2) -> U12(X1, X2)
     , a__U12(tt(), V2) -> a__U13(a__isNat(V2))
     , a__isNat(X) -> isNat(X)
     , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
     , a__isNat(0()) -> tt()
     , a__isNat(plus(V1, V2)) ->
       a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2)
     , a__U13(X) -> U13(X)
     , a__U13(tt()) -> tt()
     , a__U21(X1, X2) -> U21(X1, X2)
     , a__U21(tt(), V1) -> a__U22(a__isNat(V1))
     , a__U22(X) -> U22(X)
     , a__U22(tt()) -> tt()
     , a__U31(X1, X2) -> U31(X1, X2)
     , a__U31(tt(), N) -> mark(N)
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(isNatKind(X)) -> a__isNatKind(X)
     , mark(and(X1, X2)) -> a__and(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
     , mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
     , mark(U13(X)) -> a__U13(mark(X))
     , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
     , mark(U22(X)) -> a__U22(mark(X))
     , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
     , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
     , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
     , a__U41(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__plus(N, s(M)) ->
       a__U41(a__and(a__and(a__isNat(M), isNatKind(M)),
                     and(isNat(N), isNatKind(N))),
              M,
              N)
     , a__plus(N, 0()) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N)
     , a__and(X1, X2) -> and(X1, X2)
     , a__and(tt(), X) -> mark(X)
     , a__isNatKind(X) -> isNatKind(X)
     , a__isNatKind(s(V1)) -> a__isNatKind(V1)
     , a__isNatKind(0()) -> tt()
     , a__isNatKind(plus(V1, V2)) ->
       a__and(a__isNatKind(V1), isNatKind(V2)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {6,9,14,17,19,36} by
   applications of Pre({6,9,14,17,19,36}) =
   {1,3,4,5,7,11,12,13,15,16,18,21,23,26,28,31,34,35,38,39,40}. Here
   rules are labeled as follows:
   
     DPs:
       { 1: a__U11^#(X1, X2, X3) -> c_1(X1, X2, X3)
       , 2: a__U11^#(tt(), V1, V2) -> c_2(a__U12^#(a__isNat(V1), V2))
       , 3: a__U12^#(X1, X2) -> c_3(X1, X2)
       , 4: a__U12^#(tt(), V2) -> c_4(a__U13^#(a__isNat(V2)))
       , 5: a__U13^#(X) -> c_9(X)
       , 6: a__U13^#(tt()) -> c_10()
       , 7: a__isNat^#(X) -> c_5(X)
       , 8: a__isNat^#(s(V1)) -> c_6(a__U21^#(a__isNatKind(V1), V1))
       , 9: a__isNat^#(0()) -> c_7()
       , 10: a__isNat^#(plus(V1, V2)) ->
             c_8(a__U11^#(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2))
       , 11: a__U21^#(X1, X2) -> c_11(X1, X2)
       , 12: a__U21^#(tt(), V1) -> c_12(a__U22^#(a__isNat(V1)))
       , 13: a__U22^#(X) -> c_13(X)
       , 14: a__U22^#(tt()) -> c_14()
       , 15: a__U31^#(X1, X2) -> c_15(X1, X2)
       , 16: a__U31^#(tt(), N) -> c_16(mark^#(N))
       , 17: mark^#(tt()) -> c_17()
       , 18: mark^#(s(X)) -> c_18(mark^#(X))
       , 19: mark^#(0()) -> c_19()
       , 20: mark^#(plus(X1, X2)) -> c_20(a__plus^#(mark(X1), mark(X2)))
       , 21: mark^#(isNatKind(X)) -> c_21(a__isNatKind^#(X))
       , 22: mark^#(and(X1, X2)) -> c_22(a__and^#(mark(X1), X2))
       , 23: mark^#(isNat(X)) -> c_23(a__isNat^#(X))
       , 24: mark^#(U11(X1, X2, X3)) -> c_24(a__U11^#(mark(X1), X2, X3))
       , 25: mark^#(U12(X1, X2)) -> c_25(a__U12^#(mark(X1), X2))
       , 26: mark^#(U13(X)) -> c_26(a__U13^#(mark(X)))
       , 27: mark^#(U21(X1, X2)) -> c_27(a__U21^#(mark(X1), X2))
       , 28: mark^#(U22(X)) -> c_28(a__U22^#(mark(X)))
       , 29: mark^#(U31(X1, X2)) -> c_29(a__U31^#(mark(X1), X2))
       , 30: mark^#(U41(X1, X2, X3)) -> c_30(a__U41^#(mark(X1), X2, X3))
       , 31: a__plus^#(X1, X2) -> c_33(X1, X2)
       , 32: a__plus^#(N, s(M)) ->
             c_34(a__U41^#(a__and(a__and(a__isNat(M), isNatKind(M)),
                                  and(isNat(N), isNatKind(N))),
                           M,
                           N))
       , 33: a__plus^#(N, 0()) ->
             c_35(a__U31^#(a__and(a__isNat(N), isNatKind(N)), N))
       , 34: a__isNatKind^#(X) -> c_38(X)
       , 35: a__isNatKind^#(s(V1)) -> c_39(a__isNatKind^#(V1))
       , 36: a__isNatKind^#(0()) -> c_40()
       , 37: a__isNatKind^#(plus(V1, V2)) ->
             c_41(a__and^#(a__isNatKind(V1), isNatKind(V2)))
       , 38: a__and^#(X1, X2) -> c_36(X1, X2)
       , 39: a__and^#(tt(), X) -> c_37(mark^#(X))
       , 40: a__U41^#(X1, X2, X3) -> c_31(X1, X2, X3)
       , 41: a__U41^#(tt(), M, N) -> c_32(a__plus^#(mark(N), mark(M))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { a__U11^#(X1, X2, X3) -> c_1(X1, X2, X3)
     , a__U11^#(tt(), V1, V2) -> c_2(a__U12^#(a__isNat(V1), V2))
     , a__U12^#(X1, X2) -> c_3(X1, X2)
     , a__U12^#(tt(), V2) -> c_4(a__U13^#(a__isNat(V2)))
     , a__U13^#(X) -> c_9(X)
     , a__isNat^#(X) -> c_5(X)
     , a__isNat^#(s(V1)) -> c_6(a__U21^#(a__isNatKind(V1), V1))
     , a__isNat^#(plus(V1, V2)) ->
       c_8(a__U11^#(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2))
     , a__U21^#(X1, X2) -> c_11(X1, X2)
     , a__U21^#(tt(), V1) -> c_12(a__U22^#(a__isNat(V1)))
     , a__U22^#(X) -> c_13(X)
     , a__U31^#(X1, X2) -> c_15(X1, X2)
     , a__U31^#(tt(), N) -> c_16(mark^#(N))
     , mark^#(s(X)) -> c_18(mark^#(X))
     , mark^#(plus(X1, X2)) -> c_20(a__plus^#(mark(X1), mark(X2)))
     , mark^#(isNatKind(X)) -> c_21(a__isNatKind^#(X))
     , mark^#(and(X1, X2)) -> c_22(a__and^#(mark(X1), X2))
     , mark^#(isNat(X)) -> c_23(a__isNat^#(X))
     , mark^#(U11(X1, X2, X3)) -> c_24(a__U11^#(mark(X1), X2, X3))
     , mark^#(U12(X1, X2)) -> c_25(a__U12^#(mark(X1), X2))
     , mark^#(U13(X)) -> c_26(a__U13^#(mark(X)))
     , mark^#(U21(X1, X2)) -> c_27(a__U21^#(mark(X1), X2))
     , mark^#(U22(X)) -> c_28(a__U22^#(mark(X)))
     , mark^#(U31(X1, X2)) -> c_29(a__U31^#(mark(X1), X2))
     , mark^#(U41(X1, X2, X3)) -> c_30(a__U41^#(mark(X1), X2, X3))
     , a__plus^#(X1, X2) -> c_33(X1, X2)
     , a__plus^#(N, s(M)) ->
       c_34(a__U41^#(a__and(a__and(a__isNat(M), isNatKind(M)),
                            and(isNat(N), isNatKind(N))),
                     M,
                     N))
     , a__plus^#(N, 0()) ->
       c_35(a__U31^#(a__and(a__isNat(N), isNatKind(N)), N))
     , a__isNatKind^#(X) -> c_38(X)
     , a__isNatKind^#(s(V1)) -> c_39(a__isNatKind^#(V1))
     , a__isNatKind^#(plus(V1, V2)) ->
       c_41(a__and^#(a__isNatKind(V1), isNatKind(V2)))
     , a__and^#(X1, X2) -> c_36(X1, X2)
     , a__and^#(tt(), X) -> c_37(mark^#(X))
     , a__U41^#(X1, X2, X3) -> c_31(X1, X2, X3)
     , a__U41^#(tt(), M, N) -> c_32(a__plus^#(mark(N), mark(M))) }
   Strict Trs:
     { a__U11(X1, X2, X3) -> U11(X1, X2, X3)
     , a__U11(tt(), V1, V2) -> a__U12(a__isNat(V1), V2)
     , a__U12(X1, X2) -> U12(X1, X2)
     , a__U12(tt(), V2) -> a__U13(a__isNat(V2))
     , a__isNat(X) -> isNat(X)
     , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
     , a__isNat(0()) -> tt()
     , a__isNat(plus(V1, V2)) ->
       a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2)
     , a__U13(X) -> U13(X)
     , a__U13(tt()) -> tt()
     , a__U21(X1, X2) -> U21(X1, X2)
     , a__U21(tt(), V1) -> a__U22(a__isNat(V1))
     , a__U22(X) -> U22(X)
     , a__U22(tt()) -> tt()
     , a__U31(X1, X2) -> U31(X1, X2)
     , a__U31(tt(), N) -> mark(N)
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(isNatKind(X)) -> a__isNatKind(X)
     , mark(and(X1, X2)) -> a__and(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
     , mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
     , mark(U13(X)) -> a__U13(mark(X))
     , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
     , mark(U22(X)) -> a__U22(mark(X))
     , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
     , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
     , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
     , a__U41(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__plus(N, s(M)) ->
       a__U41(a__and(a__and(a__isNat(M), isNatKind(M)),
                     and(isNat(N), isNatKind(N))),
              M,
              N)
     , a__plus(N, 0()) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N)
     , a__and(X1, X2) -> and(X1, X2)
     , a__and(tt(), X) -> mark(X)
     , a__isNatKind(X) -> isNatKind(X)
     , a__isNatKind(s(V1)) -> a__isNatKind(V1)
     , a__isNatKind(0()) -> tt()
     , a__isNatKind(plus(V1, V2)) ->
       a__and(a__isNatKind(V1), isNatKind(V2)) }
   Weak DPs:
     { a__U13^#(tt()) -> c_10()
     , a__isNat^#(0()) -> c_7()
     , a__U22^#(tt()) -> c_14()
     , mark^#(tt()) -> c_17()
     , mark^#(0()) -> c_19()
     , a__isNatKind^#(0()) -> c_40() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..