MAYBE

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

Strict Trs:
  { from(X) -> cons(X, n__from(n__s(X)))
  , from(X) -> n__from(X)
  , cons(X1, X2) -> n__cons(X1, X2)
  , 2ndspos(0(), Z) -> rnil()
  , 2ndspos(s(N), cons(X, n__cons(Y, Z))) ->
    rcons(posrecip(activate(Y)), 2ndsneg(N, activate(Z)))
  , s(X) -> n__s(X)
  , activate(X) -> X
  , activate(n__from(X)) -> from(activate(X))
  , activate(n__s(X)) -> s(activate(X))
  , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
  , 2ndsneg(0(), Z) -> rnil()
  , 2ndsneg(s(N), cons(X, n__cons(Y, Z))) ->
    rcons(negrecip(activate(Y)), 2ndspos(N, activate(Z)))
  , pi(X) -> 2ndspos(X, from(0()))
  , plus(0(), Y) -> Y
  , plus(s(X), Y) -> s(plus(X, Y))
  , times(0(), Y) -> 0()
  , times(s(X), Y) -> plus(Y, times(X, Y))
  , square(X) -> times(X, X) }
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:
     { from^#(X) -> c_1(cons^#(X, n__from(n__s(X))))
     , from^#(X) -> c_2(X)
     , cons^#(X1, X2) -> c_3(X1, X2)
     , 2ndspos^#(0(), Z) -> c_4()
     , 2ndspos^#(s(N), cons(X, n__cons(Y, Z))) ->
       c_5(activate^#(Y), 2ndsneg^#(N, activate(Z)))
     , activate^#(X) -> c_7(X)
     , activate^#(n__from(X)) -> c_8(from^#(activate(X)))
     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
     , activate^#(n__cons(X1, X2)) -> c_10(cons^#(activate(X1), X2))
     , 2ndsneg^#(0(), Z) -> c_11()
     , 2ndsneg^#(s(N), cons(X, n__cons(Y, Z))) ->
       c_12(activate^#(Y), 2ndspos^#(N, activate(Z)))
     , s^#(X) -> c_6(X)
     , pi^#(X) -> c_13(2ndspos^#(X, from(0())))
     , plus^#(0(), Y) -> c_14(Y)
     , plus^#(s(X), Y) -> c_15(s^#(plus(X, Y)))
     , times^#(0(), Y) -> c_16()
     , times^#(s(X), Y) -> c_17(plus^#(Y, times(X, Y)))
     , square^#(X) -> c_18(times^#(X, X)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { from^#(X) -> c_1(cons^#(X, n__from(n__s(X))))
     , from^#(X) -> c_2(X)
     , cons^#(X1, X2) -> c_3(X1, X2)
     , 2ndspos^#(0(), Z) -> c_4()
     , 2ndspos^#(s(N), cons(X, n__cons(Y, Z))) ->
       c_5(activate^#(Y), 2ndsneg^#(N, activate(Z)))
     , activate^#(X) -> c_7(X)
     , activate^#(n__from(X)) -> c_8(from^#(activate(X)))
     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
     , activate^#(n__cons(X1, X2)) -> c_10(cons^#(activate(X1), X2))
     , 2ndsneg^#(0(), Z) -> c_11()
     , 2ndsneg^#(s(N), cons(X, n__cons(Y, Z))) ->
       c_12(activate^#(Y), 2ndspos^#(N, activate(Z)))
     , s^#(X) -> c_6(X)
     , pi^#(X) -> c_13(2ndspos^#(X, from(0())))
     , plus^#(0(), Y) -> c_14(Y)
     , plus^#(s(X), Y) -> c_15(s^#(plus(X, Y)))
     , times^#(0(), Y) -> c_16()
     , times^#(s(X), Y) -> c_17(plus^#(Y, times(X, Y)))
     , square^#(X) -> c_18(times^#(X, X)) }
   Strict Trs:
     { from(X) -> cons(X, n__from(n__s(X)))
     , from(X) -> n__from(X)
     , cons(X1, X2) -> n__cons(X1, X2)
     , 2ndspos(0(), Z) -> rnil()
     , 2ndspos(s(N), cons(X, n__cons(Y, Z))) ->
       rcons(posrecip(activate(Y)), 2ndsneg(N, activate(Z)))
     , s(X) -> n__s(X)
     , activate(X) -> X
     , activate(n__from(X)) -> from(activate(X))
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
     , 2ndsneg(0(), Z) -> rnil()
     , 2ndsneg(s(N), cons(X, n__cons(Y, Z))) ->
       rcons(negrecip(activate(Y)), 2ndspos(N, activate(Z)))
     , pi(X) -> 2ndspos(X, from(0()))
     , plus(0(), Y) -> Y
     , plus(s(X), Y) -> s(plus(X, Y))
     , times(0(), Y) -> 0()
     , times(s(X), Y) -> plus(Y, times(X, Y))
     , square(X) -> times(X, X) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {4,10,16} by applications
   of Pre({4,10,16}) = {2,3,5,6,11,12,13,14,18}. Here rules are
   labeled as follows:
   
     DPs:
       { 1: from^#(X) -> c_1(cons^#(X, n__from(n__s(X))))
       , 2: from^#(X) -> c_2(X)
       , 3: cons^#(X1, X2) -> c_3(X1, X2)
       , 4: 2ndspos^#(0(), Z) -> c_4()
       , 5: 2ndspos^#(s(N), cons(X, n__cons(Y, Z))) ->
            c_5(activate^#(Y), 2ndsneg^#(N, activate(Z)))
       , 6: activate^#(X) -> c_7(X)
       , 7: activate^#(n__from(X)) -> c_8(from^#(activate(X)))
       , 8: activate^#(n__s(X)) -> c_9(s^#(activate(X)))
       , 9: activate^#(n__cons(X1, X2)) -> c_10(cons^#(activate(X1), X2))
       , 10: 2ndsneg^#(0(), Z) -> c_11()
       , 11: 2ndsneg^#(s(N), cons(X, n__cons(Y, Z))) ->
             c_12(activate^#(Y), 2ndspos^#(N, activate(Z)))
       , 12: s^#(X) -> c_6(X)
       , 13: pi^#(X) -> c_13(2ndspos^#(X, from(0())))
       , 14: plus^#(0(), Y) -> c_14(Y)
       , 15: plus^#(s(X), Y) -> c_15(s^#(plus(X, Y)))
       , 16: times^#(0(), Y) -> c_16()
       , 17: times^#(s(X), Y) -> c_17(plus^#(Y, times(X, Y)))
       , 18: square^#(X) -> c_18(times^#(X, X)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { from^#(X) -> c_1(cons^#(X, n__from(n__s(X))))
     , from^#(X) -> c_2(X)
     , cons^#(X1, X2) -> c_3(X1, X2)
     , 2ndspos^#(s(N), cons(X, n__cons(Y, Z))) ->
       c_5(activate^#(Y), 2ndsneg^#(N, activate(Z)))
     , activate^#(X) -> c_7(X)
     , activate^#(n__from(X)) -> c_8(from^#(activate(X)))
     , activate^#(n__s(X)) -> c_9(s^#(activate(X)))
     , activate^#(n__cons(X1, X2)) -> c_10(cons^#(activate(X1), X2))
     , 2ndsneg^#(s(N), cons(X, n__cons(Y, Z))) ->
       c_12(activate^#(Y), 2ndspos^#(N, activate(Z)))
     , s^#(X) -> c_6(X)
     , pi^#(X) -> c_13(2ndspos^#(X, from(0())))
     , plus^#(0(), Y) -> c_14(Y)
     , plus^#(s(X), Y) -> c_15(s^#(plus(X, Y)))
     , times^#(s(X), Y) -> c_17(plus^#(Y, times(X, Y)))
     , square^#(X) -> c_18(times^#(X, X)) }
   Strict Trs:
     { from(X) -> cons(X, n__from(n__s(X)))
     , from(X) -> n__from(X)
     , cons(X1, X2) -> n__cons(X1, X2)
     , 2ndspos(0(), Z) -> rnil()
     , 2ndspos(s(N), cons(X, n__cons(Y, Z))) ->
       rcons(posrecip(activate(Y)), 2ndsneg(N, activate(Z)))
     , s(X) -> n__s(X)
     , activate(X) -> X
     , activate(n__from(X)) -> from(activate(X))
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
     , 2ndsneg(0(), Z) -> rnil()
     , 2ndsneg(s(N), cons(X, n__cons(Y, Z))) ->
       rcons(negrecip(activate(Y)), 2ndspos(N, activate(Z)))
     , pi(X) -> 2ndspos(X, from(0()))
     , plus(0(), Y) -> Y
     , plus(s(X), Y) -> s(plus(X, Y))
     , times(0(), Y) -> 0()
     , times(s(X), Y) -> plus(Y, times(X, Y))
     , square(X) -> times(X, X) }
   Weak DPs:
     { 2ndspos^#(0(), Z) -> c_4()
     , 2ndsneg^#(0(), Z) -> c_11()
     , times^#(0(), Y) -> c_16() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..