MAYBE

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

Strict Trs:
  { from(X) -> cons(X, from(s(X)))
  , 2ndspos(s(N), cons(X, cons(Y, Z))) ->
    rcons(posrecip(Y), 2ndsneg(N, Z))
  , 2ndspos(0(), Z) -> rnil()
  , 2ndsneg(s(N), cons(X, cons(Y, Z))) ->
    rcons(negrecip(Y), 2ndspos(N, Z))
  , 2ndsneg(0(), Z) -> rnil()
  , pi(X) -> 2ndspos(X, from(0()))
  , plus(s(X), Y) -> s(plus(X, Y))
  , plus(0(), Y) -> Y
  , times(s(X), Y) -> plus(Y, times(X, Y))
  , times(0(), Y) -> 0()
  , 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) '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) '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) '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(X, from^#(s(X)))
     , 2ndspos^#(s(N), cons(X, cons(Y, Z))) -> c_2(Y, 2ndsneg^#(N, Z))
     , 2ndspos^#(0(), Z) -> c_3()
     , 2ndsneg^#(s(N), cons(X, cons(Y, Z))) -> c_4(Y, 2ndspos^#(N, Z))
     , 2ndsneg^#(0(), Z) -> c_5()
     , pi^#(X) -> c_6(2ndspos^#(X, from(0())))
     , plus^#(s(X), Y) -> c_7(plus^#(X, Y))
     , plus^#(0(), Y) -> c_8(Y)
     , times^#(s(X), Y) -> c_9(plus^#(Y, times(X, Y)))
     , times^#(0(), Y) -> c_10()
     , square^#(X) -> c_11(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(X, from^#(s(X)))
     , 2ndspos^#(s(N), cons(X, cons(Y, Z))) -> c_2(Y, 2ndsneg^#(N, Z))
     , 2ndspos^#(0(), Z) -> c_3()
     , 2ndsneg^#(s(N), cons(X, cons(Y, Z))) -> c_4(Y, 2ndspos^#(N, Z))
     , 2ndsneg^#(0(), Z) -> c_5()
     , pi^#(X) -> c_6(2ndspos^#(X, from(0())))
     , plus^#(s(X), Y) -> c_7(plus^#(X, Y))
     , plus^#(0(), Y) -> c_8(Y)
     , times^#(s(X), Y) -> c_9(plus^#(Y, times(X, Y)))
     , times^#(0(), Y) -> c_10()
     , square^#(X) -> c_11(times^#(X, X)) }
   Strict Trs:
     { from(X) -> cons(X, from(s(X)))
     , 2ndspos(s(N), cons(X, cons(Y, Z))) ->
       rcons(posrecip(Y), 2ndsneg(N, Z))
     , 2ndspos(0(), Z) -> rnil()
     , 2ndsneg(s(N), cons(X, cons(Y, Z))) ->
       rcons(negrecip(Y), 2ndspos(N, Z))
     , 2ndsneg(0(), Z) -> rnil()
     , pi(X) -> 2ndspos(X, from(0()))
     , plus(s(X), Y) -> s(plus(X, Y))
     , plus(0(), Y) -> Y
     , times(s(X), Y) -> plus(Y, times(X, Y))
     , times(0(), Y) -> 0()
     , square(X) -> times(X, X) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3,5,10} by applications
   of Pre({3,5,10}) = {1,2,4,6,8,11}. Here rules are labeled as
   follows:
   
     DPs:
       { 1: from^#(X) -> c_1(X, from^#(s(X)))
       , 2: 2ndspos^#(s(N), cons(X, cons(Y, Z))) ->
            c_2(Y, 2ndsneg^#(N, Z))
       , 3: 2ndspos^#(0(), Z) -> c_3()
       , 4: 2ndsneg^#(s(N), cons(X, cons(Y, Z))) ->
            c_4(Y, 2ndspos^#(N, Z))
       , 5: 2ndsneg^#(0(), Z) -> c_5()
       , 6: pi^#(X) -> c_6(2ndspos^#(X, from(0())))
       , 7: plus^#(s(X), Y) -> c_7(plus^#(X, Y))
       , 8: plus^#(0(), Y) -> c_8(Y)
       , 9: times^#(s(X), Y) -> c_9(plus^#(Y, times(X, Y)))
       , 10: times^#(0(), Y) -> c_10()
       , 11: square^#(X) -> c_11(times^#(X, X)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { from^#(X) -> c_1(X, from^#(s(X)))
     , 2ndspos^#(s(N), cons(X, cons(Y, Z))) -> c_2(Y, 2ndsneg^#(N, Z))
     , 2ndsneg^#(s(N), cons(X, cons(Y, Z))) -> c_4(Y, 2ndspos^#(N, Z))
     , pi^#(X) -> c_6(2ndspos^#(X, from(0())))
     , plus^#(s(X), Y) -> c_7(plus^#(X, Y))
     , plus^#(0(), Y) -> c_8(Y)
     , times^#(s(X), Y) -> c_9(plus^#(Y, times(X, Y)))
     , square^#(X) -> c_11(times^#(X, X)) }
   Strict Trs:
     { from(X) -> cons(X, from(s(X)))
     , 2ndspos(s(N), cons(X, cons(Y, Z))) ->
       rcons(posrecip(Y), 2ndsneg(N, Z))
     , 2ndspos(0(), Z) -> rnil()
     , 2ndsneg(s(N), cons(X, cons(Y, Z))) ->
       rcons(negrecip(Y), 2ndspos(N, Z))
     , 2ndsneg(0(), Z) -> rnil()
     , pi(X) -> 2ndspos(X, from(0()))
     , plus(s(X), Y) -> s(plus(X, Y))
     , plus(0(), Y) -> Y
     , times(s(X), Y) -> plus(Y, times(X, Y))
     , times(0(), Y) -> 0()
     , square(X) -> times(X, X) }
   Weak DPs:
     { 2ndspos^#(0(), Z) -> c_3()
     , 2ndsneg^#(0(), Z) -> c_5()
     , times^#(0(), Y) -> c_10() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..