MAYBE

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

Strict Trs:
  { a(a(x, y), z) -> a(x, a(y, z))
  , a(lambda(x), y) -> lambda(a(x, p(1(), a(y, t()))))
  , a(p(x, y), z) -> p(a(x, z), a(y, z))
  , a(1(), p(x, y)) -> x
  , a(1(), id()) -> 1()
  , a(t(), p(x, y)) -> y
  , a(t(), id()) -> t()
  , a(id(), 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:
     { a^#(a(x, y), z) -> c_1(a^#(x, a(y, z)))
     , a^#(lambda(x), y) -> c_2(a^#(x, p(1(), a(y, t()))))
     , a^#(p(x, y), z) -> c_3(a^#(x, z), a^#(y, z))
     , a^#(1(), p(x, y)) -> c_4(x)
     , a^#(1(), id()) -> c_5()
     , a^#(t(), p(x, y)) -> c_6(y)
     , a^#(t(), id()) -> c_7()
     , a^#(id(), x) -> c_8(x) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { a^#(a(x, y), z) -> c_1(a^#(x, a(y, z)))
     , a^#(lambda(x), y) -> c_2(a^#(x, p(1(), a(y, t()))))
     , a^#(p(x, y), z) -> c_3(a^#(x, z), a^#(y, z))
     , a^#(1(), p(x, y)) -> c_4(x)
     , a^#(1(), id()) -> c_5()
     , a^#(t(), p(x, y)) -> c_6(y)
     , a^#(t(), id()) -> c_7()
     , a^#(id(), x) -> c_8(x) }
   Strict Trs:
     { a(a(x, y), z) -> a(x, a(y, z))
     , a(lambda(x), y) -> lambda(a(x, p(1(), a(y, t()))))
     , a(p(x, y), z) -> p(a(x, z), a(y, z))
     , a(1(), p(x, y)) -> x
     , a(1(), id()) -> 1()
     , a(t(), p(x, y)) -> y
     , a(t(), id()) -> t()
     , a(id(), x) -> x }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {5,7} by applications of
   Pre({5,7}) = {1,3,4,6,8}. Here rules are labeled as follows:
   
     DPs:
       { 1: a^#(a(x, y), z) -> c_1(a^#(x, a(y, z)))
       , 2: a^#(lambda(x), y) -> c_2(a^#(x, p(1(), a(y, t()))))
       , 3: a^#(p(x, y), z) -> c_3(a^#(x, z), a^#(y, z))
       , 4: a^#(1(), p(x, y)) -> c_4(x)
       , 5: a^#(1(), id()) -> c_5()
       , 6: a^#(t(), p(x, y)) -> c_6(y)
       , 7: a^#(t(), id()) -> c_7()
       , 8: a^#(id(), x) -> c_8(x) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { a^#(a(x, y), z) -> c_1(a^#(x, a(y, z)))
     , a^#(lambda(x), y) -> c_2(a^#(x, p(1(), a(y, t()))))
     , a^#(p(x, y), z) -> c_3(a^#(x, z), a^#(y, z))
     , a^#(1(), p(x, y)) -> c_4(x)
     , a^#(t(), p(x, y)) -> c_6(y)
     , a^#(id(), x) -> c_8(x) }
   Strict Trs:
     { a(a(x, y), z) -> a(x, a(y, z))
     , a(lambda(x), y) -> lambda(a(x, p(1(), a(y, t()))))
     , a(p(x, y), z) -> p(a(x, z), a(y, z))
     , a(1(), p(x, y)) -> x
     , a(1(), id()) -> 1()
     , a(t(), p(x, y)) -> y
     , a(t(), id()) -> t()
     , a(id(), x) -> x }
   Weak DPs:
     { a^#(1(), id()) -> c_5()
     , a^#(t(), id()) -> c_7() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..