MAYBE

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

Strict Trs:
  { O(0()) -> 0()
  , +(x, 0()) -> x
  , +(O(x), O(y)) -> O(+(x, y))
  , +(O(x), I(y)) -> I(+(x, y))
  , +(0(), x) -> x
  , +(I(x), O(y)) -> I(+(x, y))
  , +(I(x), I(y)) -> O(+(+(x, y), I(0())))
  , *(x, 0()) -> 0()
  , *(O(x), y) -> O(*(x, y))
  , *(0(), x) -> 0()
  , *(I(x), y) -> +(O(*(x, y)), y)
  , -(x, 0()) -> x
  , -(O(x), O(y)) -> O(-(x, y))
  , -(O(x), I(y)) -> I(-(-(x, y), I(1())))
  , -(0(), x) -> 0()
  , -(I(x), O(y)) -> I(-(x, y))
  , -(I(x), I(y)) -> O(-(x, y)) }
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:
     { O^#(0()) -> c_1()
     , +^#(x, 0()) -> c_2(x)
     , +^#(O(x), O(y)) -> c_3(O^#(+(x, y)))
     , +^#(O(x), I(y)) -> c_4(+^#(x, y))
     , +^#(0(), x) -> c_5(x)
     , +^#(I(x), O(y)) -> c_6(+^#(x, y))
     , +^#(I(x), I(y)) -> c_7(O^#(+(+(x, y), I(0()))))
     , *^#(x, 0()) -> c_8()
     , *^#(O(x), y) -> c_9(O^#(*(x, y)))
     , *^#(0(), x) -> c_10()
     , *^#(I(x), y) -> c_11(+^#(O(*(x, y)), y))
     , -^#(x, 0()) -> c_12(x)
     , -^#(O(x), O(y)) -> c_13(O^#(-(x, y)))
     , -^#(O(x), I(y)) -> c_14(-^#(-(x, y), I(1())))
     , -^#(0(), x) -> c_15()
     , -^#(I(x), O(y)) -> c_16(-^#(x, y))
     , -^#(I(x), I(y)) -> c_17(O^#(-(x, y))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { O^#(0()) -> c_1()
     , +^#(x, 0()) -> c_2(x)
     , +^#(O(x), O(y)) -> c_3(O^#(+(x, y)))
     , +^#(O(x), I(y)) -> c_4(+^#(x, y))
     , +^#(0(), x) -> c_5(x)
     , +^#(I(x), O(y)) -> c_6(+^#(x, y))
     , +^#(I(x), I(y)) -> c_7(O^#(+(+(x, y), I(0()))))
     , *^#(x, 0()) -> c_8()
     , *^#(O(x), y) -> c_9(O^#(*(x, y)))
     , *^#(0(), x) -> c_10()
     , *^#(I(x), y) -> c_11(+^#(O(*(x, y)), y))
     , -^#(x, 0()) -> c_12(x)
     , -^#(O(x), O(y)) -> c_13(O^#(-(x, y)))
     , -^#(O(x), I(y)) -> c_14(-^#(-(x, y), I(1())))
     , -^#(0(), x) -> c_15()
     , -^#(I(x), O(y)) -> c_16(-^#(x, y))
     , -^#(I(x), I(y)) -> c_17(O^#(-(x, y))) }
   Strict Trs:
     { O(0()) -> 0()
     , +(x, 0()) -> x
     , +(O(x), O(y)) -> O(+(x, y))
     , +(O(x), I(y)) -> I(+(x, y))
     , +(0(), x) -> x
     , +(I(x), O(y)) -> I(+(x, y))
     , +(I(x), I(y)) -> O(+(+(x, y), I(0())))
     , *(x, 0()) -> 0()
     , *(O(x), y) -> O(*(x, y))
     , *(0(), x) -> 0()
     , *(I(x), y) -> +(O(*(x, y)), y)
     , -(x, 0()) -> x
     , -(O(x), O(y)) -> O(-(x, y))
     , -(O(x), I(y)) -> I(-(-(x, y), I(1())))
     , -(0(), x) -> 0()
     , -(I(x), O(y)) -> I(-(x, y))
     , -(I(x), I(y)) -> O(-(x, y)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,8,10,15} by
   applications of Pre({1,8,10,15}) = {2,3,5,7,9,12,13,14,16,17}. Here
   rules are labeled as follows:
   
     DPs:
       { 1: O^#(0()) -> c_1()
       , 2: +^#(x, 0()) -> c_2(x)
       , 3: +^#(O(x), O(y)) -> c_3(O^#(+(x, y)))
       , 4: +^#(O(x), I(y)) -> c_4(+^#(x, y))
       , 5: +^#(0(), x) -> c_5(x)
       , 6: +^#(I(x), O(y)) -> c_6(+^#(x, y))
       , 7: +^#(I(x), I(y)) -> c_7(O^#(+(+(x, y), I(0()))))
       , 8: *^#(x, 0()) -> c_8()
       , 9: *^#(O(x), y) -> c_9(O^#(*(x, y)))
       , 10: *^#(0(), x) -> c_10()
       , 11: *^#(I(x), y) -> c_11(+^#(O(*(x, y)), y))
       , 12: -^#(x, 0()) -> c_12(x)
       , 13: -^#(O(x), O(y)) -> c_13(O^#(-(x, y)))
       , 14: -^#(O(x), I(y)) -> c_14(-^#(-(x, y), I(1())))
       , 15: -^#(0(), x) -> c_15()
       , 16: -^#(I(x), O(y)) -> c_16(-^#(x, y))
       , 17: -^#(I(x), I(y)) -> c_17(O^#(-(x, y))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { +^#(x, 0()) -> c_2(x)
     , +^#(O(x), O(y)) -> c_3(O^#(+(x, y)))
     , +^#(O(x), I(y)) -> c_4(+^#(x, y))
     , +^#(0(), x) -> c_5(x)
     , +^#(I(x), O(y)) -> c_6(+^#(x, y))
     , +^#(I(x), I(y)) -> c_7(O^#(+(+(x, y), I(0()))))
     , *^#(O(x), y) -> c_9(O^#(*(x, y)))
     , *^#(I(x), y) -> c_11(+^#(O(*(x, y)), y))
     , -^#(x, 0()) -> c_12(x)
     , -^#(O(x), O(y)) -> c_13(O^#(-(x, y)))
     , -^#(O(x), I(y)) -> c_14(-^#(-(x, y), I(1())))
     , -^#(I(x), O(y)) -> c_16(-^#(x, y))
     , -^#(I(x), I(y)) -> c_17(O^#(-(x, y))) }
   Strict Trs:
     { O(0()) -> 0()
     , +(x, 0()) -> x
     , +(O(x), O(y)) -> O(+(x, y))
     , +(O(x), I(y)) -> I(+(x, y))
     , +(0(), x) -> x
     , +(I(x), O(y)) -> I(+(x, y))
     , +(I(x), I(y)) -> O(+(+(x, y), I(0())))
     , *(x, 0()) -> 0()
     , *(O(x), y) -> O(*(x, y))
     , *(0(), x) -> 0()
     , *(I(x), y) -> +(O(*(x, y)), y)
     , -(x, 0()) -> x
     , -(O(x), O(y)) -> O(-(x, y))
     , -(O(x), I(y)) -> I(-(-(x, y), I(1())))
     , -(0(), x) -> 0()
     , -(I(x), O(y)) -> I(-(x, y))
     , -(I(x), I(y)) -> O(-(x, y)) }
   Weak DPs:
     { O^#(0()) -> c_1()
     , *^#(x, 0()) -> c_8()
     , *^#(0(), x) -> c_10()
     , -^#(0(), x) -> c_15() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {2,6,7,10,13} by
   applications of Pre({2,6,7,10,13}) = {1,3,4,5,8,9,11,12}. Here
   rules are labeled as follows:
   
     DPs:
       { 1: +^#(x, 0()) -> c_2(x)
       , 2: +^#(O(x), O(y)) -> c_3(O^#(+(x, y)))
       , 3: +^#(O(x), I(y)) -> c_4(+^#(x, y))
       , 4: +^#(0(), x) -> c_5(x)
       , 5: +^#(I(x), O(y)) -> c_6(+^#(x, y))
       , 6: +^#(I(x), I(y)) -> c_7(O^#(+(+(x, y), I(0()))))
       , 7: *^#(O(x), y) -> c_9(O^#(*(x, y)))
       , 8: *^#(I(x), y) -> c_11(+^#(O(*(x, y)), y))
       , 9: -^#(x, 0()) -> c_12(x)
       , 10: -^#(O(x), O(y)) -> c_13(O^#(-(x, y)))
       , 11: -^#(O(x), I(y)) -> c_14(-^#(-(x, y), I(1())))
       , 12: -^#(I(x), O(y)) -> c_16(-^#(x, y))
       , 13: -^#(I(x), I(y)) -> c_17(O^#(-(x, y)))
       , 14: O^#(0()) -> c_1()
       , 15: *^#(x, 0()) -> c_8()
       , 16: *^#(0(), x) -> c_10()
       , 17: -^#(0(), x) -> c_15() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { +^#(x, 0()) -> c_2(x)
     , +^#(O(x), I(y)) -> c_4(+^#(x, y))
     , +^#(0(), x) -> c_5(x)
     , +^#(I(x), O(y)) -> c_6(+^#(x, y))
     , *^#(I(x), y) -> c_11(+^#(O(*(x, y)), y))
     , -^#(x, 0()) -> c_12(x)
     , -^#(O(x), I(y)) -> c_14(-^#(-(x, y), I(1())))
     , -^#(I(x), O(y)) -> c_16(-^#(x, y)) }
   Strict Trs:
     { O(0()) -> 0()
     , +(x, 0()) -> x
     , +(O(x), O(y)) -> O(+(x, y))
     , +(O(x), I(y)) -> I(+(x, y))
     , +(0(), x) -> x
     , +(I(x), O(y)) -> I(+(x, y))
     , +(I(x), I(y)) -> O(+(+(x, y), I(0())))
     , *(x, 0()) -> 0()
     , *(O(x), y) -> O(*(x, y))
     , *(0(), x) -> 0()
     , *(I(x), y) -> +(O(*(x, y)), y)
     , -(x, 0()) -> x
     , -(O(x), O(y)) -> O(-(x, y))
     , -(O(x), I(y)) -> I(-(-(x, y), I(1())))
     , -(0(), x) -> 0()
     , -(I(x), O(y)) -> I(-(x, y))
     , -(I(x), I(y)) -> O(-(x, y)) }
   Weak DPs:
     { O^#(0()) -> c_1()
     , +^#(O(x), O(y)) -> c_3(O^#(+(x, y)))
     , +^#(I(x), I(y)) -> c_7(O^#(+(+(x, y), I(0()))))
     , *^#(x, 0()) -> c_8()
     , *^#(O(x), y) -> c_9(O^#(*(x, y)))
     , *^#(0(), x) -> c_10()
     , -^#(O(x), O(y)) -> c_13(O^#(-(x, y)))
     , -^#(0(), x) -> c_15()
     , -^#(I(x), I(y)) -> c_17(O^#(-(x, y))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..