MAYBE

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

Strict Trs:
  { le(0(), Y) -> true()
  , le(s(X), 0()) -> false()
  , le(s(X), s(Y)) -> le(X, Y)
  , minus(0(), Y) -> 0()
  , minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y)
  , ifMinus(true(), s(X), Y) -> 0()
  , ifMinus(false(), s(X), Y) -> s(minus(X, Y))
  , quot(0(), s(Y)) -> 0()
  , quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(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) '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
      
      2) '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
      
   
   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:
     { le^#(0(), Y) -> c_1()
     , le^#(s(X), 0()) -> c_2()
     , le^#(s(X), s(Y)) -> c_3(le^#(X, Y))
     , minus^#(0(), Y) -> c_4()
     , minus^#(s(X), Y) -> c_5(ifMinus^#(le(s(X), Y), s(X), Y))
     , ifMinus^#(true(), s(X), Y) -> c_6()
     , ifMinus^#(false(), s(X), Y) -> c_7(minus^#(X, Y))
     , quot^#(0(), s(Y)) -> c_8()
     , quot^#(s(X), s(Y)) -> c_9(quot^#(minus(X, Y), s(Y))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { le^#(0(), Y) -> c_1()
     , le^#(s(X), 0()) -> c_2()
     , le^#(s(X), s(Y)) -> c_3(le^#(X, Y))
     , minus^#(0(), Y) -> c_4()
     , minus^#(s(X), Y) -> c_5(ifMinus^#(le(s(X), Y), s(X), Y))
     , ifMinus^#(true(), s(X), Y) -> c_6()
     , ifMinus^#(false(), s(X), Y) -> c_7(minus^#(X, Y))
     , quot^#(0(), s(Y)) -> c_8()
     , quot^#(s(X), s(Y)) -> c_9(quot^#(minus(X, Y), s(Y))) }
   Strict Trs:
     { le(0(), Y) -> true()
     , le(s(X), 0()) -> false()
     , le(s(X), s(Y)) -> le(X, Y)
     , minus(0(), Y) -> 0()
     , minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y)
     , ifMinus(true(), s(X), Y) -> 0()
     , ifMinus(false(), s(X), Y) -> s(minus(X, Y))
     , quot(0(), s(Y)) -> 0()
     , quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,4,6,8} by
   applications of Pre({1,2,4,6,8}) = {3,5,7,9}. Here rules are
   labeled as follows:
   
     DPs:
       { 1: le^#(0(), Y) -> c_1()
       , 2: le^#(s(X), 0()) -> c_2()
       , 3: le^#(s(X), s(Y)) -> c_3(le^#(X, Y))
       , 4: minus^#(0(), Y) -> c_4()
       , 5: minus^#(s(X), Y) -> c_5(ifMinus^#(le(s(X), Y), s(X), Y))
       , 6: ifMinus^#(true(), s(X), Y) -> c_6()
       , 7: ifMinus^#(false(), s(X), Y) -> c_7(minus^#(X, Y))
       , 8: quot^#(0(), s(Y)) -> c_8()
       , 9: quot^#(s(X), s(Y)) -> c_9(quot^#(minus(X, Y), s(Y))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { le^#(s(X), s(Y)) -> c_3(le^#(X, Y))
     , minus^#(s(X), Y) -> c_5(ifMinus^#(le(s(X), Y), s(X), Y))
     , ifMinus^#(false(), s(X), Y) -> c_7(minus^#(X, Y))
     , quot^#(s(X), s(Y)) -> c_9(quot^#(minus(X, Y), s(Y))) }
   Strict Trs:
     { le(0(), Y) -> true()
     , le(s(X), 0()) -> false()
     , le(s(X), s(Y)) -> le(X, Y)
     , minus(0(), Y) -> 0()
     , minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y)
     , ifMinus(true(), s(X), Y) -> 0()
     , ifMinus(false(), s(X), Y) -> s(minus(X, Y))
     , quot(0(), s(Y)) -> 0()
     , quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) }
   Weak DPs:
     { le^#(0(), Y) -> c_1()
     , le^#(s(X), 0()) -> c_2()
     , minus^#(0(), Y) -> c_4()
     , ifMinus^#(true(), s(X), Y) -> c_6()
     , quot^#(0(), s(Y)) -> c_8() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..