MAYBE

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

Strict Trs:
  { minus(x, y) -> cond(ge(x, s(y)), x, y)
  , cond(false(), x, y) -> 0()
  , cond(true(), x, y) -> s(minus(x, s(y)))
  , ge(u, 0()) -> true()
  , ge(s(u), s(v)) -> ge(u, v)
  , ge(0(), s(v)) -> false() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { minus^#(x, y) -> c_1(cond^#(ge(x, s(y)), x, y), ge^#(x, s(y)))
  , cond^#(false(), x, y) -> c_2()
  , cond^#(true(), x, y) -> c_3(minus^#(x, s(y)))
  , ge^#(u, 0()) -> c_4()
  , ge^#(s(u), s(v)) -> c_5(ge^#(u, v))
  , ge^#(0(), s(v)) -> c_6() }

and mark the set of starting terms.

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

Strict DPs:
  { minus^#(x, y) -> c_1(cond^#(ge(x, s(y)), x, y), ge^#(x, s(y)))
  , cond^#(false(), x, y) -> c_2()
  , cond^#(true(), x, y) -> c_3(minus^#(x, s(y)))
  , ge^#(u, 0()) -> c_4()
  , ge^#(s(u), s(v)) -> c_5(ge^#(u, v))
  , ge^#(0(), s(v)) -> c_6() }
Weak Trs:
  { minus(x, y) -> cond(ge(x, s(y)), x, y)
  , cond(false(), x, y) -> 0()
  , cond(true(), x, y) -> s(minus(x, s(y)))
  , ge(u, 0()) -> true()
  , ge(s(u), s(v)) -> ge(u, v)
  , ge(0(), s(v)) -> false() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {2,4,6} by applications of
Pre({2,4,6}) = {1,5}. Here rules are labeled as follows:

  DPs:
    { 1: minus^#(x, y) -> c_1(cond^#(ge(x, s(y)), x, y), ge^#(x, s(y)))
    , 2: cond^#(false(), x, y) -> c_2()
    , 3: cond^#(true(), x, y) -> c_3(minus^#(x, s(y)))
    , 4: ge^#(u, 0()) -> c_4()
    , 5: ge^#(s(u), s(v)) -> c_5(ge^#(u, v))
    , 6: ge^#(0(), s(v)) -> c_6() }

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

Strict DPs:
  { minus^#(x, y) -> c_1(cond^#(ge(x, s(y)), x, y), ge^#(x, s(y)))
  , cond^#(true(), x, y) -> c_3(minus^#(x, s(y)))
  , ge^#(s(u), s(v)) -> c_5(ge^#(u, v)) }
Weak DPs:
  { cond^#(false(), x, y) -> c_2()
  , ge^#(u, 0()) -> c_4()
  , ge^#(0(), s(v)) -> c_6() }
Weak Trs:
  { minus(x, y) -> cond(ge(x, s(y)), x, y)
  , cond(false(), x, y) -> 0()
  , cond(true(), x, y) -> s(minus(x, s(y)))
  , ge(u, 0()) -> true()
  , ge(s(u), s(v)) -> ge(u, v)
  , ge(0(), s(v)) -> false() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ cond^#(false(), x, y) -> c_2()
, ge^#(u, 0()) -> c_4()
, ge^#(0(), s(v)) -> c_6() }

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

Strict DPs:
  { minus^#(x, y) -> c_1(cond^#(ge(x, s(y)), x, y), ge^#(x, s(y)))
  , cond^#(true(), x, y) -> c_3(minus^#(x, s(y)))
  , ge^#(s(u), s(v)) -> c_5(ge^#(u, v)) }
Weak Trs:
  { minus(x, y) -> cond(ge(x, s(y)), x, y)
  , cond(false(), x, y) -> 0()
  , cond(true(), x, y) -> s(minus(x, s(y)))
  , ge(u, 0()) -> true()
  , ge(s(u), s(v)) -> ge(u, v)
  , ge(0(), s(v)) -> false() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { ge(u, 0()) -> true()
    , ge(s(u), s(v)) -> ge(u, v)
    , ge(0(), s(v)) -> false() }

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

Strict DPs:
  { minus^#(x, y) -> c_1(cond^#(ge(x, s(y)), x, y), ge^#(x, s(y)))
  , cond^#(true(), x, y) -> c_3(minus^#(x, s(y)))
  , ge^#(s(u), s(v)) -> c_5(ge^#(u, v)) }
Weak Trs:
  { ge(u, 0()) -> true()
  , ge(s(u), s(v)) -> ge(u, v)
  , ge(0(), s(v)) -> false() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'matrices' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'matrix interpretation of dimension 4' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   2) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   3) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   4) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   5) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   6) 'matrix interpretation of dimension 1' failed due to the
      following reason:
      
      The input cannot be shown compatible
   

2) 'empty' failed due to the following reason:
   
   Empty strict component of the problem is NOT empty.


Arrrr..