MAYBE

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

Strict Trs:
  { f(0(x1)) -> s(0(x1))
  , f(s(x1)) -> d(f(p(s(x1))))
  , d(0(x1)) -> 0(x1)
  , d(s(x1)) -> s(s(d(p(s(x1)))))
  , p(s(x1)) -> x1 }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { f^#(0(x1)) -> c_1()
  , f^#(s(x1)) -> c_2(d^#(f(p(s(x1)))), f^#(p(s(x1))), p^#(s(x1)))
  , d^#(0(x1)) -> c_3()
  , d^#(s(x1)) -> c_4(d^#(p(s(x1))), p^#(s(x1)))
  , p^#(s(x1)) -> c_5() }

and mark the set of starting terms.

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

Strict DPs:
  { f^#(0(x1)) -> c_1()
  , f^#(s(x1)) -> c_2(d^#(f(p(s(x1)))), f^#(p(s(x1))), p^#(s(x1)))
  , d^#(0(x1)) -> c_3()
  , d^#(s(x1)) -> c_4(d^#(p(s(x1))), p^#(s(x1)))
  , p^#(s(x1)) -> c_5() }
Weak Trs:
  { f(0(x1)) -> s(0(x1))
  , f(s(x1)) -> d(f(p(s(x1))))
  , d(0(x1)) -> 0(x1)
  , d(s(x1)) -> s(s(d(p(s(x1)))))
  , p(s(x1)) -> x1 }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,3,5} by applications of
Pre({1,3,5}) = {2,4}. Here rules are labeled as follows:

  DPs:
    { 1: f^#(0(x1)) -> c_1()
    , 2: f^#(s(x1)) -> c_2(d^#(f(p(s(x1)))), f^#(p(s(x1))), p^#(s(x1)))
    , 3: d^#(0(x1)) -> c_3()
    , 4: d^#(s(x1)) -> c_4(d^#(p(s(x1))), p^#(s(x1)))
    , 5: p^#(s(x1)) -> c_5() }

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

Strict DPs:
  { f^#(s(x1)) -> c_2(d^#(f(p(s(x1)))), f^#(p(s(x1))), p^#(s(x1)))
  , d^#(s(x1)) -> c_4(d^#(p(s(x1))), p^#(s(x1))) }
Weak DPs:
  { f^#(0(x1)) -> c_1()
  , d^#(0(x1)) -> c_3()
  , p^#(s(x1)) -> c_5() }
Weak Trs:
  { f(0(x1)) -> s(0(x1))
  , f(s(x1)) -> d(f(p(s(x1))))
  , d(0(x1)) -> 0(x1)
  , d(s(x1)) -> s(s(d(p(s(x1)))))
  , p(s(x1)) -> x1 }
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.

{ f^#(0(x1)) -> c_1()
, d^#(0(x1)) -> c_3()
, p^#(s(x1)) -> c_5() }

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

Strict DPs:
  { f^#(s(x1)) -> c_2(d^#(f(p(s(x1)))), f^#(p(s(x1))), p^#(s(x1)))
  , d^#(s(x1)) -> c_4(d^#(p(s(x1))), p^#(s(x1))) }
Weak Trs:
  { f(0(x1)) -> s(0(x1))
  , f(s(x1)) -> d(f(p(s(x1))))
  , d(0(x1)) -> 0(x1)
  , d(s(x1)) -> s(s(d(p(s(x1)))))
  , p(s(x1)) -> x1 }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Due to missing edges in the dependency-graph, the right-hand sides
of following rules could be simplified:

  { f^#(s(x1)) -> c_2(d^#(f(p(s(x1)))), f^#(p(s(x1))), p^#(s(x1)))
  , d^#(s(x1)) -> c_4(d^#(p(s(x1))), p^#(s(x1))) }

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

Strict DPs:
  { f^#(s(x1)) -> c_1(d^#(f(p(s(x1)))), f^#(p(s(x1))))
  , d^#(s(x1)) -> c_2(d^#(p(s(x1)))) }
Weak Trs:
  { f(0(x1)) -> s(0(x1))
  , f(s(x1)) -> d(f(p(s(x1))))
  , d(0(x1)) -> 0(x1)
  , d(s(x1)) -> s(s(d(p(s(x1)))))
  , p(s(x1)) -> x1 }
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:
      
      Following exception was raised:
        stack overflow
   
   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..