Problem Transformed CSR 04 ExProp7 Luc06 L

YES(?,O(n^3))

We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^3)).

Strict Trs:
  { f(0()) -> cons(0())
  , f(s(0())) -> f(p(s(0())))
  , p(s(X)) -> X }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^3))

The following argument positions are usable:
  Uargs(f) = {1}, Uargs(cons) = {}, Uargs(s) = {}, Uargs(p) = {}

TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).

               [1 0 2]      [0]
     [f](x1) = [0 0 0] x1 + [0]
               [0 0 0]      [0]
                               
               [0]
         [0] = [0]
               [2]
                  
               [3]
  [cons](x1) = [0]
               [0]
                  
               [1 0 2]      [3]
     [s](x1) = [1 1 1] x1 + [1]
               [0 0 1]      [1]
                               
               [0 1 0]      [2]
     [p](x1) = [0 1 0] x1 + [0]
               [0 0 1]      [0]

This order satisfies following ordering constraints

     [f(0())] = [4]            
                [0]            
                [0]            
              > [3]            
                [0]            
                [0]            
              = [cons(0())]    
                               
  [f(s(0()))] = [13]           
                [0]            
                [0]            
              > [11]           
                [0]            
                [0]            
              = [f(p(s(0())))] 
                               
    [p(s(X))] = [1 1 1]     [3]
                [1 1 1] X + [1]
                [0 0 1]     [1]
              > [1 0 0]     [0]
                [0 1 0] X + [0]
                [0 0 1]     [0]
              = [X]            
                               

Hurray, we answered YES(?,O(n^3))

MAYBE

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

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

The input cannot be shown compatible

Arrrr..

MAYBE

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

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

The input cannot be shown compatible

Arrrr..

MAYBE

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

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

The input cannot be shown compatible

Arrrr..

MAYBE

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

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

The input cannot be shown compatible

Arrrr..