MAYBE

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

Strict Trs:
  { eq() -> eq()
  , eq() -> true()
  , eq() -> false()
  , inf(X) -> cons()
  , take(0(), X) -> nil()
  , take(s(), cons()) -> cons()
  , length(cons()) -> s()
  , length(nil()) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { eq^#() -> c_1(eq^#())
  , eq^#() -> c_2()
  , eq^#() -> c_3()
  , inf^#(X) -> c_4()
  , take^#(0(), X) -> c_5()
  , take^#(s(), cons()) -> c_6()
  , length^#(cons()) -> c_7()
  , length^#(nil()) -> c_8() }

and mark the set of starting terms.

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

Strict DPs:
  { eq^#() -> c_1(eq^#())
  , eq^#() -> c_2()
  , eq^#() -> c_3()
  , inf^#(X) -> c_4()
  , take^#(0(), X) -> c_5()
  , take^#(s(), cons()) -> c_6()
  , length^#(cons()) -> c_7()
  , length^#(nil()) -> c_8() }
Strict Trs:
  { eq() -> eq()
  , eq() -> true()
  , eq() -> false()
  , inf(X) -> cons()
  , take(0(), X) -> nil()
  , take(s(), cons()) -> cons()
  , length(cons()) -> s()
  , length(nil()) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

No rule is usable, rules are removed from the input problem.

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

Strict DPs:
  { eq^#() -> c_1(eq^#())
  , eq^#() -> c_2()
  , eq^#() -> c_3()
  , inf^#(X) -> c_4()
  , take^#(0(), X) -> c_5()
  , take^#(s(), cons()) -> c_6()
  , length^#(cons()) -> c_7()
  , length^#(nil()) -> c_8() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The weightgap principle applies (using the following constant
growth matrix-interpretation)

The following argument positions are usable:
  Uargs(c_1) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

            [cons] = [2]                  
                                          
               [0] = [1]                  
                                          
             [nil] = [2]                  
                                          
               [s] = [1]                  
                                          
            [eq^#] = [1]                  
                                          
         [c_1](x1) = [1] x1 + [2]         
                                          
             [c_2] = [0]                  
                                          
             [c_3] = [0]                  
                                          
       [inf^#](x1) = [2]                  
                                          
             [c_4] = [1]                  
                                          
  [take^#](x1, x2) = [1] x1 + [1] x2 + [1]
                                          
             [c_5] = [1]                  
                                          
             [c_6] = [2]                  
                                          
    [length^#](x1) = [2] x1 + [2]         
                                          
             [c_7] = [1]                  
                                          
             [c_8] = [1]                  

This order satisfies following ordering constraints:


Further, it can be verified that all rules not oriented are covered by the weightgap condition.

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

Strict DPs: { eq^#() -> c_1(eq^#()) }
Weak DPs:
  { eq^#() -> c_2()
  , eq^#() -> c_3()
  , inf^#(X) -> c_4()
  , take^#(0(), X) -> c_5()
  , take^#(s(), cons()) -> c_6()
  , length^#(cons()) -> c_7()
  , length^#(nil()) -> c_8() }
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.

{ eq^#() -> c_2()
, eq^#() -> c_3()
, inf^#(X) -> c_4()
, take^#(0(), X) -> c_5()
, take^#(s(), cons()) -> c_6()
, length^#(cons()) -> c_7()
, length^#(nil()) -> c_8() }

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

Strict DPs: { eq^#() -> c_1(eq^#()) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..