MAYBE

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

Strict Trs:
  { f(x, x) -> f(0(), 1())
  , f(x, 2()) -> 2()
  , f(2(), x) -> 2()
  , 0() -> 2()
  , 1() -> 2() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { f^#(x, x) -> c_1(f^#(0(), 1()))
  , f^#(x, 2()) -> c_2()
  , f^#(2(), x) -> c_3()
  , 0^#() -> c_4()
  , 1^#() -> 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^#(x, x) -> c_1(f^#(0(), 1()))
  , f^#(x, 2()) -> c_2()
  , f^#(2(), x) -> c_3()
  , 0^#() -> c_4()
  , 1^#() -> c_5() }
Strict Trs:
  { f(x, x) -> f(0(), 1())
  , f(x, 2()) -> 2()
  , f(2(), x) -> 2()
  , 0() -> 2()
  , 1() -> 2() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Strict Usable Rules:
    { 0() -> 2()
    , 1() -> 2() }

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

Strict DPs:
  { f^#(x, x) -> c_1(f^#(0(), 1()))
  , f^#(x, 2()) -> c_2()
  , f^#(2(), x) -> c_3()
  , 0^#() -> c_4()
  , 1^#() -> c_5() }
Strict Trs:
  { 0() -> 2()
  , 1() -> 2() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

The following argument positions are usable:
  Uargs(f^#) = {1, 2}, Uargs(c_1) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

            [0] = [2]                  
                                       
            [1] = [2]                  
                                       
            [2] = [1]                  
                                       
  [f^#](x1, x2) = [1] x1 + [2] x2 + [1]
                                       
      [c_1](x1) = [1] x1 + [0]         
                                       
          [c_2] = [1]                  
                                       
          [c_3] = [1]                  
                                       
          [0^#] = [1]                  
                                       
          [c_4] = [0]                  
                                       
          [1^#] = [1]                  
                                       
          [c_5] = [0]                  

This order satisfies following ordering constraints:

  [0()] = [2]  
        > [1]  
        = [2()]
               
  [1()] = [2]  
        > [1]  
        = [2()]
               

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: { f^#(x, x) -> c_1(f^#(0(), 1())) }
Weak DPs:
  { f^#(x, 2()) -> c_2()
  , f^#(2(), x) -> c_3()
  , 0^#() -> c_4()
  , 1^#() -> c_5() }
Weak Trs:
  { 0() -> 2()
  , 1() -> 2() }
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^#(x, 2()) -> c_2()
, f^#(2(), x) -> c_3()
, 0^#() -> c_4()
, 1^#() -> c_5() }

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

Strict DPs: { f^#(x, x) -> c_1(f^#(0(), 1())) }
Weak Trs:
  { 0() -> 2()
  , 1() -> 2() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..