MAYBE

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

Strict Trs:
  { a__g(X) -> a__h(X)
  , a__g(X) -> g(X)
  , a__h(X) -> h(X)
  , a__h(d()) -> a__g(c())
  , a__c() -> d()
  , a__c() -> c()
  , mark(d()) -> d()
  , mark(c()) -> a__c()
  , mark(g(X)) -> a__g(X)
  , mark(h(X)) -> a__h(X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { a__g^#(X) -> c_1(a__h^#(X))
  , a__g^#(X) -> c_2()
  , a__h^#(X) -> c_3()
  , a__h^#(d()) -> c_4(a__g^#(c()))
  , a__c^#() -> c_5()
  , a__c^#() -> c_6()
  , mark^#(d()) -> c_7()
  , mark^#(c()) -> c_8(a__c^#())
  , mark^#(g(X)) -> c_9(a__g^#(X))
  , mark^#(h(X)) -> c_10(a__h^#(X)) }

and mark the set of starting terms.

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

Strict DPs:
  { a__g^#(X) -> c_1(a__h^#(X))
  , a__g^#(X) -> c_2()
  , a__h^#(X) -> c_3()
  , a__h^#(d()) -> c_4(a__g^#(c()))
  , a__c^#() -> c_5()
  , a__c^#() -> c_6()
  , mark^#(d()) -> c_7()
  , mark^#(c()) -> c_8(a__c^#())
  , mark^#(g(X)) -> c_9(a__g^#(X))
  , mark^#(h(X)) -> c_10(a__h^#(X)) }
Strict Trs:
  { a__g(X) -> a__h(X)
  , a__g(X) -> g(X)
  , a__h(X) -> h(X)
  , a__h(d()) -> a__g(c())
  , a__c() -> d()
  , a__c() -> c()
  , mark(d()) -> d()
  , mark(c()) -> a__c()
  , mark(g(X)) -> a__g(X)
  , mark(h(X)) -> a__h(X) }
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:
  { a__g^#(X) -> c_1(a__h^#(X))
  , a__g^#(X) -> c_2()
  , a__h^#(X) -> c_3()
  , a__h^#(d()) -> c_4(a__g^#(c()))
  , a__c^#() -> c_5()
  , a__c^#() -> c_6()
  , mark^#(d()) -> c_7()
  , mark^#(c()) -> c_8(a__c^#())
  , mark^#(g(X)) -> c_9(a__g^#(X))
  , mark^#(h(X)) -> c_10(a__h^#(X)) }
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}, Uargs(c_4) = {1}, Uargs(c_8) = {1},
  Uargs(c_9) = {1}, Uargs(c_10) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

           [d] = [2]         
                             
           [c] = [1]         
                             
       [g](x1) = [1] x1 + [1]
                             
       [h](x1) = [1] x1 + [1]
                             
  [a__g^#](x1) = [1] x1 + [1]
                             
     [c_1](x1) = [1] x1 + [1]
                             
  [a__h^#](x1) = [1] x1 + [1]
                             
         [c_2] = [0]         
                             
         [c_3] = [0]         
                             
     [c_4](x1) = [1] x1 + [0]
                             
      [a__c^#] = [1]         
                             
         [c_5] = [0]         
                             
         [c_6] = [0]         
                             
  [mark^#](x1) = [2] x1 + [2]
                             
         [c_7] = [1]         
                             
     [c_8](x1) = [1] x1 + [1]
                             
     [c_9](x1) = [1] x1 + [1]
                             
    [c_10](x1) = [1] x1 + [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: { a__g^#(X) -> c_1(a__h^#(X)) }
Weak DPs:
  { a__g^#(X) -> c_2()
  , a__h^#(X) -> c_3()
  , a__h^#(d()) -> c_4(a__g^#(c()))
  , a__c^#() -> c_5()
  , a__c^#() -> c_6()
  , mark^#(d()) -> c_7()
  , mark^#(c()) -> c_8(a__c^#())
  , mark^#(g(X)) -> c_9(a__g^#(X))
  , mark^#(h(X)) -> c_10(a__h^#(X)) }
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.

{ a__g^#(X) -> c_2()
, a__h^#(X) -> c_3()
, a__c^#() -> c_5()
, a__c^#() -> c_6()
, mark^#(d()) -> c_7()
, mark^#(c()) -> c_8(a__c^#()) }

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

Strict DPs: { a__g^#(X) -> c_1(a__h^#(X)) }
Weak DPs:
  { a__h^#(d()) -> c_4(a__g^#(c()))
  , mark^#(g(X)) -> c_9(a__g^#(X))
  , mark^#(h(X)) -> c_10(a__h^#(X)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Consider the dependency graph

  1: a__g^#(X) -> c_1(a__h^#(X))
     -->_1 a__h^#(d()) -> c_4(a__g^#(c())) :2
  
  2: a__h^#(d()) -> c_4(a__g^#(c()))
     -->_1 a__g^#(X) -> c_1(a__h^#(X)) :1
  
  3: mark^#(g(X)) -> c_9(a__g^#(X))
     -->_1 a__g^#(X) -> c_1(a__h^#(X)) :1
  
  4: mark^#(h(X)) -> c_10(a__h^#(X))
     -->_1 a__h^#(d()) -> c_4(a__g^#(c())) :2
  

Following roots of the dependency graph are removed, as the
considered set of starting terms is closed under reduction with
respect to these rules (modulo compound contexts).

  { mark^#(g(X)) -> c_9(a__g^#(X))
  , mark^#(h(X)) -> c_10(a__h^#(X)) }


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

Strict DPs: { a__g^#(X) -> c_1(a__h^#(X)) }
Weak DPs: { a__h^#(d()) -> c_4(a__g^#(c())) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..