YES(O(1),O(n^1))

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict Trs:
  { f(x, x) -> a()
  , f(g(x), y) -> f(x, y) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(n^1))

We add following weak dependency pairs:

Strict DPs:
  { f^#(x, x) -> c_1()
  , f^#(g(x), y) -> c_2(f^#(x, y)) }

and mark the set of starting terms.

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict DPs:
  { f^#(x, x) -> c_1()
  , f^#(g(x), y) -> c_2(f^#(x, y)) }
Strict Trs:
  { f(x, x) -> a()
  , f(g(x), y) -> f(x, y) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(n^1))

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

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).

Strict DPs:
  { f^#(x, x) -> c_1()
  , f^#(g(x), y) -> c_2(f^#(x, y)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(n^1))

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

The following argument positions are usable:
  Uargs(c_2) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

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

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 YES(O(1),O(1)).

Weak DPs:
  { f^#(x, x) -> c_1()
  , f^#(g(x), y) -> c_2(f^#(x, y)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(1))

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ f^#(x, x) -> c_1()
, f^#(g(x), y) -> c_2(f^#(x, y)) }

We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(1)).

Rules: Empty
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(1))

Empty rules are trivially bounded

Hurray, we answered YES(O(1),O(n^1))