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

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

We add the following weak dependency pairs:

Strict DPs: { f^#(g(x), y, y) -> c_1(f^#(x, 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^#(g(x), y, y) -> c_1(f^#(x, x, y)) }
Strict Trs: { f(g(x), y, y) -> g(f(x, 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^#(g(x), y, y) -> c_1(f^#(x, 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_1) = {1}

TcT has computed the following constructor-restricted matrix
interpretation.

            [g](x1) = [1 0] x1 + [0]
                      [0 1]      [2]
                                    
  [f^#](x1, x2, x3) = [0 1] x1 + [0]
                      [0 0]      [0]
                                    
          [c_1](x1) = [1 0] x1 + [0]
                      [0 1]      [0]

The order satisfies the following ordering constraints:

  [f^#(g(x), y, y)] = [0 1] x + [2]      
                      [0 0]     [0]      
                    > [0 1] x + [0]      
                      [0 0]     [0]      
                    = [c_1(f^#(x, x, y))]
                                         

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