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

We use the processor 'matrix interpretation of dimension 1' to
orient following rules strictly.

Trs: { f(g(x)) -> g(g(f(x))) }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^1)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
  TcT has computed the following constructor-based matrix
  interpretation satisfying not(EDA).
  
    [f](x1) = [3] x1 + [0]
                          
    [g](x1) = [1] x1 + [2]
  
  This order satisfies the following ordering constraints:
  
    [f(g(x))] =  [3] x + [6] 
              >  [3] x + [4] 
              =  [g(g(f(x)))]
                             
    [f(g(x))] =  [3] x + [6] 
              >= [1] x + [6] 
              =  [g(g(g(x)))]
                             

We return to the main proof.

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

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

We use the processor 'matrix interpretation of dimension 1' to
orient following rules strictly.

Trs: { f(g(x)) -> g(g(g(x))) }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^1)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
  TcT has computed the following constructor-based matrix
  interpretation satisfying not(EDA).
  
    [f](x1) = [3] x1 + [2]
                          
    [g](x1) = [1] x1 + [0]
  
  This order satisfies the following ordering constraints:
  
    [f(g(x))] =  [3] x + [2] 
              >= [3] x + [2] 
              =  [g(g(f(x)))]
                             
    [f(g(x))] =  [3] x + [2] 
              >  [1] x + [0] 
              =  [g(g(g(x)))]
                             

We return to the main proof.

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

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

Empty rules are trivially bounded

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