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

Strict Trs: { a(b(x)) -> a(c(b(x))) }
Obligation:
  runtime complexity
Answer:
  YES(O(1),O(1))

The input is overlay and right-linear. Switching to innermost
rewriting.

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

Strict Trs: { a(b(x)) -> a(c(b(x))) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(1))

We add the following weak dependency pairs:

Strict DPs: { a^#(b(x)) -> c_1(a^#(c(b(x)))) }

and mark the set of starting terms.

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

Strict DPs: { a^#(b(x)) -> c_1(a^#(c(b(x)))) }
Strict Trs: { a(b(x)) -> a(c(b(x))) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(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(1)).

Strict DPs: { a^#(b(x)) -> c_1(a^#(c(b(x)))) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(1))

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

The following argument positions are usable:
  none

TcT has computed the following constructor-restricted matrix
interpretation.

    [b](x1) = [0]           
              [2]           
                            
    [c](x1) = [0]           
              [0]           
                            
  [a^#](x1) = [0 2] x1 + [0]
              [0 0]      [0]
                            
  [c_1](x1) = [0]           
              [0]           

The order satisfies the following ordering constraints:

  [a^#(b(x))] = [4]                
                [0]                
              > [0]                
                [0]                
              = [c_1(a^#(c(b(x))))]
                                   

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: { a^#(b(x)) -> c_1(a^#(c(b(x)))) }
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.

{ a^#(b(x)) -> c_1(a^#(c(b(x)))) }

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(1))