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

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

Strict Trs:
  { h(x, c(y, z), t(w)) -> h(c(s(y), x), z, t(c(t(w), w)))
  , h(c(x, y), c(s(z), z), t(w)) ->
    h(z, c(y, x), t(t(c(x, c(y, t(w))))))
  , h(c(s(x), c(s(0()), y)), z, t(x)) ->
    h(y, c(s(0()), c(x, z)), t(t(c(x, s(x)))))
  , t(x) -> x
  , t(x) -> c(0(), c(0(), c(0(), c(0(), c(0(), x)))))
  , t(t(x)) -> t(c(t(x), x)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(1))

Arguments of following rules are not normal-forms:

{ h(x, c(y, z), t(w)) -> h(c(s(y), x), z, t(c(t(w), w)))
, h(c(x, y), c(s(z), z), t(w)) ->
  h(z, c(y, x), t(t(c(x, c(y, t(w))))))
, h(c(s(x), c(s(0()), y)), z, t(x)) ->
  h(y, c(s(0()), c(x, z)), t(t(c(x, s(x)))))
, t(t(x)) -> t(c(t(x), x)) }

All above mentioned rules can be savely removed.

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

Strict Trs:
  { t(x) -> x
  , t(x) -> c(0(), c(0(), c(0(), c(0(), c(0(), x))))) }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(1))

We add the following innermost weak dependency pairs:

Strict DPs:
  { t^#(x) -> c_1()
  , t^#(x) -> c_2() }

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:
  { t^#(x) -> c_1()
  , t^#(x) -> c_2() }
Strict Trs:
  { t(x) -> x
  , t(x) -> c(0(), c(0(), c(0(), c(0(), c(0(), 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:
  { t^#(x) -> c_1()
  , t^#(x) -> c_2() }
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.

  [t^#](x1) = [2]
              [2]
                 
      [c_1] = [1]
              [2]
                 
      [c_2] = [1]
              [1]

The following symbols are considered usable

  {t^#}

The order satisfies the following ordering constraints:

  [t^#(x)] = [2]    
             [2]    
           > [1]    
             [2]    
           = [c_1()]
                    
  [t^#(x)] = [2]    
             [2]    
           > [1]    
             [1]    
           = [c_2()]
                    

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:
  { t^#(x) -> c_1()
  , t^#(x) -> c_2() }
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.

{ t^#(x) -> c_1()
, t^#(x) -> c_2() }

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))