MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { minus(x, y) -> cond(gt(x, y), x, y)
  , cond(false(), x, y) -> 0()
  , cond(true(), x, y) -> s(minus(x, s(y)))
  , gt(0(), v) -> false()
  , gt(s(u), 0()) -> true()
  , gt(s(u), s(v)) -> gt(u, v) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { minus^#(x, y) -> c_1(cond^#(gt(x, y), x, y), gt^#(x, y))
  , cond^#(false(), x, y) -> c_2()
  , cond^#(true(), x, y) -> c_3(minus^#(x, s(y)))
  , gt^#(0(), v) -> c_4()
  , gt^#(s(u), 0()) -> c_5()
  , gt^#(s(u), s(v)) -> c_6(gt^#(u, v)) }

and mark the set of starting terms.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { minus^#(x, y) -> c_1(cond^#(gt(x, y), x, y), gt^#(x, y))
  , cond^#(false(), x, y) -> c_2()
  , cond^#(true(), x, y) -> c_3(minus^#(x, s(y)))
  , gt^#(0(), v) -> c_4()
  , gt^#(s(u), 0()) -> c_5()
  , gt^#(s(u), s(v)) -> c_6(gt^#(u, v)) }
Weak Trs:
  { minus(x, y) -> cond(gt(x, y), x, y)
  , cond(false(), x, y) -> 0()
  , cond(true(), x, y) -> s(minus(x, s(y)))
  , gt(0(), v) -> false()
  , gt(s(u), 0()) -> true()
  , gt(s(u), s(v)) -> gt(u, v) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {2,4,5} by applications of
Pre({2,4,5}) = {1,6}. Here rules are labeled as follows:

  DPs:
    { 1: minus^#(x, y) -> c_1(cond^#(gt(x, y), x, y), gt^#(x, y))
    , 2: cond^#(false(), x, y) -> c_2()
    , 3: cond^#(true(), x, y) -> c_3(minus^#(x, s(y)))
    , 4: gt^#(0(), v) -> c_4()
    , 5: gt^#(s(u), 0()) -> c_5()
    , 6: gt^#(s(u), s(v)) -> c_6(gt^#(u, v)) }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { minus^#(x, y) -> c_1(cond^#(gt(x, y), x, y), gt^#(x, y))
  , cond^#(true(), x, y) -> c_3(minus^#(x, s(y)))
  , gt^#(s(u), s(v)) -> c_6(gt^#(u, v)) }
Weak DPs:
  { cond^#(false(), x, y) -> c_2()
  , gt^#(0(), v) -> c_4()
  , gt^#(s(u), 0()) -> c_5() }
Weak Trs:
  { minus(x, y) -> cond(gt(x, y), x, y)
  , cond(false(), x, y) -> 0()
  , cond(true(), x, y) -> s(minus(x, s(y)))
  , gt(0(), v) -> false()
  , gt(s(u), 0()) -> true()
  , gt(s(u), s(v)) -> gt(u, v) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

{ cond^#(false(), x, y) -> c_2()
, gt^#(0(), v) -> c_4()
, gt^#(s(u), 0()) -> c_5() }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { minus^#(x, y) -> c_1(cond^#(gt(x, y), x, y), gt^#(x, y))
  , cond^#(true(), x, y) -> c_3(minus^#(x, s(y)))
  , gt^#(s(u), s(v)) -> c_6(gt^#(u, v)) }
Weak Trs:
  { minus(x, y) -> cond(gt(x, y), x, y)
  , cond(false(), x, y) -> 0()
  , cond(true(), x, y) -> s(minus(x, s(y)))
  , gt(0(), v) -> false()
  , gt(s(u), 0()) -> true()
  , gt(s(u), s(v)) -> gt(u, v) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { gt(0(), v) -> false()
    , gt(s(u), 0()) -> true()
    , gt(s(u), s(v)) -> gt(u, v) }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { minus^#(x, y) -> c_1(cond^#(gt(x, y), x, y), gt^#(x, y))
  , cond^#(true(), x, y) -> c_3(minus^#(x, s(y)))
  , gt^#(s(u), s(v)) -> c_6(gt^#(u, v)) }
Weak Trs:
  { gt(0(), v) -> false()
  , gt(s(u), 0()) -> true()
  , gt(s(u), s(v)) -> gt(u, v) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..