MAYBE

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

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

We add following dependency tuples:

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

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^#(min(x, y), x, y), min^#(x, y))
  , cond^#(y, x, y) -> c_2(minus^#(x, s(y)))
  , min^#(u, 0()) -> c_3()
  , min^#(s(u), s(v)) -> c_4(min^#(u, v))
  , min^#(0(), v) -> c_5() }
Weak Trs:
  { minus(x, y) -> cond(min(x, y), x, y)
  , cond(y, x, y) -> s(minus(x, s(y)))
  , min(u, 0()) -> 0()
  , min(s(u), s(v)) -> s(min(u, v))
  , min(0(), v) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {3,5} by applications of
Pre({3,5}) = {1,4}. Here rules are labeled as follows:

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

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

Strict DPs:
  { minus^#(x, y) -> c_1(cond^#(min(x, y), x, y), min^#(x, y))
  , cond^#(y, x, y) -> c_2(minus^#(x, s(y)))
  , min^#(s(u), s(v)) -> c_4(min^#(u, v)) }
Weak DPs:
  { min^#(u, 0()) -> c_3()
  , min^#(0(), v) -> c_5() }
Weak Trs:
  { minus(x, y) -> cond(min(x, y), x, y)
  , cond(y, x, y) -> s(minus(x, s(y)))
  , min(u, 0()) -> 0()
  , min(s(u), s(v)) -> s(min(u, v))
  , min(0(), v) -> 0() }
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.

{ min^#(u, 0()) -> c_3()
, min^#(0(), v) -> c_5() }

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

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

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { min(u, 0()) -> 0()
    , min(s(u), s(v)) -> s(min(u, v))
    , min(0(), v) -> 0() }

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

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

The input cannot be shown compatible

Arrrr..