* Step 1: DependencyPairs WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: p(0()) -> g(0()) - Signature: {p/1} / {0/0,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {p} and constructors {0,g} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs p#(0()) -> c_1() Weak DPs and mark the set of starting terms. * Step 2: UsableRules WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: p#(0()) -> c_1() - Weak TRS: p(0()) -> g(0()) - Signature: {p/1,p#/1} / {0/0,g/1,c_1/0} - Obligation: innermost runtime complexity wrt. defined symbols {p#} and constructors {0,g} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: p#(0()) -> c_1() * Step 3: Trivial WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: p#(0()) -> c_1() - Signature: {p/1,p#/1} / {0/0,g/1,c_1/0} - Obligation: innermost runtime complexity wrt. defined symbols {p#} and constructors {0,g} + Applied Processor: Trivial + Details: Consider the dependency graph 1:S:p#(0()) -> c_1() The dependency graph contains no loops, we remove all dependency pairs. * Step 4: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Signature: {p/1,p#/1} / {0/0,g/1,c_1/0} - Obligation: innermost runtime complexity wrt. defined symbols {p#} and constructors {0,g} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(1))