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