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