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