MAYBE * Step 1: DependencyPairs MAYBE + Considered Problem: - Strict TRS: f(x) -> f(g(x)) - Signature: {f/1} / {g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs f#(x) -> c_1(f#(g(x))) Weak DPs and mark the set of starting terms. * Step 2: UsableRules MAYBE + Considered Problem: - Strict DPs: f#(x) -> c_1(f#(g(x))) - Weak TRS: f(x) -> f(g(x)) - Signature: {f/1,f#/1} / {g/1,c_1/1} - Obligation: innermost runtime complexity wrt. defined symbols {f#} and constructors {g} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: f#(x) -> c_1(f#(g(x))) * Step 3: Failure MAYBE + Considered Problem: - Strict DPs: f#(x) -> c_1(f#(g(x))) - Signature: {f/1,f#/1} / {g/1,c_1/1} - Obligation: innermost runtime complexity wrt. defined symbols {f#} and constructors {g} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE