* Step 1: Sum WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: f(s(X),Y) -> h(s(f(h(Y),X))) - Signature: {f/2} / {h/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {h,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DependencyPairs WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: f(s(X),Y) -> h(s(f(h(Y),X))) - Signature: {f/2} / {h/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {h,s} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs f#(s(X),Y) -> c_1(f#(h(Y),X)) Weak DPs and mark the set of starting terms. * Step 3: UsableRules WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: f#(s(X),Y) -> c_1(f#(h(Y),X)) - Weak TRS: f(s(X),Y) -> h(s(f(h(Y),X))) - Signature: {f/2,f#/2} / {h/1,s/1,c_1/1} - Obligation: innermost runtime complexity wrt. defined symbols {f#} and constructors {h,s} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: f#(s(X),Y) -> c_1(f#(h(Y),X)) * Step 4: Trivial WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: f#(s(X),Y) -> c_1(f#(h(Y),X)) - Signature: {f/2,f#/2} / {h/1,s/1,c_1/1} - Obligation: innermost runtime complexity wrt. defined symbols {f#} and constructors {h,s} + Applied Processor: Trivial + Details: Consider the dependency graph 1:S:f#(s(X),Y) -> c_1(f#(h(Y),X)) The dependency graph contains no loops, we remove all dependency pairs. * Step 5: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Signature: {f/2,f#/2} / {h/1,s/1,c_1/1} - Obligation: innermost runtime complexity wrt. defined symbols {f#} and constructors {h,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(1))