WORST_CASE(?,O(1)) * Step 1: 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 2: PredecessorEstimation 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: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {1} by application of Pre({1}) = {}. Here rules are labelled as follows: 1: f#(s(X),Y) -> c_1(f#(h(Y),X)) * Step 3: RemoveWeakSuffixes WORST_CASE(?,O(1)) + Considered Problem: - Weak 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: RemoveWeakSuffixes + Details: Consider the dependency graph 1:W:f#(s(X),Y) -> c_1(f#(h(Y),X)) The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. 1: f#(s(X),Y) -> c_1(f#(h(Y),X)) * Step 4: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - 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: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(1))