MAYBE * Step 1: InnermostRuleRemoval MAYBE + Considered Problem: - Strict TRS: b() -> c() f() -> f() g(b()) -> c() - Signature: {b/0,f/0,g/1} / {c/0} - Obligation: innermost runtime complexity wrt. defined symbols {b,f,g} and constructors {c} + Applied Processor: InnermostRuleRemoval + Details: Arguments of following rules are not normal-forms. g(b()) -> c() All above mentioned rules can be savely removed. * Step 2: DependencyPairs MAYBE + Considered Problem: - Strict TRS: b() -> c() f() -> f() - Signature: {b/0,f/0,g/1} / {c/0} - Obligation: innermost runtime complexity wrt. defined symbols {b,f,g} and constructors {c} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs b#() -> c_1() f#() -> c_2(f#()) Weak DPs and mark the set of starting terms. * Step 3: UsableRules MAYBE + Considered Problem: - Strict DPs: b#() -> c_1() f#() -> c_2(f#()) - Weak TRS: b() -> c() f() -> f() - Signature: {b/0,f/0,g/1,b#/0,f#/0,g#/1} / {c/0,c_1/0,c_2/1} - Obligation: innermost runtime complexity wrt. defined symbols {b#,f#,g#} and constructors {c} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: b#() -> c_1() f#() -> c_2(f#()) * Step 4: PredecessorEstimation MAYBE + Considered Problem: - Strict DPs: b#() -> c_1() f#() -> c_2(f#()) - Signature: {b/0,f/0,g/1,b#/0,f#/0,g#/1} / {c/0,c_1/0,c_2/1} - Obligation: innermost runtime complexity wrt. defined symbols {b#,f#,g#} and constructors {c} + 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: b#() -> c_1() 2: f#() -> c_2(f#()) * Step 5: RemoveWeakSuffixes MAYBE + Considered Problem: - Strict DPs: f#() -> c_2(f#()) - Weak DPs: b#() -> c_1() - Signature: {b/0,f/0,g/1,b#/0,f#/0,g#/1} / {c/0,c_1/0,c_2/1} - Obligation: innermost runtime complexity wrt. defined symbols {b#,f#,g#} and constructors {c} + Applied Processor: RemoveWeakSuffixes + Details: Consider the dependency graph 1:S:f#() -> c_2(f#()) -->_1 f#() -> c_2(f#()):1 2:W:b#() -> c_1() The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. 2: b#() -> c_1() * Step 6: Failure MAYBE + Considered Problem: - Strict DPs: f#() -> c_2(f#()) - Signature: {b/0,f/0,g/1,b#/0,f#/0,g#/1} / {c/0,c_1/0,c_2/1} - Obligation: innermost runtime complexity wrt. defined symbols {b#,f#,g#} and constructors {c} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE