* Step 1: DependencyPairs WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) - Signature: {t/1} / {0/0,c/2} - Obligation: innermost runtime complexity wrt. defined symbols {t} and constructors {0,c} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs t#(x) -> c_1() t#(x) -> c_2() Weak DPs and mark the set of starting terms. * Step 2: UsableRules WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: t#(x) -> c_1() t#(x) -> c_2() - Weak TRS: t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) - Signature: {t/1,t#/1} / {0/0,c/2,c_1/0,c_2/0} - Obligation: innermost runtime complexity wrt. defined symbols {t#} and constructors {0,c} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: t#(x) -> c_1() t#(x) -> c_2() * Step 3: Trivial WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: t#(x) -> c_1() t#(x) -> c_2() - Signature: {t/1,t#/1} / {0/0,c/2,c_1/0,c_2/0} - Obligation: innermost runtime complexity wrt. defined symbols {t#} and constructors {0,c} + Applied Processor: Trivial + Details: Consider the dependency graph 1:S:t#(x) -> c_1() 2:S:t#(x) -> c_2() The dependency graph contains no loops, we remove all dependency pairs. * Step 4: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Signature: {t/1,t#/1} / {0/0,c/2,c_1/0,c_2/0} - Obligation: innermost runtime complexity wrt. defined symbols {t#} and constructors {0,c} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(1))