* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: r1(cons(x,k),a) -> r1(k,cons(x,a)) r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: r1(cons(x,k),a) -> r1(k,cons(x,a)) r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: r1(y,z){y -> cons(x,y)} = r1(cons(x,y),z) ->^+ r1(y,cons(x,z)) = C[r1(y,cons(x,z)) = r1(y,z){z -> cons(x,z)}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: r1(cons(x,k),a) -> r1(k,cons(x,a)) r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. cons_0(2,2) -> 1 cons_0(2,2) -> 2 cons_1(2,2) -> 1 cons_1(2,2) -> 3 cons_1(2,3) -> 1 cons_1(2,3) -> 3 empty_0() -> 1 empty_0() -> 2 empty_1() -> 1 empty_1() -> 3 r1_0(2,2) -> 1 r1_1(2,3) -> 1 rev_0(2) -> 1 2 -> 1 3 -> 1 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: r1(cons(x,k),a) -> r1(k,cons(x,a)) r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))