* Step 1: Sum WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__f(X)) -> f(X) f(X) -> if(X,c(),n__f(true())) f(X) -> n__f(X) if(false(),X,Y) -> activate(Y) if(true(),X,Y) -> X - Signature: {activate/1,f/1,if/3} / {c/0,false/0,n__f/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,if} and constructors {c,false,n__f,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__f(X)) -> f(X) f(X) -> if(X,c(),n__f(true())) f(X) -> n__f(X) if(false(),X,Y) -> activate(Y) if(true(),X,Y) -> X - Signature: {activate/1,f/1,if/3} / {c/0,false/0,n__f/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,if} and constructors {c,false,n__f,true} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 3. The enriched problem is compatible with follwoing automaton. activate_0(2) -> 1 activate_1(2) -> 1 activate_1(4) -> 1 activate_1(7) -> 1 c_0() -> 1 c_0() -> 2 c_1() -> 1 c_1() -> 3 c_2() -> 1 c_2() -> 6 c_3() -> 1 c_3() -> 9 f_0(2) -> 1 f_1(2) -> 1 f_2(5) -> 1 f_2(8) -> 1 false_0() -> 1 false_0() -> 2 if_0(2,2,2) -> 1 if_1(2,3,4) -> 1 if_2(2,6,7) -> 1 if_3(5,9,10) -> 1 if_3(8,9,10) -> 1 n__f_0(2) -> 1 n__f_0(2) -> 2 n__f_1(2) -> 1 n__f_1(5) -> 1 n__f_1(5) -> 4 n__f_2(2) -> 1 n__f_2(8) -> 1 n__f_2(8) -> 7 n__f_3(5) -> 1 n__f_3(8) -> 1 n__f_3(11) -> 10 true_0() -> 1 true_0() -> 2 true_1() -> 5 true_2() -> 8 true_3() -> 11 2 -> 1 3 -> 1 4 -> 1 6 -> 1 7 -> 1 9 -> 1 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: activate(X) -> X activate(n__f(X)) -> f(X) f(X) -> if(X,c(),n__f(true())) f(X) -> n__f(X) if(false(),X,Y) -> activate(Y) if(true(),X,Y) -> X - Signature: {activate/1,f/1,if/3} / {c/0,false/0,n__f/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,if} and constructors {c,false,n__f,true} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))