* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: f(a(),a()) -> f(a(),b()) f(a(),b()) -> f(s(a()),c()) f(c(),c()) -> f(a(),a()) f(s(X),c()) -> f(X,c()) - Signature: {f/2} / {a/0,b/0,c/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(a(),a()) -> f(a(),b()) f(a(),b()) -> f(s(a()),c()) f(c(),c()) -> f(a(),a()) f(s(X),c()) -> f(X,c()) - Signature: {f/2} / {a/0,b/0,c/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x,c()){x -> s(x)} = f(s(x),c()) ->^+ f(x,c()) = C[f(x,c()) = f(x,c()){}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(a(),a()) -> f(a(),b()) f(a(),b()) -> f(s(a()),c()) f(c(),c()) -> f(a(),a()) f(s(X),c()) -> f(X,c()) - Signature: {f/2} / {a/0,b/0,c/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c,s} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 4. The enriched problem is compatible with follwoing automaton. a_0() -> 1 a_1() -> 6 a_2() -> 10 a_3() -> 13 b_0() -> 2 b_1() -> 7 b_2() -> 12 c_0() -> 3 c_1() -> 7 c_2() -> 9 c_3() -> 11 c_4() -> 14 f_0(1,1) -> 4 f_0(1,2) -> 4 f_0(1,3) -> 4 f_0(1,5) -> 4 f_0(2,1) -> 4 f_0(2,2) -> 4 f_0(2,3) -> 4 f_0(2,5) -> 4 f_0(3,1) -> 4 f_0(3,2) -> 4 f_0(3,3) -> 4 f_0(3,5) -> 4 f_0(5,1) -> 4 f_0(5,2) -> 4 f_0(5,3) -> 4 f_0(5,5) -> 4 f_1(1,7) -> 4 f_1(2,7) -> 4 f_1(3,7) -> 4 f_1(5,7) -> 4 f_1(6,6) -> 4 f_1(6,7) -> 4 f_2(6,9) -> 4 f_2(8,9) -> 4 f_2(10,12) -> 4 f_3(10,11) -> 4 f_4(13,14) -> 4 s_0(1) -> 5 s_0(2) -> 5 s_0(3) -> 5 s_0(5) -> 5 s_1(6) -> 6 s_2(10) -> 8 s_3(13) -> 10 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(a(),a()) -> f(a(),b()) f(a(),b()) -> f(s(a()),c()) f(c(),c()) -> f(a(),a()) f(s(X),c()) -> f(X,c()) - Signature: {f/2} / {a/0,b/0,c/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))