* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__A() -> A() a__A() -> a__h(a__f(a__a()),a__f(a__b())) a__a() -> a() a__a() -> a__c() a__a() -> a__d() a__b() -> a__c() a__b() -> a__d() a__b() -> b() a__c() -> c() a__c() -> e() a__c() -> l() a__d() -> d() a__d() -> m() a__f(X) -> a__z(mark(X),X) a__f(X) -> f(X) a__g(X1,X2,X3) -> g(X1,X2,X3) a__g(d(),X,X) -> a__A() a__h(X,X) -> a__g(mark(X),mark(X),a__f(a__k())) a__h(X1,X2) -> h(X1,X2) a__k() -> k() a__k() -> l() a__k() -> m() a__z(X1,X2) -> z(X1,X2) a__z(e(),X) -> mark(X) mark(A()) -> a__A() mark(a()) -> a__a() mark(b()) -> a__b() mark(c()) -> a__c() mark(d()) -> a__d() mark(e()) -> e() mark(f(X)) -> a__f(mark(X)) mark(g(X1,X2,X3)) -> a__g(mark(X1),mark(X2),mark(X3)) mark(h(X1,X2)) -> a__h(mark(X1),mark(X2)) mark(k()) -> a__k() mark(l()) -> l() mark(m()) -> m() mark(z(X1,X2)) -> a__z(mark(X1),X2) - Signature: {a__A/0,a__a/0,a__b/0,a__c/0,a__d/0,a__f/1,a__g/3,a__h/2,a__k/0,a__z/2,mark/1} / {A/0,a/0,b/0,c/0,d/0,e/0 ,f/1,g/3,h/2,k/0,l/0,m/0,z/2} - Obligation: innermost runtime complexity wrt. defined symbols {a__A,a__a,a__b,a__c,a__d,a__f,a__g,a__h,a__k,a__z ,mark} and constructors {A,a,b,c,d,e,f,g,h,k,l,m,z} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__A() -> A() a__A() -> a__h(a__f(a__a()),a__f(a__b())) a__a() -> a() a__a() -> a__c() a__a() -> a__d() a__b() -> a__c() a__b() -> a__d() a__b() -> b() a__c() -> c() a__c() -> e() a__c() -> l() a__d() -> d() a__d() -> m() a__f(X) -> a__z(mark(X),X) a__f(X) -> f(X) a__g(X1,X2,X3) -> g(X1,X2,X3) a__g(d(),X,X) -> a__A() a__h(X,X) -> a__g(mark(X),mark(X),a__f(a__k())) a__h(X1,X2) -> h(X1,X2) a__k() -> k() a__k() -> l() a__k() -> m() a__z(X1,X2) -> z(X1,X2) a__z(e(),X) -> mark(X) mark(A()) -> a__A() mark(a()) -> a__a() mark(b()) -> a__b() mark(c()) -> a__c() mark(d()) -> a__d() mark(e()) -> e() mark(f(X)) -> a__f(mark(X)) mark(g(X1,X2,X3)) -> a__g(mark(X1),mark(X2),mark(X3)) mark(h(X1,X2)) -> a__h(mark(X1),mark(X2)) mark(k()) -> a__k() mark(l()) -> l() mark(m()) -> m() mark(z(X1,X2)) -> a__z(mark(X1),X2) - Signature: {a__A/0,a__a/0,a__b/0,a__c/0,a__d/0,a__f/1,a__g/3,a__h/2,a__k/0,a__z/2,mark/1} / {A/0,a/0,b/0,c/0,d/0,e/0 ,f/1,g/3,h/2,k/0,l/0,m/0,z/2} - Obligation: innermost runtime complexity wrt. defined symbols {a__A,a__a,a__b,a__c,a__d,a__f,a__g,a__h,a__k,a__z ,mark} and constructors {A,a,b,c,d,e,f,g,h,k,l,m,z} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: mark(x){x -> f(x)} = mark(f(x)) ->^+ a__f(mark(x)) = C[mark(x) = mark(x){}] WORST_CASE(Omega(n^1),?)