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