WORST_CASE(Omega(n^1),?) * Step 1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__C() -> c4() A__C() -> c5() A__C() -> c6() A__F(z0,z1,z2) -> c3() A__F(a(),b(),z0) -> c1(A__F(mark(z0),z0,mark(z0)),MARK(z0)) A__F(a(),b(),z0) -> c2(A__F(mark(z0),z0,mark(z0)),MARK(z0)) MARK(a()) -> c10() MARK(b()) -> c11() MARK(c()) -> c9(A__C()) MARK(f(z0,z1,z2)) -> c7(A__F(mark(z0),z1,mark(z2)),MARK(z0)) MARK(f(z0,z1,z2)) -> c8(A__F(mark(z0),z1,mark(z2)),MARK(z2)) - Weak TRS: a__c() -> a() a__c() -> b() a__c() -> c() a__f(z0,z1,z2) -> f(z0,z1,z2) a__f(a(),b(),z0) -> a__f(mark(z0),z0,mark(z0)) mark(a()) -> a() mark(b()) -> b() mark(c()) -> a__c() mark(f(z0,z1,z2)) -> a__f(mark(z0),z1,mark(z2)) - Signature: {A__C/0,A__F/3,MARK/1,a__c/0,a__f/3,mark/1} / {a/0,b/0,c/0,c1/2,c10/0,c11/0,c2/2,c3/0,c4/0,c5/0,c6/0,c7/2 ,c8/2,c9/1,f/3} - Obligation: innermost runtime complexity wrt. defined symbols {A__C,A__F,MARK,a__c,a__f,mark} and constructors {a,b,c,c1 ,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,f} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__C() -> c4() A__C() -> c5() A__C() -> c6() A__F(z0,z1,z2) -> c3() A__F(a(),b(),z0) -> c1(A__F(mark(z0),z0,mark(z0)),MARK(z0)) A__F(a(),b(),z0) -> c2(A__F(mark(z0),z0,mark(z0)),MARK(z0)) MARK(a()) -> c10() MARK(b()) -> c11() MARK(c()) -> c9(A__C()) MARK(f(z0,z1,z2)) -> c7(A__F(mark(z0),z1,mark(z2)),MARK(z0)) MARK(f(z0,z1,z2)) -> c8(A__F(mark(z0),z1,mark(z2)),MARK(z2)) - Weak TRS: a__c() -> a() a__c() -> b() a__c() -> c() a__f(z0,z1,z2) -> f(z0,z1,z2) a__f(a(),b(),z0) -> a__f(mark(z0),z0,mark(z0)) mark(a()) -> a() mark(b()) -> b() mark(c()) -> a__c() mark(f(z0,z1,z2)) -> a__f(mark(z0),z1,mark(z2)) - Signature: {A__C/0,A__F/3,MARK/1,a__c/0,a__f/3,mark/1} / {a/0,b/0,c/0,c1/2,c10/0,c11/0,c2/2,c3/0,c4/0,c5/0,c6/0,c7/2 ,c8/2,c9/1,f/3} - Obligation: innermost runtime complexity wrt. defined symbols {A__C,A__F,MARK,a__c,a__f,mark} and constructors {a,b,c,c1 ,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,f} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__C() -> c4() A__C() -> c5() A__C() -> c6() A__F(z0,z1,z2) -> c3() A__F(a(),b(),z0) -> c1(A__F(mark(z0),z0,mark(z0)),MARK(z0)) A__F(a(),b(),z0) -> c2(A__F(mark(z0),z0,mark(z0)),MARK(z0)) MARK(a()) -> c10() MARK(b()) -> c11() MARK(c()) -> c9(A__C()) MARK(f(z0,z1,z2)) -> c7(A__F(mark(z0),z1,mark(z2)),MARK(z0)) MARK(f(z0,z1,z2)) -> c8(A__F(mark(z0),z1,mark(z2)),MARK(z2)) - Weak TRS: a__c() -> a() a__c() -> b() a__c() -> c() a__f(z0,z1,z2) -> f(z0,z1,z2) a__f(a(),b(),z0) -> a__f(mark(z0),z0,mark(z0)) mark(a()) -> a() mark(b()) -> b() mark(c()) -> a__c() mark(f(z0,z1,z2)) -> a__f(mark(z0),z1,mark(z2)) - Signature: {A__C/0,A__F/3,MARK/1,a__c/0,a__f/3,mark/1} / {a/0,b/0,c/0,c1/2,c10/0,c11/0,c2/2,c3/0,c4/0,c5/0,c6/0,c7/2 ,c8/2,c9/1,f/3} - Obligation: innermost runtime complexity wrt. defined symbols {A__C,A__F,MARK,a__c,a__f,mark} and constructors {a,b,c,c1 ,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,f} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: MARK(x){x -> f(x,y,z)} = MARK(f(x,y,z)) ->^+ c7(A__F(mark(x),y,mark(z)),MARK(x)) = C[MARK(x) = MARK(x){}] WORST_CASE(Omega(n^1),?)