* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(0(),0(),0(),0(),0()) -> 0() f(0(),0(),0(),0(),s(x5)) -> f(x5,x5,x5,x5,x5) f(0(),0(),0(),s(x4),x5) -> f(x4,x4,x4,x4,x5) f(0(),0(),s(x3),x4,x5) -> f(x3,x3,x3,x4,x5) f(0(),s(x2),x3,x4,x5) -> f(x2,x2,x3,x4,x5) f(s(x1),x2,x3,x4,x5) -> f(x1,x2,x3,x4,x5) - Signature: {f/5} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {0,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(0(),0(),0(),0(),0()) -> 0() f(0(),0(),0(),0(),s(x5)) -> f(x5,x5,x5,x5,x5) f(0(),0(),0(),s(x4),x5) -> f(x4,x4,x4,x4,x5) f(0(),0(),s(x3),x4,x5) -> f(x3,x3,x3,x4,x5) f(0(),s(x2),x3,x4,x5) -> f(x2,x2,x3,x4,x5) f(s(x1),x2,x3,x4,x5) -> f(x1,x2,x3,x4,x5) - Signature: {f/5} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {0,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x,y,z,u,v){x -> s(x)} = f(s(x),y,z,u,v) ->^+ f(x,y,z,u,v) = C[f(x,y,z,u,v) = f(x,y,z,u,v){}] WORST_CASE(Omega(n^1),?)