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