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