* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: add0(x,0()) -> x add0(x',S(x)) -> +(S(0()),add0(x',x)) mult(x,0()) -> 0() mult(x',S(x)) -> add0(x',mult(x',x)) power(x,0()) -> S(0()) power(x',S(x)) -> mult(x',power(x',x)) - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) - Signature: {+/2,add0/2,mult/2,power/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,add0,mult,power} and constructors {0,S} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: add0(x,0()) -> x add0(x',S(x)) -> +(S(0()),add0(x',x)) mult(x,0()) -> 0() mult(x',S(x)) -> add0(x',mult(x',x)) power(x,0()) -> S(0()) power(x',S(x)) -> mult(x',power(x',x)) - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) - Signature: {+/2,add0/2,mult/2,power/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,add0,mult,power} and constructors {0,S} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: add0(x,y){y -> S(y)} = add0(x,S(y)) ->^+ +(S(0()),add0(x,y)) = C[add0(x,y) = add0(x,y){}] WORST_CASE(Omega(n^1),?)