* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: cond(y,x,y) -> s(minus(x,s(y))) min(u,0()) -> 0() min(0(),v) -> 0() min(s(u),s(v)) -> s(min(u,v)) minus(x,y) -> cond(min(x,y),x,y) - Signature: {cond/3,min/2,minus/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {cond,min,minus} and constructors {0,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: cond(y,x,y) -> s(minus(x,s(y))) min(u,0()) -> 0() min(0(),v) -> 0() min(s(u),s(v)) -> s(min(u,v)) minus(x,y) -> cond(min(x,y),x,y) - Signature: {cond/3,min/2,minus/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {cond,min,minus} and constructors {0,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: min(x,y){x -> s(x),y -> s(y)} = min(s(x),s(y)) ->^+ s(min(x,y)) = C[min(x,y) = min(x,y){}] WORST_CASE(Omega(n^1),?)