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