* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: double(0()) -> 0() double(s(x)) -> s(s(double(x))) if(false(),x,y,z) -> loop(x,double(y),s(z)) if(true(),x,y,z) -> z le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) log(0()) -> logError() log(s(x)) -> loop(s(x),s(0()),0()) loop(x,s(y),z) -> if(le(x,s(y)),x,s(y),z) - Signature: {double/1,if/4,le/2,log/1,loop/3} / {0/0,false/0,logError/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {double,if,le,log,loop} and constructors {0,false,logError ,s,true} + 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))) if(false(),x,y,z) -> loop(x,double(y),s(z)) if(true(),x,y,z) -> z le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) log(0()) -> logError() log(s(x)) -> loop(s(x),s(0()),0()) loop(x,s(y),z) -> if(le(x,s(y)),x,s(y),z) - Signature: {double/1,if/4,le/2,log/1,loop/3} / {0/0,false/0,logError/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {double,if,le,log,loop} and constructors {0,false,logError ,s,true} + 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),?)