* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: if(false(),x,y,z,u) -> if2(le(y,s(u)),x,y,s(z),s(u)) if(true(),x,y,z,u) -> u if2(false(),x,y,z,u) -> modIter(x,y,z,u) if2(true(),x,y,z,u) -> modIter(x,y,z,0()) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) mod(x,0()) -> modZeroErro() mod(x,s(y)) -> modIter(x,s(y),0(),0()) modIter(x,s(y),z,u) -> if(le(x,z),x,s(y),z,u) - Signature: {if/5,if2/5,le/2,mod/2,modIter/4} / {0/0,false/0,modZeroErro/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {if,if2,le,mod,modIter} and constructors {0,false ,modZeroErro,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: if(false(),x,y,z,u) -> if2(le(y,s(u)),x,y,s(z),s(u)) if(true(),x,y,z,u) -> u if2(false(),x,y,z,u) -> modIter(x,y,z,u) if2(true(),x,y,z,u) -> modIter(x,y,z,0()) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) mod(x,0()) -> modZeroErro() mod(x,s(y)) -> modIter(x,s(y),0(),0()) modIter(x,s(y),z,u) -> if(le(x,z),x,s(y),z,u) - Signature: {if/5,if2/5,le/2,mod/2,modIter/4} / {0/0,false/0,modZeroErro/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {if,if2,le,mod,modIter} and constructors {0,false ,modZeroErro,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: le(x,y){x -> s(x),y -> s(y)} = le(s(x),s(y)) ->^+ le(x,y) = C[le(x,y) = le(x,y){}] WORST_CASE(Omega(n^1),?)