* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: average(x,y) -> if(le(x,0()),le(y,0()),le(y,s(0())),le(y,s(s(0()))),x,y) if(false(),b1,b2,b3,x,y) -> average(p(x),s(y)) if(true(),b1,b2,b3,x,y) -> if2(b1,b2,b3,x,y) if2(false(),b2,b3,x,y) -> if3(b2,b3,x,y) if2(true(),b2,b3,x,y) -> 0() if3(false(),b3,x,y) -> if4(b3,x,y) if3(true(),b3,x,y) -> 0() if4(false(),x,y) -> average(s(x),p(p(y))) if4(true(),x,y) -> s(0()) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) p(0()) -> 0() p(s(x)) -> x - Signature: {average/2,if/6,if2/5,if3/4,if4/3,le/2,p/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {average,if,if2,if3,if4,le,p} and constructors {0,false,s ,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: average(x,y) -> if(le(x,0()),le(y,0()),le(y,s(0())),le(y,s(s(0()))),x,y) if(false(),b1,b2,b3,x,y) -> average(p(x),s(y)) if(true(),b1,b2,b3,x,y) -> if2(b1,b2,b3,x,y) if2(false(),b2,b3,x,y) -> if3(b2,b3,x,y) if2(true(),b2,b3,x,y) -> 0() if3(false(),b3,x,y) -> if4(b3,x,y) if3(true(),b3,x,y) -> 0() if4(false(),x,y) -> average(s(x),p(p(y))) if4(true(),x,y) -> s(0()) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) p(0()) -> 0() p(s(x)) -> x - Signature: {average/2,if/6,if2/5,if3/4,if4/3,le/2,p/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {average,if,if2,if3,if4,le,p} and constructors {0,false,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),?)