* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: 10() -> s(s(s(s(s(s(s(s(s(s(0())))))))))) gen(x) -> if1(le(x,10()),x) if1(false(),x) -> nil() if1(true(),x) -> if2(x,x) if2(x,y) -> if3(le(y,10()),x,y) if3(false(),x,y) -> gen(s(x)) if3(true(),x,y) -> cons(entry(x,y,times(x,y)),if2(x,s(y))) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) table() -> gen(s(0())) times(0(),y) -> 0() times(s(x),y) -> plus(y,times(x,y)) - Signature: {10/0,gen/1,if1/2,if2/2,if3/3,le/2,plus/2,table/0,times/2} / {0/0,cons/2,entry/3,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {10,gen,if1,if2,if3,le,plus,table ,times} and constructors {0,cons,entry,false,nil,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: 10() -> s(s(s(s(s(s(s(s(s(s(0())))))))))) gen(x) -> if1(le(x,10()),x) if1(false(),x) -> nil() if1(true(),x) -> if2(x,x) if2(x,y) -> if3(le(y,10()),x,y) if3(false(),x,y) -> gen(s(x)) if3(true(),x,y) -> cons(entry(x,y,times(x,y)),if2(x,s(y))) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) table() -> gen(s(0())) times(0(),y) -> 0() times(s(x),y) -> plus(y,times(x,y)) - Signature: {10/0,gen/1,if1/2,if2/2,if3/3,le/2,plus/2,table/0,times/2} / {0/0,cons/2,entry/3,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {10,gen,if1,if2,if3,le,plus,table ,times} and constructors {0,cons,entry,false,nil,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),?)