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