* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: function(if(),false(),x,y) -> function(plus(),function(third(),x,y,y),function(p(),x,x,y),s(y)) function(if(),true(),x,y) -> y function(iszero(),0(),dummy,dummy2) -> true() function(iszero(),s(x),dummy,dummy2) -> false() function(p(),0(),dummy,dummy2) -> 0() function(p(),s(0()),dummy,dummy2) -> 0() function(p(),s(s(x)),dummy,dummy2) -> s(function(p(),s(x),x,x)) function(plus(),dummy,x,y) -> function(if(),function(iszero(),x,x,x),x,y) function(third(),x,y,z) -> z - Signature: {function/4} / {0/0,false/0,if/0,iszero/0,p/0,plus/0,s/1,third/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {function} and constructors {0,false,if,iszero,p,plus,s ,third,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: function(if(),false(),x,y) -> function(plus(),function(third(),x,y,y),function(p(),x,x,y),s(y)) function(if(),true(),x,y) -> y function(iszero(),0(),dummy,dummy2) -> true() function(iszero(),s(x),dummy,dummy2) -> false() function(p(),0(),dummy,dummy2) -> 0() function(p(),s(0()),dummy,dummy2) -> 0() function(p(),s(s(x)),dummy,dummy2) -> s(function(p(),s(x),x,x)) function(plus(),dummy,x,y) -> function(if(),function(iszero(),x,x,x),x,y) function(third(),x,y,z) -> z - Signature: {function/4} / {0/0,false/0,if/0,iszero/0,p/0,plus/0,s/1,third/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {function} and constructors {0,false,if,iszero,p,plus,s ,third,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: function(p(),s(x),y,z){x -> s(x)} = function(p(),s(s(x)),y,z) ->^+ s(function(p(),s(x),x,x)) = C[function(p(),s(x),x,x) = function(p(),s(x),y,z){y -> x,z -> x}] WORST_CASE(Omega(n^1),?)