* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: concat(cons(u,v),y) -> cons(u,concat(v,y)) concat(leaf(),y) -> y if1(b,false(),u,v) -> if2(b,u,v) if1(b,true(),u,v) -> false() if2(false(),u,v) -> less_leaves(concat(left(u),right(u)),concat(left(v),right(v))) if2(true(),u,v) -> true() isLeaf(cons(u,v)) -> false() isLeaf(leaf()) -> true() left(cons(u,v)) -> u less_leaves(u,v) -> if1(isLeaf(u),isLeaf(v),u,v) right(cons(u,v)) -> v - Signature: {concat/2,if1/4,if2/3,isLeaf/1,left/1,less_leaves/2,right/1} / {cons/2,false/0,leaf/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {concat,if1,if2,isLeaf,left,less_leaves ,right} and constructors {cons,false,leaf,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: concat(cons(u,v),y) -> cons(u,concat(v,y)) concat(leaf(),y) -> y if1(b,false(),u,v) -> if2(b,u,v) if1(b,true(),u,v) -> false() if2(false(),u,v) -> less_leaves(concat(left(u),right(u)),concat(left(v),right(v))) if2(true(),u,v) -> true() isLeaf(cons(u,v)) -> false() isLeaf(leaf()) -> true() left(cons(u,v)) -> u less_leaves(u,v) -> if1(isLeaf(u),isLeaf(v),u,v) right(cons(u,v)) -> v - Signature: {concat/2,if1/4,if2/3,isLeaf/1,left/1,less_leaves/2,right/1} / {cons/2,false/0,leaf/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {concat,if1,if2,isLeaf,left,less_leaves ,right} and constructors {cons,false,leaf,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: concat(y,z){y -> cons(x,y)} = concat(cons(x,y),z) ->^+ cons(x,concat(y,z)) = C[concat(y,z) = concat(y,z){}] WORST_CASE(Omega(n^1),?)