* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: count(n,x) -> if(isEmpty(n) ,isEmpty(left(n)) ,right(n) ,node(left(left(n)),node(right(left(n)),right(n))) ,x ,inc(x)) if(false(),false(),n,m,x,y) -> count(m,x) if(false(),true(),n,m,x,y) -> count(n,y) if(true(),b,n,m,x,y) -> x inc(0()) -> s(0()) inc(s(x)) -> s(inc(x)) isEmpty(empty()) -> true() isEmpty(node(l,r)) -> false() left(empty()) -> empty() left(node(l,r)) -> l nrOfNodes(n) -> count(n,0()) right(empty()) -> empty() right(node(l,r)) -> r - Signature: {count/2,if/6,inc/1,isEmpty/1,left/1,nrOfNodes/1,right/1} / {0/0,empty/0,false/0,node/2,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {count,if,inc,isEmpty,left,nrOfNodes ,right} and constructors {0,empty,false,node,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: count(n,x) -> if(isEmpty(n) ,isEmpty(left(n)) ,right(n) ,node(left(left(n)),node(right(left(n)),right(n))) ,x ,inc(x)) if(false(),false(),n,m,x,y) -> count(m,x) if(false(),true(),n,m,x,y) -> count(n,y) if(true(),b,n,m,x,y) -> x inc(0()) -> s(0()) inc(s(x)) -> s(inc(x)) isEmpty(empty()) -> true() isEmpty(node(l,r)) -> false() left(empty()) -> empty() left(node(l,r)) -> l nrOfNodes(n) -> count(n,0()) right(empty()) -> empty() right(node(l,r)) -> r - Signature: {count/2,if/6,inc/1,isEmpty/1,left/1,nrOfNodes/1,right/1} / {0/0,empty/0,false/0,node/2,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {count,if,inc,isEmpty,left,nrOfNodes ,right} and constructors {0,empty,false,node,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: inc(x){x -> s(x)} = inc(s(x)) ->^+ s(inc(x)) = C[inc(x) = inc(x){}] WORST_CASE(Omega(n^1),?)