* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: if(false(),x,y) -> s(minus(p(x),y)) if(true(),x,y) -> 0() le(0(),y) -> true() le(p(s(x)),x) -> le(x,x) le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,y) -> if(le(x,y),x,y) p(0()) -> s(s(0())) p(p(s(x))) -> p(x) p(s(x)) -> x - Signature: {if/3,le/2,minus/2,p/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {if,le,minus,p} and constructors {0,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: if(false(),x,y) -> s(minus(p(x),y)) if(true(),x,y) -> 0() le(0(),y) -> true() le(p(s(x)),x) -> le(x,x) le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,y) -> if(le(x,y),x,y) p(0()) -> s(s(0())) p(p(s(x))) -> p(x) p(s(x)) -> x - Signature: {if/3,le/2,minus/2,p/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {if,le,minus,p} and constructors {0,false,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),?)