* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: sub(0(),0()) -> 0() sub(0(),s(x)) -> 0() sub(s(x),0()) -> s(x) sub(s(x),s(y)) -> sub(x,y) zero(cons(x,xs)) -> zero2(sub(x,x),cons(x,xs)) zero(nil()) -> zero2(0(),nil()) zero2(0(),cons(x,xs)) -> cons(sub(x,x),zero(xs)) zero2(0(),nil()) -> nil() zero2(s(y),cons(x,xs)) -> zero(cons(x,xs)) zero2(s(y),nil()) -> zero(nil()) - Signature: {sub/2,zero/1,zero2/2} / {0/0,cons/2,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {sub,zero,zero2} and constructors {0,cons,nil,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: sub(0(),0()) -> 0() sub(0(),s(x)) -> 0() sub(s(x),0()) -> s(x) sub(s(x),s(y)) -> sub(x,y) zero(cons(x,xs)) -> zero2(sub(x,x),cons(x,xs)) zero(nil()) -> zero2(0(),nil()) zero2(0(),cons(x,xs)) -> cons(sub(x,x),zero(xs)) zero2(0(),nil()) -> nil() zero2(s(y),cons(x,xs)) -> zero(cons(x,xs)) zero2(s(y),nil()) -> zero(nil()) - Signature: {sub/2,zero/1,zero2/2} / {0/0,cons/2,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {sub,zero,zero2} and constructors {0,cons,nil,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: sub(x,y){x -> s(x),y -> s(y)} = sub(s(x),s(y)) ->^+ sub(x,y) = C[sub(x,y) = sub(x,y){}] WORST_CASE(Omega(n^1),?)