* 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),?)