* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
-(x,0()) -> x
-(s(x),s(y)) -> -(x,y)
<=(0(),y) -> true()
<=(s(x),0()) -> false()
<=(s(x),s(y)) -> <=(x,y)
f(0(),y,0(),u) -> true()
f(0(),y,s(z),u) -> false()
f(s(x),0(),z,u) -> f(x,u,-(z,s(x)),u)
f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u))
if(false(),x,y) -> y
if(true(),x,y) -> x
perfectp(0()) -> false()
perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
- Signature:
{-/2,<=/2,f/4,if/3,perfectp/1} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {-,<=,f,if,perfectp} 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:
-(x,0()) -> x
-(s(x),s(y)) -> -(x,y)
<=(0(),y) -> true()
<=(s(x),0()) -> false()
<=(s(x),s(y)) -> <=(x,y)
f(0(),y,0(),u) -> true()
f(0(),y,s(z),u) -> false()
f(s(x),0(),z,u) -> f(x,u,-(z,s(x)),u)
f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u))
if(false(),x,y) -> y
if(true(),x,y) -> x
perfectp(0()) -> false()
perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
- Signature:
{-/2,<=/2,f/4,if/3,perfectp/1} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {-,<=,f,if,perfectp} and constructors {0,false,s,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
-(x,y){x -> s(x),y -> s(y)} =
-(s(x),s(y)) ->^+ -(x,y)
= C[-(x,y) = -(x,y){}]
WORST_CASE(Omega(n^1),?)