* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
-(x,0()) -> x
-(s(x),s(y)) -> -(x,y)
gcd(0(),s(x)) -> s(x)
gcd(s(x),0()) -> s(x)
gcd(s(x),s(y)) -> gcd(-(max(x,y),min(x,y)),s(min(x,y)))
max(x,0()) -> x
max(0(),y) -> y
max(s(x),s(y)) -> s(max(x,y))
min(x,0()) -> 0()
min(0(),y) -> 0()
min(s(x),s(y)) -> s(min(x,y))
- Signature:
{-/2,gcd/2,max/2,min/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {-,gcd,max,min} and constructors {0,s}
+ 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)
gcd(0(),s(x)) -> s(x)
gcd(s(x),0()) -> s(x)
gcd(s(x),s(y)) -> gcd(-(max(x,y),min(x,y)),s(min(x,y)))
max(x,0()) -> x
max(0(),y) -> y
max(s(x),s(y)) -> s(max(x,y))
min(x,0()) -> 0()
min(0(),y) -> 0()
min(s(x),s(y)) -> s(min(x,y))
- Signature:
{-/2,gcd/2,max/2,min/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {-,gcd,max,min} and constructors {0,s}
+ 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),?)