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