* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
add0(x,0()) -> x
add0(x',S(x)) -> +(S(0()),add0(x',x))
mult(x,0()) -> 0()
mult(x',S(x)) -> add0(x',mult(x',x))
power(x,0()) -> S(0())
power(x',S(x)) -> mult(x',power(x',x))
- Weak TRS:
+(x,S(0())) -> S(x)
+(S(0()),y) -> S(y)
- Signature:
{+/2,add0/2,mult/2,power/2} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {+,add0,mult,power} and constructors {0,S}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
add0(x,0()) -> x
add0(x',S(x)) -> +(S(0()),add0(x',x))
mult(x,0()) -> 0()
mult(x',S(x)) -> add0(x',mult(x',x))
power(x,0()) -> S(0())
power(x',S(x)) -> mult(x',power(x',x))
- Weak TRS:
+(x,S(0())) -> S(x)
+(S(0()),y) -> S(y)
- Signature:
{+/2,add0/2,mult/2,power/2} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {+,add0,mult,power} and constructors {0,S}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
add0(x,y){y -> S(y)} =
add0(x,S(y)) ->^+ +(S(0()),add0(x,y))
= C[add0(x,y) = add0(x,y){}]
WORST_CASE(Omega(n^1),?)