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