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