* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
diff(X,Y) -> if(leq(X,Y),0(),s(diff(p(X),Y)))
if(false(),X,Y) -> Y
if(true(),X,Y) -> X
leq(0(),Y) -> true()
leq(s(X),0()) -> false()
leq(s(X),s(Y)) -> leq(X,Y)
p(0()) -> 0()
p(s(X)) -> X
- Signature:
{diff/2,if/3,leq/2,p/1} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {diff,if,leq,p} and constructors {0,false,s,true}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
diff(X,Y) -> if(leq(X,Y),0(),s(diff(p(X),Y)))
if(false(),X,Y) -> Y
if(true(),X,Y) -> X
leq(0(),Y) -> true()
leq(s(X),0()) -> false()
leq(s(X),s(Y)) -> leq(X,Y)
p(0()) -> 0()
p(s(X)) -> X
- Signature:
{diff/2,if/3,leq/2,p/1} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {diff,if,leq,p} and constructors {0,false,s,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
leq(x,y){x -> s(x),y -> s(y)} =
leq(s(x),s(y)) ->^+ leq(x,y)
= C[leq(x,y) = leq(x,y){}]
WORST_CASE(Omega(n^1),?)