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