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