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