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