* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
f(0(),0(),0(),0(),0(),0(),0(),0(),0(),0()) -> 0()
f(0(),0(),0(),0(),0(),0(),0(),0(),0(),s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
f(0(),0(),0(),0(),0(),0(),0(),0(),s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
f(0(),0(),0(),0(),0(),0(),0(),s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
f(0(),0(),0(),0(),0(),0(),s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
f(0(),0(),0(),0(),0(),s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
f(0(),0(),0(),0(),s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
f(0(),0(),0(),s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
f(0(),0(),s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
f(0(),s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
- Signature:
{f/10} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {0,s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
f(0(),0(),0(),0(),0(),0(),0(),0(),0(),0()) -> 0()
f(0(),0(),0(),0(),0(),0(),0(),0(),0(),s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
f(0(),0(),0(),0(),0(),0(),0(),0(),s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
f(0(),0(),0(),0(),0(),0(),0(),s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
f(0(),0(),0(),0(),0(),0(),s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
f(0(),0(),0(),0(),0(),s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
f(0(),0(),0(),0(),s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
f(0(),0(),0(),s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
f(0(),0(),s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
f(0(),s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
- Signature:
{f/10} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {0,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
f(x,y,z,u,v,w,x_6,x_7,x_8,x_9){x -> s(x)} =
f(s(x),y,z,u,v,w,x_6,x_7,x_8,x_9) ->^+ f(x,y,z,u,v,w,x_6,x_7,x_8,x_9)
= C[f(x,y,z,u,v,w,x_6,x_7,x_8,x_9) = f(x,y,z,u,v,w,x_6,x_7,x_8,x_9){}]
WORST_CASE(Omega(n^1),?)