* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
f(x,c(x),c(y)) -> f(y,y,f(y,x,y))
f(c(x),x,y) -> c(y)
f(s(x),y,z) -> f(x,s(c(y)),c(z))
g(x,y) -> x
g(x,y) -> y
- Signature:
{f/3,g/2} / {c/1,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
f(x,c(x),c(y)) -> f(y,y,f(y,x,y))
f(c(x),x,y) -> c(y)
f(s(x),y,z) -> f(x,s(c(y)),c(z))
g(x,y) -> x
g(x,y) -> y
- Signature:
{f/3,g/2} / {c/1,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
f(x,y,z){x -> s(x)} =
f(s(x),y,z) ->^+ f(x,s(c(y)),c(z))
= C[f(x,s(c(y)),c(z)) = f(x,y,z){y -> s(c(y)),z -> c(z)}]
WORST_CASE(Omega(n^1),?)