Tool CaT
stdout:
MAYBE
Problem:
a() -> f(a())
f(f(x)) -> g(x)
g(g(x)) -> h(x)
h(h(x)) -> c()
Proof:
Complexity Transformation Processor:
strict:
a() -> f(a())
f(f(x)) -> g(x)
g(g(x)) -> h(x)
h(h(x)) -> c()
weak:
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[c] = 0,
[h](x0) = x0,
[g](x0) = x0 + 3,
[f](x0) = x0 + 18,
[a] = 2
orientation:
a() = 2 >= 20 = f(a())
f(f(x)) = x + 36 >= x + 3 = g(x)
g(g(x)) = x + 6 >= x = h(x)
h(h(x)) = x >= 0 = c()
problem:
strict:
a() -> f(a())
h(h(x)) -> c()
weak:
f(f(x)) -> g(x)
g(g(x)) -> h(x)
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[c] = 0,
[h](x0) = x0 + 128,
[g](x0) = x0 + 64,
[f](x0) = x0 + 32,
[a] = 224
orientation:
a() = 224 >= 256 = f(a())
h(h(x)) = x + 256 >= 0 = c()
f(f(x)) = x + 64 >= x + 64 = g(x)
g(g(x)) = x + 128 >= x + 128 = h(x)
problem:
strict:
a() -> f(a())
weak:
h(h(x)) -> c()
f(f(x)) -> g(x)
g(g(x)) -> h(x)
Open
Tool IRC1
stdout:
MAYBE
Warning when parsing problem:
Unsupported strategy 'OUTERMOST'Tool IRC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: innermost runtime-complexity with respect to
Rules:
{ a() -> f(a())
, f(f(x)) -> g(x)
, g(g(x)) -> h(x)
, h(h(x)) -> c()}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool RC1
stdout:
MAYBE
Warning when parsing problem:
Unsupported strategy 'OUTERMOST'Tool RC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: runtime-complexity with respect to
Rules:
{ a() -> f(a())
, f(f(x)) -> g(x)
, g(g(x)) -> h(x)
, h(h(x)) -> c()}
Proof Output:
Computation stopped due to timeout after 60.0 seconds