Tool CaT
stdout:
MAYBE
Problem:
f(h(x)) -> f(i(x))
h(x) -> f(h(x))
i(x) -> h(x)
f(i(x)) -> a()
Proof:
Complexity Transformation Processor:
strict:
f(h(x)) -> f(i(x))
h(x) -> f(h(x))
i(x) -> h(x)
f(i(x)) -> a()
weak:
Matrix Interpretation Processor:
dimension: 4
max_matrix:
[1 0 0 2]
[0 0 1 0]
[0 0 0 0]
[0 0 0 0]
interpretation:
[0]
[2]
[a] = [2]
[0],
[1 0 0 2] [3]
[0 0 0 0] [2]
[i](x0) = [0 0 0 0]x0 + [2]
[0 0 0 0] [0],
[1 0 0 0] [0]
[0 0 1 0] [0]
[f](x0) = [0 0 0 0]x0 + [2]
[0 0 0 0] [0],
[1 0 0 2] [3]
[0 0 0 0] [2]
[h](x0) = [0 0 0 0]x0 + [2]
[0 0 0 0] [0]
orientation:
[1 0 0 2] [3] [1 0 0 2] [3]
[0 0 0 0] [2] [0 0 0 0] [2]
f(h(x)) = [0 0 0 0]x + [2] >= [0 0 0 0]x + [2] = f(i(x))
[0 0 0 0] [0] [0 0 0 0] [0]
[1 0 0 2] [3] [1 0 0 2] [3]
[0 0 0 0] [2] [0 0 0 0] [2]
h(x) = [0 0 0 0]x + [2] >= [0 0 0 0]x + [2] = f(h(x))
[0 0 0 0] [0] [0 0 0 0] [0]
[1 0 0 2] [3] [1 0 0 2] [3]
[0 0 0 0] [2] [0 0 0 0] [2]
i(x) = [0 0 0 0]x + [2] >= [0 0 0 0]x + [2] = h(x)
[0 0 0 0] [0] [0 0 0 0] [0]
[1 0 0 2] [3] [0]
[0 0 0 0] [2] [2]
f(i(x)) = [0 0 0 0]x + [2] >= [2] = a()
[0 0 0 0] [0] [0]
problem:
strict:
f(h(x)) -> f(i(x))
h(x) -> f(h(x))
i(x) -> h(x)
weak:
f(i(x)) -> a()
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[a] = 0,
[i](x0) = x0,
[f](x0) = x0,
[h](x0) = x0 + 144
orientation:
f(h(x)) = x + 144 >= x = f(i(x))
h(x) = x + 144 >= x + 144 = f(h(x))
i(x) = x >= x + 144 = h(x)
f(i(x)) = x >= 0 = a()
problem:
strict:
h(x) -> f(h(x))
i(x) -> h(x)
weak:
f(h(x)) -> f(i(x))
f(i(x)) -> a()
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:
{ f(h(x)) -> f(i(x))
, h(x) -> f(h(x))
, i(x) -> h(x)
, f(i(x)) -> a()}
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:
{ f(h(x)) -> f(i(x))
, h(x) -> f(h(x))
, i(x) -> h(x)
, f(i(x)) -> a()}
Proof Output:
Computation stopped due to timeout after 60.0 seconds