Tool CaT
stdout:
MAYBE
Problem:
a(x1) -> b(b(x1))
c(b(x1)) -> d(x1)
e(b(x1)) -> c(c(x1))
d(b(x1)) -> b(f(x1))
f(x1) -> a(e(x1))
c(x1) -> x1
a(a(x1)) -> f(x1)
Proof:
Complexity Transformation Processor:
strict:
a(x1) -> b(b(x1))
c(b(x1)) -> d(x1)
e(b(x1)) -> c(c(x1))
d(b(x1)) -> b(f(x1))
f(x1) -> a(e(x1))
c(x1) -> x1
a(a(x1)) -> f(x1)
weak:
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[f](x0) = x0 + 129,
[e](x0) = x0,
[d](x0) = x0 + 143,
[c](x0) = x0,
[b](x0) = x0 + 1,
[a](x0) = x0 + 40
orientation:
a(x1) = x1 + 40 >= x1 + 2 = b(b(x1))
c(b(x1)) = x1 + 1 >= x1 + 143 = d(x1)
e(b(x1)) = x1 + 1 >= x1 = c(c(x1))
d(b(x1)) = x1 + 144 >= x1 + 130 = b(f(x1))
f(x1) = x1 + 129 >= x1 + 40 = a(e(x1))
c(x1) = x1 >= x1 = x1
a(a(x1)) = x1 + 80 >= x1 + 129 = f(x1)
problem:
strict:
c(b(x1)) -> d(x1)
c(x1) -> x1
a(a(x1)) -> f(x1)
weak:
a(x1) -> b(b(x1))
e(b(x1)) -> c(c(x1))
d(b(x1)) -> b(f(x1))
f(x1) -> a(e(x1))
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[f](x0) = x0 + 22,
[e](x0) = x0,
[d](x0) = x0 + 56,
[c](x0) = x0 + 4,
[b](x0) = x0 + 8,
[a](x0) = x0 + 22
orientation:
c(b(x1)) = x1 + 12 >= x1 + 56 = d(x1)
c(x1) = x1 + 4 >= x1 = x1
a(a(x1)) = x1 + 44 >= x1 + 22 = f(x1)
a(x1) = x1 + 22 >= x1 + 16 = b(b(x1))
e(b(x1)) = x1 + 8 >= x1 + 8 = c(c(x1))
d(b(x1)) = x1 + 64 >= x1 + 30 = b(f(x1))
f(x1) = x1 + 22 >= x1 + 22 = a(e(x1))
problem:
strict:
c(b(x1)) -> d(x1)
weak:
c(x1) -> x1
a(a(x1)) -> f(x1)
a(x1) -> b(b(x1))
e(b(x1)) -> c(c(x1))
d(b(x1)) -> b(f(x1))
f(x1) -> a(e(x1))
Open
Tool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: innermost runtime-complexity with respect to
Rules:
{ a(x1) -> b(b(x1))
, c(b(x1)) -> d(x1)
, e(b(x1)) -> c(c(x1))
, d(b(x1)) -> b(f(x1))
, f(x1) -> a(e(x1))
, c(x1) -> x1
, a(a(x1)) -> f(x1)}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool RC1
stdout:
MAYBE
Tool RC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: runtime-complexity with respect to
Rules:
{ a(x1) -> b(b(x1))
, c(b(x1)) -> d(x1)
, e(b(x1)) -> c(c(x1))
, d(b(x1)) -> b(f(x1))
, f(x1) -> a(e(x1))
, c(x1) -> x1
, a(a(x1)) -> f(x1)}
Proof Output:
Computation stopped due to timeout after 60.0 seconds