Tool CaT
stdout:
MAYBE
Problem:
a(b(x1)) -> c(d(x1))
d(d(x1)) -> b(e(x1))
b(x1) -> d(c(x1))
d(x1) -> x1
e(c(x1)) -> d(a(x1))
a(x1) -> e(d(x1))
Proof:
Complexity Transformation Processor:
strict:
a(b(x1)) -> c(d(x1))
d(d(x1)) -> b(e(x1))
b(x1) -> d(c(x1))
d(x1) -> x1
e(c(x1)) -> d(a(x1))
a(x1) -> e(d(x1))
weak:
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[e](x0) = x0 + 20,
[c](x0) = x0,
[d](x0) = x0,
[a](x0) = x0 + 30,
[b](x0) = x0 + 248
orientation:
a(b(x1)) = x1 + 278 >= x1 = c(d(x1))
d(d(x1)) = x1 >= x1 + 268 = b(e(x1))
b(x1) = x1 + 248 >= x1 = d(c(x1))
d(x1) = x1 >= x1 = x1
e(c(x1)) = x1 + 20 >= x1 + 30 = d(a(x1))
a(x1) = x1 + 30 >= x1 + 20 = e(d(x1))
problem:
strict:
d(d(x1)) -> b(e(x1))
d(x1) -> x1
e(c(x1)) -> d(a(x1))
weak:
a(b(x1)) -> c(d(x1))
b(x1) -> d(c(x1))
a(x1) -> e(d(x1))
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[e](x0) = x0,
[c](x0) = x0 + 24,
[d](x0) = x0,
[a](x0) = x0,
[b](x0) = x0 + 24
orientation:
d(d(x1)) = x1 >= x1 + 24 = b(e(x1))
d(x1) = x1 >= x1 = x1
e(c(x1)) = x1 + 24 >= x1 = d(a(x1))
a(b(x1)) = x1 + 24 >= x1 + 24 = c(d(x1))
b(x1) = x1 + 24 >= x1 + 24 = d(c(x1))
a(x1) = x1 >= x1 = e(d(x1))
problem:
strict:
d(d(x1)) -> b(e(x1))
d(x1) -> x1
weak:
e(c(x1)) -> d(a(x1))
a(b(x1)) -> c(d(x1))
b(x1) -> d(c(x1))
a(x1) -> e(d(x1))
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[e](x0) = x0 + 52,
[c](x0) = x0 + 194,
[d](x0) = x0 + 24,
[a](x0) = x0 + 80,
[b](x0) = x0 + 232
orientation:
d(d(x1)) = x1 + 48 >= x1 + 284 = b(e(x1))
d(x1) = x1 + 24 >= x1 = x1
e(c(x1)) = x1 + 246 >= x1 + 104 = d(a(x1))
a(b(x1)) = x1 + 312 >= x1 + 218 = c(d(x1))
b(x1) = x1 + 232 >= x1 + 218 = d(c(x1))
a(x1) = x1 + 80 >= x1 + 76 = e(d(x1))
problem:
strict:
d(d(x1)) -> b(e(x1))
weak:
d(x1) -> x1
e(c(x1)) -> d(a(x1))
a(b(x1)) -> c(d(x1))
b(x1) -> d(c(x1))
a(x1) -> e(d(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(b(x1)) -> c(d(x1))
, d(d(x1)) -> b(e(x1))
, b(x1) -> d(c(x1))
, d(x1) -> x1
, e(c(x1)) -> d(a(x1))
, a(x1) -> e(d(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(b(x1)) -> c(d(x1))
, d(d(x1)) -> b(e(x1))
, b(x1) -> d(c(x1))
, d(x1) -> x1
, e(c(x1)) -> d(a(x1))
, a(x1) -> e(d(x1))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds