Tool CaT
stdout:
MAYBE
Problem:
a() -> f(a())
b() -> g(b())
a() -> b()
f(f(f(f(f(f(f(f(f(f(x)))))))))) -> c()
g(g(g(g(g(g(g(g(g(g(x)))))))))) -> c()
Proof:
Complexity Transformation Processor:
strict:
a() -> f(a())
b() -> g(b())
a() -> b()
f(f(f(f(f(f(f(f(f(f(x)))))))))) -> c()
g(g(g(g(g(g(g(g(g(g(x)))))))))) -> c()
weak:
Matrix Interpretation Processor:
dimension: 4
max_matrix:
[1 0 0 0]
[0 0 0 0]
[0 0 0 0]
[0 0 0 0]
interpretation:
[0]
[0]
[c] = [0]
[0],
[1 0 0 0] [0]
[0 0 0 0] [1]
[g](x0) = [0 0 0 0]x0 + [0]
[0 0 0 0] [2],
[0]
[1]
[b] = [2]
[2],
[1 0 0 0]
[0 0 0 0]
[f](x0) = [0 0 0 0]x0
[0 0 0 0] ,
[1]
[2]
[a] = [2]
[2]
orientation:
[1] [1]
[2] [0]
a() = [2] >= [0] = f(a())
[2] [0]
[0] [0]
[1] [1]
b() = [2] >= [0] = g(b())
[2] [2]
[1] [0]
[2] [1]
a() = [2] >= [2] = b()
[2] [2]
[1 0 0 0] [0]
[0 0 0 0] [0]
f(f(f(f(f(f(f(f(f(f(x)))))))))) = [0 0 0 0]x >= [0] = c()
[0 0 0 0] [0]
[1 0 0 0] [0] [0]
[0 0 0 0] [1] [0]
g(g(g(g(g(g(g(g(g(g(x)))))))))) = [0 0 0 0]x + [0] >= [0] = c()
[0 0 0 0] [2] [0]
problem:
strict:
a() -> f(a())
b() -> g(b())
f(f(f(f(f(f(f(f(f(f(x)))))))))) -> c()
g(g(g(g(g(g(g(g(g(g(x)))))))))) -> c()
weak:
a() -> b()
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[c] = 0,
[g](x0) = x0 + 7,
[b] = 107,
[f](x0) = x0,
[a] = 169
orientation:
a() = 169 >= 169 = f(a())
b() = 107 >= 114 = g(b())
f(f(f(f(f(f(f(f(f(f(x)))))))))) = x >= 0 = c()
g(g(g(g(g(g(g(g(g(g(x)))))))))) = x + 70 >= 0 = c()
a() = 169 >= 107 = b()
problem:
strict:
a() -> f(a())
b() -> g(b())
f(f(f(f(f(f(f(f(f(f(x)))))))))) -> c()
weak:
g(g(g(g(g(g(g(g(g(g(x)))))))))) -> c()
a() -> b()
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[c] = 0,
[g](x0) = x0,
[b] = 93,
[f](x0) = x0 + 1,
[a] = 141
orientation:
a() = 141 >= 142 = f(a())
b() = 93 >= 93 = g(b())
f(f(f(f(f(f(f(f(f(f(x)))))))))) = x + 10 >= 0 = c()
g(g(g(g(g(g(g(g(g(g(x)))))))))) = x >= 0 = c()
a() = 141 >= 93 = b()
problem:
strict:
a() -> f(a())
b() -> g(b())
weak:
f(f(f(f(f(f(f(f(f(f(x)))))))))) -> c()
g(g(g(g(g(g(g(g(g(g(x)))))))))) -> c()
a() -> b()
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())
, b() -> g(b())
, a() -> b()
, f(f(f(f(f(f(f(f(f(f(x)))))))))) -> c()
, g(g(g(g(g(g(g(g(g(g(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())
, b() -> g(b())
, a() -> b()
, f(f(f(f(f(f(f(f(f(f(x)))))))))) -> c()
, g(g(g(g(g(g(g(g(g(g(x)))))))))) -> c()}
Proof Output:
Computation stopped due to timeout after 60.0 seconds