Tool CaT
stdout:
MAYBE
Problem:
f(x,x) -> f(0(),1())
0() -> 2()
1() -> 2()
f(x,2()) -> 2()
f(2(),x) -> 2()
Proof:
Complexity Transformation Processor:
strict:
f(x,x) -> f(0(),1())
0() -> 2()
1() -> 2()
f(x,2()) -> 2()
f(2(),x) -> 2()
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]
[2] = [0]
[0],
[0]
[1]
[1] = [2]
[2],
[0]
[0]
[0] = [0]
[1],
[1 0 0 0] [1 0 0 0] [3]
[0 0 0 0] [0 0 0 0] [1]
[f](x0, x1) = [0 0 0 0]x0 + [0 0 0 0]x1 + [0]
[0 0 0 0] [0 0 0 0] [0]
orientation:
[2 0 0 0] [3] [3]
[0 0 0 0] [1] [1]
f(x,x) = [0 0 0 0]x + [0] >= [0] = f(0(),1())
[0 0 0 0] [0] [0]
[0] [0]
[0] [0]
0() = [0] >= [0] = 2()
[1] [0]
[0] [0]
[1] [0]
1() = [2] >= [0] = 2()
[2] [0]
[1 0 0 0] [3] [0]
[0 0 0 0] [1] [0]
f(x,2()) = [0 0 0 0]x + [0] >= [0] = 2()
[0 0 0 0] [0] [0]
[1 0 0 0] [3] [0]
[0 0 0 0] [1] [0]
f(2(),x) = [0 0 0 0]x + [0] >= [0] = 2()
[0 0 0 0] [0] [0]
problem:
strict:
f(x,x) -> f(0(),1())
0() -> 2()
1() -> 2()
weak:
f(x,2()) -> 2()
f(2(),x) -> 2()
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {22,21,17,16,10,4,3,2}
transitions:
21() -> 10,17,16,22,21*,2,4,3,1,7
f0(17,16) -> 2*
f0(22,22) -> 2*
f0(17,22) -> 2*
f0(3,17) -> 2*
f0(3,21) -> 2*
f0(10,1) -> 2*
f0(10,17) -> 2*
f0(10,21) -> 2*
f0(21,4) -> 2*
f0(16,4) -> 2*
f0(21,10) -> 2*
f0(16,10) -> 2*
f0(1,10) -> 2*
f0(21,16) -> 2*
f0(16,16) -> 2*
f0(1,16) -> 2*
f0(22,1) -> 2*
f0(17,1) -> 2*
f0(21,22) -> 2*
f0(16,22) -> 2*
f0(1,22) -> 2*
f0(22,17) -> 2*
f0(17,17) -> 2*
f0(22,21) -> 2*
f0(17,21) -> 2*
f0(3,4) -> 2*
f0(3,16) -> 2*
f0(3,22) -> 2*
f0(10,4) -> 2*
f0(10,10) -> 2*
f0(10,16) -> 2*
f0(21,1) -> 2*
f0(16,1) -> 2*
f0(10,22) -> 2*
f0(1,1) -> 2*
f0(21,17) -> 2*
f0(16,17) -> 2*
f0(21,21) -> 2*
f0(1,17) -> 2*
f0(16,21) -> 2*
f0(1,21) -> 2*
f0(22,10) -> 2*
f0(17,10) -> 2*
f0(22,16) -> 2*
00() -> 3*
10() -> 4*
20() -> 17,22*,2,4,1
7 -> 3*
problem:
strict:
f(x,x) -> f(0(),1())
1() -> 2()
weak:
0() -> 2()
f(x,2()) -> 2()
f(2(),x) -> 2()
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {18,17,13,12,8,4,3,2}
transitions:
21() -> 8,13,12,18,17*,2,4,3,1,7
f0(17,18) -> 2*
f0(12,18) -> 2*
f0(18,1) -> 2*
f0(13,1) -> 2*
f0(18,3) -> 2*
f0(8,1) -> 2*
f0(13,3) -> 2*
f0(18,13) -> 2*
f0(13,13) -> 2*
f0(8,13) -> 2*
f0(18,17) -> 2*
f0(13,17) -> 2*
f0(8,17) -> 2*
f0(4,8) -> 2*
f0(4,12) -> 2*
f0(1,8) -> 2*
f0(1,12) -> 2*
f0(17,1) -> 2*
f0(1,18) -> 2*
f0(12,1) -> 2*
f0(17,3) -> 2*
f0(12,3) -> 2*
f0(17,13) -> 2*
f0(12,13) -> 2*
f0(17,17) -> 2*
f0(12,17) -> 2*
f0(18,8) -> 2*
f0(13,8) -> 2*
f0(8,8) -> 2*
f0(18,12) -> 2*
f0(13,12) -> 2*
f0(8,12) -> 2*
f0(18,18) -> 2*
f0(13,18) -> 2*
f0(8,18) -> 2*
f0(4,3) -> 2*
f0(4,17) -> 2*
f0(1,1) -> 2*
f0(1,13) -> 2*
f0(1,17) -> 2*
f0(17,8) -> 2*
f0(12,8) -> 2*
f0(17,12) -> 2*
f0(12,12) -> 2*
00() -> 4*
10() -> 3*
20() -> 13,18*,2,4,1
7 -> 3*
problem:
strict:
f(x,x) -> f(0(),1())
weak:
1() -> 2()
0() -> 2()
f(x,2()) -> 2()
f(2(),x) -> 2()
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(x, x) -> f(0(), 1())
, 0() -> 2()
, 1() -> 2()
, f(x, 2()) -> 2()
, f(2(), x) -> 2()}
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(x, x) -> f(0(), 1())
, 0() -> 2()
, 1() -> 2()
, f(x, 2()) -> 2()
, f(2(), x) -> 2()}
Proof Output:
Computation stopped due to timeout after 60.0 seconds