Tool CaT
stdout:
MAYBE
Problem:
+(1(),x) -> +(+(0(),1()),x)
+(0(),x) -> x
Proof:
Uncurry Processor:
11(x) -> 02(1(),x)
02(x,x3) -> +(x,x3)
01(x) -> x
+(1(),x2) -> 11(x2)
+(01(x1),x2) -> 02(x1,x2)
+(0(),x2) -> 01(x2)
Complexity Transformation Processor:
strict:
11(x) -> 02(1(),x)
02(x,x3) -> +(x,x3)
01(x) -> x
+(1(),x2) -> 11(x2)
+(01(x1),x2) -> 02(x1,x2)
+(0(),x2) -> 01(x2)
weak:
Bounds Processor:
bound: 0
enrichment: match
automaton:
final states: {6,5,4,3}
transitions:
1{1,0}(2) -> 4,5,3
1{1,0}(1) -> 4,5,3
0{2,0}(1,2) -> 5,3,4
0{2,0}(2,1) -> 4*
0{2,0}(1,1) -> 5,3,4
0{2,0}(2,2) -> 4*
10() -> 1*
+0(1,2) -> 3,4,5
+0(2,1) -> 4,5
+0(1,1) -> 3,4,5
+0(2,2) -> 4,5
0{1,0}(2) -> 4,5,6
0{1,0}(1) -> 4,5,6
00() -> 2*
1 -> 4,5,6
2 -> 4,5,6
problem:
strict:
11(x) -> 02(1(),x)
02(x,x3) -> +(x,x3)
+(1(),x2) -> 11(x2)
+(0(),x2) -> 01(x2)
01(x) -> x
weak:
+(01(x1),x2) -> 02(x1,x2)
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {6,5,4,3}
transitions:
0{2,1}(9,2) -> 4,5,3
0{2,1}(9,1) -> 4,5,3
11() -> 9*
+1(9,2) -> 4,5,3
+1(9,1) -> 4,5,3
1{1,1}(2) -> 4,5,3
1{1,1}(1) -> 4,5,3
0{1,1}(2) -> 4,5
0{1,1}(1) -> 4,5
1{1,0}(2) -> 4,5,3
1{1,0}(1) -> 4,5,3
0{2,0}(1,2) -> 4*
0{2,0}(2,1) -> 4*
0{2,0}(1,1) -> 4*
0{2,0}(2,2) -> 4*
10() -> 1*
+0(1,2) -> 4,5
+0(2,1) -> 4,5
+0(1,1) -> 4,5
+0(2,2) -> 4,5
0{1,0}(2) -> 6*
0{1,0}(1) -> 6*
00() -> 2*
1 -> 4,5,6
2 -> 4,5,6
problem:
strict:
11(x) -> 02(1(),x)
02(x,x3) -> +(x,x3)
+(1(),x2) -> 11(x2)
01(x) -> x
weak:
+(0(),x2) -> 01(x2)
+(01(x1),x2) -> 02(x1,x2)
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[01](x0) = x0 + 135,
[02](x0, x1) = x0 + x1 + 213,
[11](x0) = x0,
[0] = 57,
[+](x0, x1) = x0 + x1 + 78,
[1] = 2
orientation:
11(x) = x >= x + 215 = 02(1(),x)
02(x,x3) = x + x3 + 213 >= x + x3 + 78 = +(x,x3)
+(1(),x2) = x2 + 80 >= x2 = 11(x2)
01(x) = x + 135 >= x = x
+(0(),x2) = x2 + 135 >= x2 + 135 = 01(x2)
+(01(x1),x2) = x1 + x2 + 213 >= x1 + x2 + 213 = 02(x1,x2)
problem:
strict:
11(x) -> 02(1(),x)
weak:
02(x,x3) -> +(x,x3)
+(1(),x2) -> 11(x2)
01(x) -> x
+(0(),x2) -> 01(x2)
+(01(x1),x2) -> 02(x1,x2)
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:
{ +(1(), x) -> +(+(0(), 1()), x)
, +(0(), x) -> x}
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:
{ +(1(), x) -> +(+(0(), 1()), x)
, +(0(), x) -> x}
Proof Output:
Computation stopped due to timeout after 60.0 seconds