Tool CaT
stdout:
MAYBE
Problem:
d(0()) -> 0()
d(s(x)) -> s(s(d(x)))
e(s(x),y) -> e(x,d(y))
sup(s(x),e(0(),y)) -> sup(x,e(y,s(0())))
Proof:
Complexity Transformation Processor:
strict:
d(0()) -> 0()
d(s(x)) -> s(s(d(x)))
e(s(x),y) -> e(x,d(y))
sup(s(x),e(0(),y)) -> sup(x,e(y,s(0())))
weak:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {5,4,3}
transitions:
01() -> 11*
s1(19) -> 11,3
s1(11) -> 19*
d1(2) -> 11*
d1(19) -> 11*
d1(11) -> 11*
d1(1) -> 11*
e1(2,11) -> 4*
e1(1,11) -> 4*
d0(2) -> 3*
d0(1) -> 3*
00() -> 3,1
s0(2) -> 2*
s0(1) -> 2*
e0(1,2) -> 4*
e0(2,1) -> 4*
e0(1,1) -> 4*
e0(2,2) -> 4*
sup0(1,2) -> 5*
sup0(2,1) -> 5*
sup0(1,1) -> 5*
sup0(2,2) -> 5*
problem:
strict:
d(0()) -> 0()
d(s(x)) -> s(s(d(x)))
sup(s(x),e(0(),y)) -> sup(x,e(y,s(0())))
weak:
e(s(x),y) -> e(x,d(y))
Bounds Processor:
bound: 0
enrichment: match
automaton:
final states: {5,4,3}
transitions:
d0(17) -> 3*
d0(2) -> 3*
d0(16) -> 3*
d0(11) -> 16*
d0(1) -> 3*
d0(3) -> 1*
00() -> 3,1
s0(17) -> 1*
s0(2) -> 16,2
s0(16) -> 17*
s0(11) -> 3*
s0(1) -> 2*
s0(3) -> 11*
e0(1,2) -> 5*
e0(17,1) -> 5*
e0(17,3) -> 5*
e0(2,1) -> 5*
e0(2,3) -> 5*
e0(16,1) -> 5*
e0(16,3) -> 5*
e0(1,1) -> 5*
e0(1,3) -> 5*
e0(2,2) -> 5*
sup0(1,2) -> 4*
sup0(2,1) -> 4*
sup0(1,1) -> 4*
sup0(2,2) -> 4*
problem:
strict:
d(0()) -> 0()
d(s(x)) -> s(s(d(x)))
weak:
sup(s(x),e(0(),y)) -> sup(x,e(y,s(0())))
e(s(x),y) -> e(x,d(y))
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[sup](x0, x1) = x0 + x1 + 13,
[e](x0, x1) = x0 + x1 + 48,
[s](x0) = x0 + 16,
[d](x0) = x0 + 16,
[0] = 3
orientation:
d(0()) = 19 >= 3 = 0()
d(s(x)) = x + 32 >= x + 48 = s(s(d(x)))
sup(s(x),e(0(),y)) = x + y + 80 >= x + y + 80 = sup(x,e(y,s(0())))
e(s(x),y) = x + y + 64 >= x + y + 64 = e(x,d(y))
problem:
strict:
d(s(x)) -> s(s(d(x)))
weak:
d(0()) -> 0()
sup(s(x),e(0(),y)) -> sup(x,e(y,s(0())))
e(s(x),y) -> e(x,d(y))
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:
{ d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, e(s(x), y) -> e(x, d(y))
, sup(s(x), e(0(), y)) -> sup(x, e(y, s(0())))}
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:
{ d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, e(s(x), y) -> e(x, d(y))
, sup(s(x), e(0(), y)) -> sup(x, e(y, s(0())))}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool pair1rc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, e(s(x), y) -> e(x, d(y))
, sup(s(x), e(0(), y)) -> sup(x, e(y, s(0())))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'pair1 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool pair2rc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, e(s(x), y) -> e(x, d(y))
, sup(s(x), e(0(), y)) -> sup(x, e(y, s(0())))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'pair2 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool pair3irc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, e(s(x), y) -> e(x, d(y))
, sup(s(x), e(0(), y)) -> sup(x, e(y, s(0())))}
StartTerms: basic terms
Strategy: innermost
Certificate: TIMEOUT
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool pair3rc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, e(s(x), y) -> e(x, d(y))
, sup(s(x), e(0(), y)) -> sup(x, e(y, s(0())))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool rc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, e(s(x), y) -> e(x, d(y))
, sup(s(x), e(0(), y)) -> sup(x, e(y, s(0())))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool tup3irc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, e(s(x), y) -> e(x, d(y))
, sup(s(x), e(0(), y)) -> sup(x, e(y, s(0())))}
StartTerms: basic terms
Strategy: innermost
Certificate: TIMEOUT
Application of 'tup3 (timeout of 60.0 seconds)':
------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..