Tool CaT
stdout:
MAYBE
Problem:
d(0()) -> 0()
d(s(x)) -> s(s(d(x)))
e(0()) -> s(0())
e(r(x)) -> d(e(x))
Proof:
Complexity Transformation Processor:
strict:
d(0()) -> 0()
d(s(x)) -> s(s(d(x)))
e(0()) -> s(0())
e(r(x)) -> d(e(x))
weak:
Arctic Interpretation Processor:
dimension: 1
interpretation:
[r](x0) = 8x0,
[e](x0) = 5x0,
[s](x0) = x0,
[d](x0) = x0,
[0] = 0
orientation:
d(0()) = 0 >= 0 = 0()
d(s(x)) = x >= x = s(s(d(x)))
e(0()) = 5 >= 0 = s(0())
e(r(x)) = 13x >= 5x = d(e(x))
problem:
strict:
d(0()) -> 0()
d(s(x)) -> s(s(d(x)))
weak:
e(0()) -> s(0())
e(r(x)) -> d(e(x))
Arctic Interpretation Processor:
dimension: 1
interpretation:
[r](x0) = 6x0,
[e](x0) = 3x0,
[s](x0) = x0,
[d](x0) = 1x0,
[0] = 2
orientation:
d(0()) = 3 >= 2 = 0()
d(s(x)) = 1x >= 1x = s(s(d(x)))
e(0()) = 5 >= 2 = s(0())
e(r(x)) = 9x >= 4x = d(e(x))
problem:
strict:
d(s(x)) -> s(s(d(x)))
weak:
d(0()) -> 0()
e(0()) -> s(0())
e(r(x)) -> d(e(x))
OpenTool 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(0()) -> s(0())
, e(r(x)) -> d(e(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:
{ d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, e(0()) -> s(0())
, e(r(x)) -> d(e(x))}
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(0()) -> s(0())
, e(r(x)) -> d(e(x))}
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(0()) -> s(0())
, e(r(x)) -> d(e(x))}
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(0()) -> s(0())
, e(r(x)) -> d(e(x))}
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(0()) -> s(0())
, e(r(x)) -> d(e(x))}
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 tup3irc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, e(0()) -> s(0())
, e(r(x)) -> d(e(x))}
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..