Tool CaT
stdout:
MAYBE
Problem:
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
pred(s(x)) -> x
minus(x,0()) -> x
minus(x,s(y)) -> pred(minus(x,y))
gcd(0(),y) -> y
gcd(s(x),0()) -> s(x)
gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y))
if_gcd(true(),x,y) -> gcd(minus(x,y),y)
if_gcd(false(),x,y) -> gcd(minus(y,x),x)
Proof:
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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, pred(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> pred(minus(x, y))
, gcd(0(), y) -> y
, gcd(s(x), 0()) -> s(x)
, gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
, if_gcd(true(), x, y) -> gcd(minus(x, y), y)
, if_gcd(false(), x, y) -> gcd(minus(y, 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, pred(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> pred(minus(x, y))
, gcd(0(), y) -> y
, gcd(s(x), 0()) -> s(x)
, gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
, if_gcd(true(), x, y) -> gcd(minus(x, y), y)
, if_gcd(false(), x, y) -> gcd(minus(y, x), x)}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool pair1rc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, pred(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> pred(minus(x, y))
, gcd(0(), y) -> y
, gcd(s(x), 0()) -> s(x)
, gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
, if_gcd(true(), x, y) -> gcd(minus(x, y), y)
, if_gcd(false(), x, y) -> gcd(minus(y, x), 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, pred(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> pred(minus(x, y))
, gcd(0(), y) -> y
, gcd(s(x), 0()) -> s(x)
, gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
, if_gcd(true(), x, y) -> gcd(minus(x, y), y)
, if_gcd(false(), x, y) -> gcd(minus(y, x), 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, pred(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> pred(minus(x, y))
, gcd(0(), y) -> y
, gcd(s(x), 0()) -> s(x)
, gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
, if_gcd(true(), x, y) -> gcd(minus(x, y), y)
, if_gcd(false(), x, y) -> gcd(minus(y, x), 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, pred(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> pred(minus(x, y))
, gcd(0(), y) -> y
, gcd(s(x), 0()) -> s(x)
, gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
, if_gcd(true(), x, y) -> gcd(minus(x, y), y)
, if_gcd(false(), x, y) -> gcd(minus(y, x), 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 rc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, pred(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> pred(minus(x, y))
, gcd(0(), y) -> y
, gcd(s(x), 0()) -> s(x)
, gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
, if_gcd(true(), x, y) -> gcd(minus(x, y), y)
, if_gcd(false(), x, y) -> gcd(minus(y, x), x)}
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
Execution Time | 60.06571ms |
---|
Answer | TIMEOUT |
---|
Input | AG01 4.30c |
---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, pred(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> pred(minus(x, y))
, gcd(0(), y) -> y
, gcd(s(x), 0()) -> s(x)
, gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
, if_gcd(true(), x, y) -> gcd(minus(x, y), y)
, if_gcd(false(), x, y) -> gcd(minus(y, x), 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..