Tool CaT
stdout:
MAYBE
Problem:
O(0()) -> 0()
+(0(),x) -> x
+(x,0()) -> x
+(O(x),O(y)) -> O(+(x,y))
+(O(x),I(y)) -> I(+(x,y))
+(I(x),O(y)) -> I(+(x,y))
+(I(x),I(y)) -> O(+(+(x,y),I(0())))
*(0(),x) -> 0()
*(x,0()) -> 0()
*(O(x),y) -> O(*(x,y))
*(I(x),y) -> +(O(*(x,y)),y)
-(x,0()) -> x
-(0(),x) -> 0()
-(O(x),O(y)) -> O(-(x,y))
-(O(x),I(y)) -> I(-(-(x,y),I(1())))
-(I(x),O(y)) -> I(-(x,y))
-(I(x),I(y)) -> O(-(x,y))
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:
{ O(0()) -> 0()
, +(0(), x) -> x
, +(x, 0()) -> x
, +(O(x), O(y)) -> O(+(x, y))
, +(O(x), I(y)) -> I(+(x, y))
, +(I(x), O(y)) -> I(+(x, y))
, +(I(x), I(y)) -> O(+(+(x, y), I(0())))
, *(0(), x) -> 0()
, *(x, 0()) -> 0()
, *(O(x), y) -> O(*(x, y))
, *(I(x), y) -> +(O(*(x, y)), y)
, -(x, 0()) -> x
, -(0(), x) -> 0()
, -(O(x), O(y)) -> O(-(x, y))
, -(O(x), I(y)) -> I(-(-(x, y), I(1())))
, -(I(x), O(y)) -> I(-(x, y))
, -(I(x), I(y)) -> O(-(x, y))}
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:
{ O(0()) -> 0()
, +(0(), x) -> x
, +(x, 0()) -> x
, +(O(x), O(y)) -> O(+(x, y))
, +(O(x), I(y)) -> I(+(x, y))
, +(I(x), O(y)) -> I(+(x, y))
, +(I(x), I(y)) -> O(+(+(x, y), I(0())))
, *(0(), x) -> 0()
, *(x, 0()) -> 0()
, *(O(x), y) -> O(*(x, y))
, *(I(x), y) -> +(O(*(x, y)), y)
, -(x, 0()) -> x
, -(0(), x) -> 0()
, -(O(x), O(y)) -> O(-(x, y))
, -(O(x), I(y)) -> I(-(-(x, y), I(1())))
, -(I(x), O(y)) -> I(-(x, y))
, -(I(x), I(y)) -> O(-(x, y))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds