Problem AProVE 04 IJCAR 18

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 04 IJCAR 18

stdout:

MAYBE

Problem:
plus(x,0()) -> x
plus(0(),y) -> y
plus(s(x),y) -> s(plus(x,y))
times(0(),y) -> 0()
times(s(0()),y) -> y
times(s(x),y) -> plus(y,times(x,y))
div(0(),y) -> 0()
div(x,y) -> quot(x,y,y)
quot(0(),s(y),z) -> 0()
quot(s(x),s(y),z) -> quot(x,y,z)
quot(x,0(),s(z)) -> s(div(x,s(z)))
div(div(x,y),z) -> div(x,times(y,z))
eq(0(),0()) -> true()
eq(s(x),0()) -> false()
eq(0(),s(y)) -> false()
eq(s(x),s(y)) -> eq(x,y)
divides(y,x) -> eq(x,times(div(x,y),y))
prime(s(s(x))) -> pr(s(s(x)),s(x))
pr(x,s(0())) -> true()
pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
if(true(),x,y) -> false()
if(false(),x,y) -> pr(x,y)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 04 IJCAR 18

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 04 IJCAR 18

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  plus(x, 0()) -> x
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , times(0(), y) -> 0()
     , times(s(0()), y) -> y
     , times(s(x), y) -> plus(y, times(x, y))
     , div(0(), y) -> 0()
     , div(x, y) -> quot(x, y, y)
     , quot(0(), s(y), z) -> 0()
     , quot(s(x), s(y), z) -> quot(x, y, z)
     , quot(x, 0(), s(z)) -> s(div(x, s(z)))
     , div(div(x, y), z) -> div(x, times(y, z))
     , eq(0(), 0()) -> true()
     , eq(s(x), 0()) -> false()
     , eq(0(), s(y)) -> false()
     , eq(s(x), s(y)) -> eq(x, y)
     , divides(y, x) -> eq(x, times(div(x, y), y))
     , prime(s(s(x))) -> pr(s(s(x)), s(x))
     , pr(x, s(0())) -> true()
     , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y))
     , if(true(), x, y) -> false()
     , if(false(), x, y) -> pr(x, y)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 04 IJCAR 18

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 04 IJCAR 18

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  plus(x, 0()) -> x
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , times(0(), y) -> 0()
     , times(s(0()), y) -> y
     , times(s(x), y) -> plus(y, times(x, y))
     , div(0(), y) -> 0()
     , div(x, y) -> quot(x, y, y)
     , quot(0(), s(y), z) -> 0()
     , quot(s(x), s(y), z) -> quot(x, y, z)
     , quot(x, 0(), s(z)) -> s(div(x, s(z)))
     , div(div(x, y), z) -> div(x, times(y, z))
     , eq(0(), 0()) -> true()
     , eq(s(x), 0()) -> false()
     , eq(0(), s(y)) -> false()
     , eq(s(x), s(y)) -> eq(x, y)
     , divides(y, x) -> eq(x, times(div(x, y), y))
     , prime(s(s(x))) -> pr(s(s(x)), s(x))
     , pr(x, s(0())) -> true()
     , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y))
     , if(true(), x, y) -> false()
     , if(false(), x, y) -> pr(x, y)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds