Problem AProVE 09 Inductive div

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive div

stdout:

MAYBE

Problem:
minus(s(x),y) -> if(gt(s(x),y),x,y)
if(true(),x,y) -> s(minus(x,y))
if(false(),x,y) -> 0()
ge(x,0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),s(y)) -> ge(x,y)
gt(0(),y) -> false()
gt(s(x),0()) -> true()
gt(s(x),s(y)) -> gt(x,y)
div(x,y) -> if1(ge(x,y),x,y)
if1(true(),x,y) -> if2(gt(y,0()),x,y)
if1(false(),x,y) -> 0()
if2(true(),x,y) -> s(div(minus(x,y),y))
if2(false(),x,y) -> 0()

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive div

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 09 Inductive div

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  minus(s(x), y) -> if(gt(s(x), y), x, y)
     , if(true(), x, y) -> s(minus(x, y))
     , if(false(), x, y) -> 0()
     , ge(x, 0()) -> true()
     , ge(0(), s(x)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , gt(0(), y) -> false()
     , gt(s(x), 0()) -> true()
     , gt(s(x), s(y)) -> gt(x, y)
     , div(x, y) -> if1(ge(x, y), x, y)
     , if1(true(), x, y) -> if2(gt(y, 0()), x, y)
     , if1(false(), x, y) -> 0()
     , if2(true(), x, y) -> s(div(minus(x, y), y))
     , if2(false(), x, y) -> 0()}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive div

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 09 Inductive div

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  minus(s(x), y) -> if(gt(s(x), y), x, y)
     , if(true(), x, y) -> s(minus(x, y))
     , if(false(), x, y) -> 0()
     , ge(x, 0()) -> true()
     , ge(0(), s(x)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , gt(0(), y) -> false()
     , gt(s(x), 0()) -> true()
     , gt(s(x), s(y)) -> gt(x, y)
     , div(x, y) -> if1(ge(x, y), x, y)
     , if1(true(), x, y) -> if2(gt(y, 0()), x, y)
     , if1(false(), x, y) -> 0()
     , if2(true(), x, y) -> s(div(minus(x, y), y))
     , if2(false(), x, y) -> 0()}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds