Problem AProVE 09 Inductive zerolist

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive zerolist

stdout:

MAYBE

Problem:
sub(0(),0()) -> 0()
sub(s(x),0()) -> s(x)
sub(0(),s(x)) -> 0()
sub(s(x),s(y)) -> sub(x,y)
zero(nil()) -> zero2(0(),nil())
zero(cons(x,xs)) -> zero2(sub(x,x),cons(x,xs))
zero2(0(),nil()) -> nil()
zero2(0(),cons(x,xs)) -> cons(sub(x,x),zero(xs))
zero2(s(y),nil()) -> zero(nil())
zero2(s(y),cons(x,xs)) -> zero(cons(x,xs))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive zerolist

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 09 Inductive zerolist

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  sub(0(), 0()) -> 0()
     , sub(s(x), 0()) -> s(x)
     , sub(0(), s(x)) -> 0()
     , sub(s(x), s(y)) -> sub(x, y)
     , zero(nil()) -> zero2(0(), nil())
     , zero(cons(x, xs)) -> zero2(sub(x, x), cons(x, xs))
     , zero2(0(), nil()) -> nil()
     , zero2(0(), cons(x, xs)) -> cons(sub(x, x), zero(xs))
     , zero2(s(y), nil()) -> zero(nil())
     , zero2(s(y), cons(x, xs)) -> zero(cons(x, xs))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive zerolist

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 09 Inductive zerolist

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  sub(0(), 0()) -> 0()
     , sub(s(x), 0()) -> s(x)
     , sub(0(), s(x)) -> 0()
     , sub(s(x), s(y)) -> sub(x, y)
     , zero(nil()) -> zero2(0(), nil())
     , zero(cons(x, xs)) -> zero2(sub(x, x), cons(x, xs))
     , zero2(0(), nil()) -> nil()
     , zero2(0(), cons(x, xs)) -> cons(sub(x, x), zero(xs))
     , zero2(s(y), nil()) -> zero(nil())
     , zero2(s(y), cons(x, xs)) -> zero(cons(x, xs))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds