Problem AProVE 09 Inductive mod

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive mod

stdout:

MAYBE

Problem:
minus(0(),y) -> 0()
minus(s(x),y) -> if(gt(s(x),y),x,y)
if(true(),x,y) -> s(minus(x,y))
if(false(),x,y) -> 0()
mod(x,0()) -> 0()
mod(x,s(y)) -> if1(lt(x,s(y)),x,s(y))
if1(true(),x,y) -> x
if1(false(),x,y) -> mod(minus(x,y),y)
gt(0(),y) -> false()
gt(s(x),0()) -> true()
gt(s(x),s(y)) -> gt(x,y)
lt(x,0()) -> false()
lt(0(),s(x)) -> true()
lt(s(x),s(y)) -> lt(x,y)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive mod

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 09 Inductive mod

stdout:

TIMEOUT

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

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive mod

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 09 Inductive mod

stdout:

TIMEOUT

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

Proof Output:
  Computation stopped due to timeout after 60.0 seconds