Problem Mixed TRS gcd triple

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Mixed TRS gcd triple

stdout:

MAYBE

Problem:
min(x,0()) -> 0()
min(0(),y) -> 0()
min(s(x),s(y)) -> s(min(x,y))
max(x,0()) -> x
max(0(),y) -> y
max(s(x),s(y)) -> s(max(x,y))
-(x,0()) -> x
-(s(x),s(y)) -> -(x,y)
gcd(s(x),s(y),z) -> gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)
gcd(x,s(y),s(z)) -> gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))
gcd(s(x),y,s(z)) -> gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))
gcd(x,0(),0()) -> x
gcd(0(),y,0()) -> y
gcd(0(),0(),z) -> z

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Mixed TRS gcd triple

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Mixed TRS gcd triple

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  min(x, 0()) -> 0()
     , min(0(), y) -> 0()
     , min(s(x), s(y)) -> s(min(x, y))
     , max(x, 0()) -> x
     , max(0(), y) -> y
     , max(s(x), s(y)) -> s(max(x, y))
     , -(x, 0()) -> x
     , -(s(x), s(y)) -> -(x, y)
     , gcd(s(x), s(y), z) ->
       gcd(-(max(x, y), min(x, y)), s(min(x, y)), z)
     , gcd(x, s(y), s(z)) ->
       gcd(x, -(max(y, z), min(y, z)), s(min(y, z)))
     , gcd(s(x), y, s(z)) ->
       gcd(-(max(x, z), min(x, z)), y, s(min(x, z)))
     , gcd(x, 0(), 0()) -> x
     , gcd(0(), y, 0()) -> y
     , gcd(0(), 0(), z) -> z}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Mixed TRS gcd triple

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Mixed TRS gcd triple

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  min(x, 0()) -> 0()
     , min(0(), y) -> 0()
     , min(s(x), s(y)) -> s(min(x, y))
     , max(x, 0()) -> x
     , max(0(), y) -> y
     , max(s(x), s(y)) -> s(max(x, y))
     , -(x, 0()) -> x
     , -(s(x), s(y)) -> -(x, y)
     , gcd(s(x), s(y), z) ->
       gcd(-(max(x, y), min(x, y)), s(min(x, y)), z)
     , gcd(x, s(y), s(z)) ->
       gcd(x, -(max(y, z), min(y, z)), s(min(y, z)))
     , gcd(s(x), y, s(z)) ->
       gcd(-(max(x, z), min(x, z)), y, s(min(x, z)))
     , gcd(x, 0(), 0()) -> x
     , gcd(0(), y, 0()) -> y
     , gcd(0(), 0(), z) -> z}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds