Problem Secret 07 TRS aprove08

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Secret 07 TRS aprove08

stdout:

MAYBE

Problem:
gcd(x,y) -> gcd2(x,y,0())
gcd2(x,y,i) -> if1(le(x,0()),le(y,0()),le(x,y),le(y,x),x,y,inc(i))
if1(true(),b1,b2,b3,x,y,i) -> pair(result(y),neededIterations(i))
if1(false(),b1,b2,b3,x,y,i) -> if2(b1,b2,b3,x,y,i)
if2(true(),b2,b3,x,y,i) -> pair(result(x),neededIterations(i))
if2(false(),b2,b3,x,y,i) -> if3(b2,b3,x,y,i)
if3(false(),b3,x,y,i) -> gcd2(minus(x,y),y,i)
if3(true(),b3,x,y,i) -> if4(b3,x,y,i)
if4(false(),x,y,i) -> gcd2(x,minus(y,x),i)
if4(true(),x,y,i) -> pair(result(x),neededIterations(i))
inc(0()) -> 0()
inc(s(i)) -> s(inc(i))
le(s(x),0()) -> false()
le(0(),y) -> true()
le(s(x),s(y)) -> le(x,y)
minus(x,0()) -> x
minus(0(),y) -> 0()
minus(s(x),s(y)) -> minus(x,y)
a() -> b()
a() -> c()

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Secret 07 TRS aprove08

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Secret 07 TRS aprove08

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  gcd(x, y) -> gcd2(x, y, 0())
     , gcd2(x, y, i) ->
       if1(le(x, 0()), le(y, 0()), le(x, y), le(y, x), x, y, inc(i))
     , if1(true(), b1, b2, b3, x, y, i) ->
       pair(result(y), neededIterations(i))
     , if1(false(), b1, b2, b3, x, y, i) -> if2(b1, b2, b3, x, y, i)
     , if2(true(), b2, b3, x, y, i) ->
       pair(result(x), neededIterations(i))
     , if2(false(), b2, b3, x, y, i) -> if3(b2, b3, x, y, i)
     , if3(false(), b3, x, y, i) -> gcd2(minus(x, y), y, i)
     , if3(true(), b3, x, y, i) -> if4(b3, x, y, i)
     , if4(false(), x, y, i) -> gcd2(x, minus(y, x), i)
     , if4(true(), x, y, i) -> pair(result(x), neededIterations(i))
     , inc(0()) -> 0()
     , inc(s(i)) -> s(inc(i))
     , le(s(x), 0()) -> false()
     , le(0(), y) -> true()
     , le(s(x), s(y)) -> le(x, y)
     , minus(x, 0()) -> x
     , minus(0(), y) -> 0()
     , minus(s(x), s(y)) -> minus(x, y)
     , a() -> b()
     , a() -> c()}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Secret 07 TRS aprove08

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Secret 07 TRS aprove08

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  gcd(x, y) -> gcd2(x, y, 0())
     , gcd2(x, y, i) ->
       if1(le(x, 0()), le(y, 0()), le(x, y), le(y, x), x, y, inc(i))
     , if1(true(), b1, b2, b3, x, y, i) ->
       pair(result(y), neededIterations(i))
     , if1(false(), b1, b2, b3, x, y, i) -> if2(b1, b2, b3, x, y, i)
     , if2(true(), b2, b3, x, y, i) ->
       pair(result(x), neededIterations(i))
     , if2(false(), b2, b3, x, y, i) -> if3(b2, b3, x, y, i)
     , if3(false(), b3, x, y, i) -> gcd2(minus(x, y), y, i)
     , if3(true(), b3, x, y, i) -> if4(b3, x, y, i)
     , if4(false(), x, y, i) -> gcd2(x, minus(y, x), i)
     , if4(true(), x, y, i) -> pair(result(x), neededIterations(i))
     , inc(0()) -> 0()
     , inc(s(i)) -> s(inc(i))
     , le(s(x), 0()) -> false()
     , le(0(), y) -> true()
     , le(s(x), s(y)) -> le(x, y)
     , minus(x, 0()) -> x
     , minus(0(), y) -> 0()
     , minus(s(x), s(y)) -> minus(x, y)
     , a() -> b()
     , a() -> c()}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds