Problem Secret 07 TRS aprove09

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Secret 07 TRS aprove09

stdout:

MAYBE

Problem:
div(x,y) -> div2(x,y,0())
div2(x,y,i) -> if1(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i))
if1(true(),b,x,y,i,j) -> divZeroError()
if1(false(),b,x,y,i,j) -> if2(b,x,y,i,j)
if2(true(),x,y,i,j) -> div2(minus(x,y),y,j)
if2(false(),x,y,i,j) -> 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)
plus(x,y) -> plusIter(x,y,0())
plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z)
ifPlus(true(),x,y,z) -> y
ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z))
a() -> c()
a() -> d()

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Secret 07 TRS aprove09

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Secret 07 TRS aprove09

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  div(x, y) -> div2(x, y, 0())
     , div2(x, y, i) ->
       if1(le(y, 0()), le(y, x), x, y, plus(i, 0()), inc(i))
     , if1(true(), b, x, y, i, j) -> divZeroError()
     , if1(false(), b, x, y, i, j) -> if2(b, x, y, i, j)
     , if2(true(), x, y, i, j) -> div2(minus(x, y), y, j)
     , if2(false(), x, y, i, j) -> 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)
     , plus(x, y) -> plusIter(x, y, 0())
     , plusIter(x, y, z) -> ifPlus(le(x, z), x, y, z)
     , ifPlus(true(), x, y, z) -> y
     , ifPlus(false(), x, y, z) -> plusIter(x, s(y), s(z))
     , a() -> c()
     , a() -> d()}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Secret 07 TRS aprove09

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Secret 07 TRS aprove09

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  div(x, y) -> div2(x, y, 0())
     , div2(x, y, i) ->
       if1(le(y, 0()), le(y, x), x, y, plus(i, 0()), inc(i))
     , if1(true(), b, x, y, i, j) -> divZeroError()
     , if1(false(), b, x, y, i, j) -> if2(b, x, y, i, j)
     , if2(true(), x, y, i, j) -> div2(minus(x, y), y, j)
     , if2(false(), x, y, i, j) -> 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)
     , plus(x, y) -> plusIter(x, y, 0())
     , plusIter(x, y, z) -> ifPlus(le(x, z), x, y, z)
     , ifPlus(true(), x, y, z) -> y
     , ifPlus(false(), x, y, z) -> plusIter(x, s(y), s(z))
     , a() -> c()
     , a() -> d()}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds