LMPO

Execution Time (secs)	0.230
Answer	MAYBE
Input	Secret 07 TRS aprove04

MAYBE

We consider the following Problem:

  Strict Trs:
    {  lcm(x, y) -> lcmIter(x, y, 0(), times(x, y))
     , lcmIter(x, y, z, u) -> if(or(ge(0(), x), ge(z, u)), x, y, z, u)
     , if(true(), x, y, z, u) -> z
     , if(false(), x, y, z, u) -> if2(divisible(z, y), x, y, z, u)
     , if2(true(), x, y, z, u) -> z
     , if2(false(), x, y, z, u) -> lcmIter(x, y, plus(x, z), u)
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , times(x, y) -> ifTimes(ge(0(), x), x, y)
     , ifTimes(true(), x, y) -> 0()
     , ifTimes(false(), x, y) -> plus(y, times(y, p(x)))
     , p(s(x)) -> x
     , p(0()) -> s(s(0()))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , or(true(), y) -> true()
     , or(false(), y) -> y
     , divisible(0(), s(y)) -> true()
     , divisible(s(x), s(y)) -> div(s(x), s(y), s(y))
     , div(x, y, 0()) -> divisible(x, y)
     , div(0(), y, s(z)) -> false()
     , div(s(x), y, s(z)) -> div(x, y, z)
     , a() -> b()
     , a() -> c()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.262
Answer	MAYBE
Input	Secret 07 TRS aprove04

MAYBE

We consider the following Problem:

  Strict Trs:
    {  lcm(x, y) -> lcmIter(x, y, 0(), times(x, y))
     , lcmIter(x, y, z, u) -> if(or(ge(0(), x), ge(z, u)), x, y, z, u)
     , if(true(), x, y, z, u) -> z
     , if(false(), x, y, z, u) -> if2(divisible(z, y), x, y, z, u)
     , if2(true(), x, y, z, u) -> z
     , if2(false(), x, y, z, u) -> lcmIter(x, y, plus(x, z), u)
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , times(x, y) -> ifTimes(ge(0(), x), x, y)
     , ifTimes(true(), x, y) -> 0()
     , ifTimes(false(), x, y) -> plus(y, times(y, p(x)))
     , p(s(x)) -> x
     , p(0()) -> s(s(0()))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , or(true(), y) -> true()
     , or(false(), y) -> y
     , divisible(0(), s(y)) -> true()
     , divisible(s(x), s(y)) -> div(s(x), s(y), s(y))
     , div(x, y, 0()) -> divisible(x, y)
     , div(0(), y, s(z)) -> false()
     , div(s(x), y, s(z)) -> div(x, y, z)
     , a() -> b()
     , a() -> c()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.186
Answer	MAYBE
Input	Secret 07 TRS aprove04

MAYBE

We consider the following Problem:

  Strict Trs:
    {  lcm(x, y) -> lcmIter(x, y, 0(), times(x, y))
     , lcmIter(x, y, z, u) -> if(or(ge(0(), x), ge(z, u)), x, y, z, u)
     , if(true(), x, y, z, u) -> z
     , if(false(), x, y, z, u) -> if2(divisible(z, y), x, y, z, u)
     , if2(true(), x, y, z, u) -> z
     , if2(false(), x, y, z, u) -> lcmIter(x, y, plus(x, z), u)
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , times(x, y) -> ifTimes(ge(0(), x), x, y)
     , ifTimes(true(), x, y) -> 0()
     , ifTimes(false(), x, y) -> plus(y, times(y, p(x)))
     , p(s(x)) -> x
     , p(0()) -> s(s(0()))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , or(true(), y) -> true()
     , or(false(), y) -> y
     , divisible(0(), s(y)) -> true()
     , divisible(s(x), s(y)) -> div(s(x), s(y), s(y))
     , div(x, y, 0()) -> divisible(x, y)
     , div(0(), y, s(z)) -> false()
     , div(s(x), y, s(z)) -> div(x, y, z)
     , a() -> b()
     , a() -> c()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.261
Answer	MAYBE
Input	Secret 07 TRS aprove04

MAYBE

We consider the following Problem:

  Strict Trs:
    {  lcm(x, y) -> lcmIter(x, y, 0(), times(x, y))
     , lcmIter(x, y, z, u) -> if(or(ge(0(), x), ge(z, u)), x, y, z, u)
     , if(true(), x, y, z, u) -> z
     , if(false(), x, y, z, u) -> if2(divisible(z, y), x, y, z, u)
     , if2(true(), x, y, z, u) -> z
     , if2(false(), x, y, z, u) -> lcmIter(x, y, plus(x, z), u)
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , times(x, y) -> ifTimes(ge(0(), x), x, y)
     , ifTimes(true(), x, y) -> 0()
     , ifTimes(false(), x, y) -> plus(y, times(y, p(x)))
     , p(s(x)) -> x
     , p(0()) -> s(s(0()))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , or(true(), y) -> true()
     , or(false(), y) -> y
     , divisible(0(), s(y)) -> true()
     , divisible(s(x), s(y)) -> div(s(x), s(y), s(y))
     , div(x, y, 0()) -> divisible(x, y)
     , div(0(), y, s(z)) -> false()
     , div(s(x), y, s(z)) -> div(x, y, z)
     , a() -> b()
     , a() -> c()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.260
Answer	MAYBE
Input	Secret 07 TRS aprove04

MAYBE

We consider the following Problem:

  Strict Trs:
    {  lcm(x, y) -> lcmIter(x, y, 0(), times(x, y))
     , lcmIter(x, y, z, u) -> if(or(ge(0(), x), ge(z, u)), x, y, z, u)
     , if(true(), x, y, z, u) -> z
     , if(false(), x, y, z, u) -> if2(divisible(z, y), x, y, z, u)
     , if2(true(), x, y, z, u) -> z
     , if2(false(), x, y, z, u) -> lcmIter(x, y, plus(x, z), u)
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , times(x, y) -> ifTimes(ge(0(), x), x, y)
     , ifTimes(true(), x, y) -> 0()
     , ifTimes(false(), x, y) -> plus(y, times(y, p(x)))
     , p(s(x)) -> x
     , p(0()) -> s(s(0()))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , or(true(), y) -> true()
     , or(false(), y) -> y
     , divisible(0(), s(y)) -> true()
     , divisible(s(x), s(y)) -> div(s(x), s(y), s(y))
     , div(x, y, 0()) -> divisible(x, y)
     , div(0(), y, s(z)) -> false()
     , div(s(x), y, s(z)) -> div(x, y, z)
     , a() -> b()
     , a() -> c()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.362
Answer	MAYBE
Input	Secret 07 TRS aprove04

MAYBE

We consider the following Problem:

  Strict Trs:
    {  lcm(x, y) -> lcmIter(x, y, 0(), times(x, y))
     , lcmIter(x, y, z, u) -> if(or(ge(0(), x), ge(z, u)), x, y, z, u)
     , if(true(), x, y, z, u) -> z
     , if(false(), x, y, z, u) -> if2(divisible(z, y), x, y, z, u)
     , if2(true(), x, y, z, u) -> z
     , if2(false(), x, y, z, u) -> lcmIter(x, y, plus(x, z), u)
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , times(x, y) -> ifTimes(ge(0(), x), x, y)
     , ifTimes(true(), x, y) -> 0()
     , ifTimes(false(), x, y) -> plus(y, times(y, p(x)))
     , p(s(x)) -> x
     , p(0()) -> s(s(0()))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , or(true(), y) -> true()
     , or(false(), y) -> y
     , divisible(0(), s(y)) -> true()
     , divisible(s(x), s(y)) -> div(s(x), s(y), s(y))
     , div(x, y, 0()) -> divisible(x, y)
     , div(0(), y, s(z)) -> false()
     , div(s(x), y, s(z)) -> div(x, y, z)
     , a() -> b()
     , a() -> c()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Secret 07 TRS aprove04

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)