LMPO

Execution Time (secs)	0.165
Answer	MAYBE
Input	Secret 07 TRS aprove01

MAYBE

We consider the following Problem:

  Strict Trs:
    {  times(x, y) -> sum(generate(x, y))
     , generate(x, y) -> gen(x, y, 0())
     , gen(x, y, z) -> if(ge(z, x), x, y, z)
     , if(true(), x, y, z) -> nil()
     , if(false(), x, y, z) -> cons(y, gen(x, y, s(z)))
     , sum(xs) -> sum2(xs, 0())
     , sum2(xs, y) -> ifsum(isNil(xs), isZero(head(xs)), xs, y)
     , ifsum(true(), b, xs, y) -> y
     , ifsum(false(), b, xs, y) -> ifsum2(b, xs, y)
     , ifsum2(true(), xs, y) -> sum2(tail(xs), y)
     , ifsum2(false(), xs, y) -> sum2(cons(p(head(xs)), tail(xs)), s(y))
     , isNil(nil()) -> true()
     , isNil(cons(x, xs)) -> false()
     , tail(nil()) -> nil()
     , tail(cons(x, xs)) -> xs
     , head(cons(x, xs)) -> x
     , head(nil()) -> error()
     , isZero(0()) -> true()
     , isZero(s(0())) -> false()
     , isZero(s(s(x))) -> isZero(s(x))
     , p(0()) -> s(s(0()))
     , p(s(0())) -> 0()
     , p(s(s(x))) -> s(p(s(x)))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , a() -> c()
     , a() -> d()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.276
Answer	MAYBE
Input	Secret 07 TRS aprove01

MAYBE

We consider the following Problem:

  Strict Trs:
    {  times(x, y) -> sum(generate(x, y))
     , generate(x, y) -> gen(x, y, 0())
     , gen(x, y, z) -> if(ge(z, x), x, y, z)
     , if(true(), x, y, z) -> nil()
     , if(false(), x, y, z) -> cons(y, gen(x, y, s(z)))
     , sum(xs) -> sum2(xs, 0())
     , sum2(xs, y) -> ifsum(isNil(xs), isZero(head(xs)), xs, y)
     , ifsum(true(), b, xs, y) -> y
     , ifsum(false(), b, xs, y) -> ifsum2(b, xs, y)
     , ifsum2(true(), xs, y) -> sum2(tail(xs), y)
     , ifsum2(false(), xs, y) -> sum2(cons(p(head(xs)), tail(xs)), s(y))
     , isNil(nil()) -> true()
     , isNil(cons(x, xs)) -> false()
     , tail(nil()) -> nil()
     , tail(cons(x, xs)) -> xs
     , head(cons(x, xs)) -> x
     , head(nil()) -> error()
     , isZero(0()) -> true()
     , isZero(s(0())) -> false()
     , isZero(s(s(x))) -> isZero(s(x))
     , p(0()) -> s(s(0()))
     , p(s(0())) -> 0()
     , p(s(s(x))) -> s(p(s(x)))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , a() -> c()
     , a() -> d()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.196
Answer	MAYBE
Input	Secret 07 TRS aprove01

MAYBE

We consider the following Problem:

  Strict Trs:
    {  times(x, y) -> sum(generate(x, y))
     , generate(x, y) -> gen(x, y, 0())
     , gen(x, y, z) -> if(ge(z, x), x, y, z)
     , if(true(), x, y, z) -> nil()
     , if(false(), x, y, z) -> cons(y, gen(x, y, s(z)))
     , sum(xs) -> sum2(xs, 0())
     , sum2(xs, y) -> ifsum(isNil(xs), isZero(head(xs)), xs, y)
     , ifsum(true(), b, xs, y) -> y
     , ifsum(false(), b, xs, y) -> ifsum2(b, xs, y)
     , ifsum2(true(), xs, y) -> sum2(tail(xs), y)
     , ifsum2(false(), xs, y) -> sum2(cons(p(head(xs)), tail(xs)), s(y))
     , isNil(nil()) -> true()
     , isNil(cons(x, xs)) -> false()
     , tail(nil()) -> nil()
     , tail(cons(x, xs)) -> xs
     , head(cons(x, xs)) -> x
     , head(nil()) -> error()
     , isZero(0()) -> true()
     , isZero(s(0())) -> false()
     , isZero(s(s(x))) -> isZero(s(x))
     , p(0()) -> s(s(0()))
     , p(s(0())) -> 0()
     , p(s(s(x))) -> s(p(s(x)))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , a() -> c()
     , a() -> d()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.179
Answer	MAYBE
Input	Secret 07 TRS aprove01

MAYBE

We consider the following Problem:

  Strict Trs:
    {  times(x, y) -> sum(generate(x, y))
     , generate(x, y) -> gen(x, y, 0())
     , gen(x, y, z) -> if(ge(z, x), x, y, z)
     , if(true(), x, y, z) -> nil()
     , if(false(), x, y, z) -> cons(y, gen(x, y, s(z)))
     , sum(xs) -> sum2(xs, 0())
     , sum2(xs, y) -> ifsum(isNil(xs), isZero(head(xs)), xs, y)
     , ifsum(true(), b, xs, y) -> y
     , ifsum(false(), b, xs, y) -> ifsum2(b, xs, y)
     , ifsum2(true(), xs, y) -> sum2(tail(xs), y)
     , ifsum2(false(), xs, y) -> sum2(cons(p(head(xs)), tail(xs)), s(y))
     , isNil(nil()) -> true()
     , isNil(cons(x, xs)) -> false()
     , tail(nil()) -> nil()
     , tail(cons(x, xs)) -> xs
     , head(cons(x, xs)) -> x
     , head(nil()) -> error()
     , isZero(0()) -> true()
     , isZero(s(0())) -> false()
     , isZero(s(s(x))) -> isZero(s(x))
     , p(0()) -> s(s(0()))
     , p(s(0())) -> 0()
     , p(s(s(x))) -> s(p(s(x)))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , a() -> c()
     , a() -> d()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.201
Answer	MAYBE
Input	Secret 07 TRS aprove01

MAYBE

We consider the following Problem:

  Strict Trs:
    {  times(x, y) -> sum(generate(x, y))
     , generate(x, y) -> gen(x, y, 0())
     , gen(x, y, z) -> if(ge(z, x), x, y, z)
     , if(true(), x, y, z) -> nil()
     , if(false(), x, y, z) -> cons(y, gen(x, y, s(z)))
     , sum(xs) -> sum2(xs, 0())
     , sum2(xs, y) -> ifsum(isNil(xs), isZero(head(xs)), xs, y)
     , ifsum(true(), b, xs, y) -> y
     , ifsum(false(), b, xs, y) -> ifsum2(b, xs, y)
     , ifsum2(true(), xs, y) -> sum2(tail(xs), y)
     , ifsum2(false(), xs, y) -> sum2(cons(p(head(xs)), tail(xs)), s(y))
     , isNil(nil()) -> true()
     , isNil(cons(x, xs)) -> false()
     , tail(nil()) -> nil()
     , tail(cons(x, xs)) -> xs
     , head(cons(x, xs)) -> x
     , head(nil()) -> error()
     , isZero(0()) -> true()
     , isZero(s(0())) -> false()
     , isZero(s(s(x))) -> isZero(s(x))
     , p(0()) -> s(s(0()))
     , p(s(0())) -> 0()
     , p(s(s(x))) -> s(p(s(x)))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , a() -> c()
     , a() -> d()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.210
Answer	MAYBE
Input	Secret 07 TRS aprove01

MAYBE

We consider the following Problem:

  Strict Trs:
    {  times(x, y) -> sum(generate(x, y))
     , generate(x, y) -> gen(x, y, 0())
     , gen(x, y, z) -> if(ge(z, x), x, y, z)
     , if(true(), x, y, z) -> nil()
     , if(false(), x, y, z) -> cons(y, gen(x, y, s(z)))
     , sum(xs) -> sum2(xs, 0())
     , sum2(xs, y) -> ifsum(isNil(xs), isZero(head(xs)), xs, y)
     , ifsum(true(), b, xs, y) -> y
     , ifsum(false(), b, xs, y) -> ifsum2(b, xs, y)
     , ifsum2(true(), xs, y) -> sum2(tail(xs), y)
     , ifsum2(false(), xs, y) -> sum2(cons(p(head(xs)), tail(xs)), s(y))
     , isNil(nil()) -> true()
     , isNil(cons(x, xs)) -> false()
     , tail(nil()) -> nil()
     , tail(cons(x, xs)) -> xs
     , head(cons(x, xs)) -> x
     , head(nil()) -> error()
     , isZero(0()) -> true()
     , isZero(s(0())) -> false()
     , isZero(s(s(x))) -> isZero(s(x))
     , p(0()) -> s(s(0()))
     , p(s(0())) -> 0()
     , p(s(s(x))) -> s(p(s(x)))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , a() -> c()
     , a() -> d()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Secret 07 TRS aprove01

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)