LMPO

Execution Time (secs)	0.115
Answer	MAYBE
Input	Secret 06 TRS times

MAYBE

We consider the following Problem:

  Strict Trs:
    {  inc(s(x)) -> s(inc(x))
     , inc(0()) -> s(0())
     , plus(x, y) -> ifPlus(eq(x, 0()), minus(x, s(0())), x, inc(x))
     , ifPlus(false(), x, y, z) -> plus(x, z)
     , ifPlus(true(), x, y, z) -> y
     , minus(s(x), s(y)) -> minus(x, y)
     , minus(0(), x) -> 0()
     , minus(x, 0()) -> x
     , minus(x, x) -> 0()
     , eq(s(x), s(y)) -> eq(x, y)
     , eq(0(), s(x)) -> false()
     , eq(s(x), 0()) -> false()
     , eq(0(), 0()) -> true()
     , eq(x, x) -> true()
     , times(x, y) -> timesIter(x, y, 0())
     , timesIter(x, y, z) ->
       ifTimes(eq(x, 0()), minus(x, s(0())), y, z, plus(y, z))
     , ifTimes(true(), x, y, z, u) -> z
     , ifTimes(false(), x, y, z, u) -> timesIter(x, y, u)
     , f() -> g()
     , f() -> h()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.145
Answer	MAYBE
Input	Secret 06 TRS times

MAYBE

We consider the following Problem:

  Strict Trs:
    {  inc(s(x)) -> s(inc(x))
     , inc(0()) -> s(0())
     , plus(x, y) -> ifPlus(eq(x, 0()), minus(x, s(0())), x, inc(x))
     , ifPlus(false(), x, y, z) -> plus(x, z)
     , ifPlus(true(), x, y, z) -> y
     , minus(s(x), s(y)) -> minus(x, y)
     , minus(0(), x) -> 0()
     , minus(x, 0()) -> x
     , minus(x, x) -> 0()
     , eq(s(x), s(y)) -> eq(x, y)
     , eq(0(), s(x)) -> false()
     , eq(s(x), 0()) -> false()
     , eq(0(), 0()) -> true()
     , eq(x, x) -> true()
     , times(x, y) -> timesIter(x, y, 0())
     , timesIter(x, y, z) ->
       ifTimes(eq(x, 0()), minus(x, s(0())), y, z, plus(y, z))
     , ifTimes(true(), x, y, z, u) -> z
     , ifTimes(false(), x, y, z, u) -> timesIter(x, y, u)
     , f() -> g()
     , f() -> h()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.122
Answer	MAYBE
Input	Secret 06 TRS times

MAYBE

We consider the following Problem:

  Strict Trs:
    {  inc(s(x)) -> s(inc(x))
     , inc(0()) -> s(0())
     , plus(x, y) -> ifPlus(eq(x, 0()), minus(x, s(0())), x, inc(x))
     , ifPlus(false(), x, y, z) -> plus(x, z)
     , ifPlus(true(), x, y, z) -> y
     , minus(s(x), s(y)) -> minus(x, y)
     , minus(0(), x) -> 0()
     , minus(x, 0()) -> x
     , minus(x, x) -> 0()
     , eq(s(x), s(y)) -> eq(x, y)
     , eq(0(), s(x)) -> false()
     , eq(s(x), 0()) -> false()
     , eq(0(), 0()) -> true()
     , eq(x, x) -> true()
     , times(x, y) -> timesIter(x, y, 0())
     , timesIter(x, y, z) ->
       ifTimes(eq(x, 0()), minus(x, s(0())), y, z, plus(y, z))
     , ifTimes(true(), x, y, z, u) -> z
     , ifTimes(false(), x, y, z, u) -> timesIter(x, y, u)
     , f() -> g()
     , f() -> h()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.187
Answer	MAYBE
Input	Secret 06 TRS times

MAYBE

We consider the following Problem:

  Strict Trs:
    {  inc(s(x)) -> s(inc(x))
     , inc(0()) -> s(0())
     , plus(x, y) -> ifPlus(eq(x, 0()), minus(x, s(0())), x, inc(x))
     , ifPlus(false(), x, y, z) -> plus(x, z)
     , ifPlus(true(), x, y, z) -> y
     , minus(s(x), s(y)) -> minus(x, y)
     , minus(0(), x) -> 0()
     , minus(x, 0()) -> x
     , minus(x, x) -> 0()
     , eq(s(x), s(y)) -> eq(x, y)
     , eq(0(), s(x)) -> false()
     , eq(s(x), 0()) -> false()
     , eq(0(), 0()) -> true()
     , eq(x, x) -> true()
     , times(x, y) -> timesIter(x, y, 0())
     , timesIter(x, y, z) ->
       ifTimes(eq(x, 0()), minus(x, s(0())), y, z, plus(y, z))
     , ifTimes(true(), x, y, z, u) -> z
     , ifTimes(false(), x, y, z, u) -> timesIter(x, y, u)
     , f() -> g()
     , f() -> h()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.122
Answer	MAYBE
Input	Secret 06 TRS times

MAYBE

We consider the following Problem:

  Strict Trs:
    {  inc(s(x)) -> s(inc(x))
     , inc(0()) -> s(0())
     , plus(x, y) -> ifPlus(eq(x, 0()), minus(x, s(0())), x, inc(x))
     , ifPlus(false(), x, y, z) -> plus(x, z)
     , ifPlus(true(), x, y, z) -> y
     , minus(s(x), s(y)) -> minus(x, y)
     , minus(0(), x) -> 0()
     , minus(x, 0()) -> x
     , minus(x, x) -> 0()
     , eq(s(x), s(y)) -> eq(x, y)
     , eq(0(), s(x)) -> false()
     , eq(s(x), 0()) -> false()
     , eq(0(), 0()) -> true()
     , eq(x, x) -> true()
     , times(x, y) -> timesIter(x, y, 0())
     , timesIter(x, y, z) ->
       ifTimes(eq(x, 0()), minus(x, s(0())), y, z, plus(y, z))
     , ifTimes(true(), x, y, z, u) -> z
     , ifTimes(false(), x, y, z, u) -> timesIter(x, y, u)
     , f() -> g()
     , f() -> h()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.142
Answer	MAYBE
Input	Secret 06 TRS times

MAYBE

We consider the following Problem:

  Strict Trs:
    {  inc(s(x)) -> s(inc(x))
     , inc(0()) -> s(0())
     , plus(x, y) -> ifPlus(eq(x, 0()), minus(x, s(0())), x, inc(x))
     , ifPlus(false(), x, y, z) -> plus(x, z)
     , ifPlus(true(), x, y, z) -> y
     , minus(s(x), s(y)) -> minus(x, y)
     , minus(0(), x) -> 0()
     , minus(x, 0()) -> x
     , minus(x, x) -> 0()
     , eq(s(x), s(y)) -> eq(x, y)
     , eq(0(), s(x)) -> false()
     , eq(s(x), 0()) -> false()
     , eq(0(), 0()) -> true()
     , eq(x, x) -> true()
     , times(x, y) -> timesIter(x, y, 0())
     , timesIter(x, y, z) ->
       ifTimes(eq(x, 0()), minus(x, s(0())), y, z, plus(y, z))
     , ifTimes(true(), x, y, z, u) -> z
     , ifTimes(false(), x, y, z, u) -> timesIter(x, y, u)
     , f() -> g()
     , f() -> h()}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Secret 06 TRS times

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)