LMPO
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
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*
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)
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*
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)
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..