Problem Secret 07 TRS aprove05

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Secret 07 TRS aprove05

stdout:

MAYBE

Problem:
prod(xs) -> prodIter(xs,s(0()))
prodIter(xs,x) -> ifProd(isempty(xs),xs,x)
ifProd(true(),xs,x) -> x
ifProd(false(),xs,x) -> prodIter(tail(xs),times(x,head(xs)))
plus(0(),y) -> y
plus(s(x),y) -> s(plus(x,y))
times(x,y) -> timesIter(x,y,0(),0())
timesIter(x,y,z,u) -> ifTimes(ge(u,x),x,y,z,u)
ifTimes(true(),x,y,z,u) -> z
ifTimes(false(),x,y,z,u) -> timesIter(x,y,plus(y,z),s(u))
isempty(nil()) -> true()
isempty(cons(x,xs)) -> false()
head(nil()) -> error()
head(cons(x,xs)) -> x
tail(nil()) -> nil()
tail(cons(x,xs)) -> xs
ge(x,0()) -> true()
ge(0(),s(y)) -> false()
ge(s(x),s(y)) -> ge(x,y)
a() -> b()
a() -> c()

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Secret 07 TRS aprove05

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Secret 07 TRS aprove05

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  prod(xs) -> prodIter(xs, s(0()))
     , prodIter(xs, x) -> ifProd(isempty(xs), xs, x)
     , ifProd(true(), xs, x) -> x
     , ifProd(false(), xs, x) -> prodIter(tail(xs), times(x, head(xs)))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , times(x, y) -> timesIter(x, y, 0(), 0())
     , timesIter(x, y, z, u) -> ifTimes(ge(u, x), x, y, z, u)
     , ifTimes(true(), x, y, z, u) -> z
     , ifTimes(false(), x, y, z, u) -> timesIter(x, y, plus(y, z), s(u))
     , isempty(nil()) -> true()
     , isempty(cons(x, xs)) -> false()
     , head(nil()) -> error()
     , head(cons(x, xs)) -> x
     , tail(nil()) -> nil()
     , tail(cons(x, xs)) -> xs
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , a() -> b()
     , a() -> c()}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Secret 07 TRS aprove05

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Secret 07 TRS aprove05

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  prod(xs) -> prodIter(xs, s(0()))
     , prodIter(xs, x) -> ifProd(isempty(xs), xs, x)
     , ifProd(true(), xs, x) -> x
     , ifProd(false(), xs, x) -> prodIter(tail(xs), times(x, head(xs)))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , times(x, y) -> timesIter(x, y, 0(), 0())
     , timesIter(x, y, z, u) -> ifTimes(ge(u, x), x, y, z, u)
     , ifTimes(true(), x, y, z, u) -> z
     , ifTimes(false(), x, y, z, u) -> timesIter(x, y, plus(y, z), s(u))
     , isempty(nil()) -> true()
     , isempty(cons(x, xs)) -> false()
     , head(nil()) -> error()
     , head(cons(x, xs)) -> x
     , tail(nil()) -> nil()
     , tail(cons(x, xs)) -> xs
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , a() -> b()
     , a() -> c()}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds