Problem Secret 07 TRS aprove03

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Secret 07 TRS aprove03

stdout:

MAYBE

Problem:
average(x,y) -> if(ge(x,y),x,y)
if(true(),x,y) -> averIter(y,x,y)
if(false(),x,y) -> averIter(x,y,x)
averIter(x,y,z) -> ifIter(ge(x,y),x,y,z)
ifIter(true(),x,y,z) -> z
ifIter(false(),x,y,z) -> averIter(plus(x,s(s(s(0())))),plus(y,s(0())),plus(z,s(0())))
append(nil(),y) -> y
append(cons(n,x),y) -> cons(n,app(x,y))
low(n,nil()) -> nil()
low(n,cons(m,x)) -> if_low(ge(m,n),n,cons(m,x))
if_low(false(),n,cons(m,x)) -> cons(m,low(n,x))
if_low(true(),n,cons(m,x)) -> low(n,x)
high(n,nil()) -> nil()
high(n,cons(m,x)) -> if_high(ge(m,n),n,cons(m,x))
if_high(false(),n,cons(m,x)) -> high(n,x)
if_high(true(),n,cons(m,x)) -> cons(average(m,m),high(n,x))
quicksort(x) -> ifquick(isempty(x),x)
ifquick(true(),x) -> nil()
ifquick(false(),x) ->
append(quicksort(low(head(x),tail(x))),cons(tail(x),quicksort(high(head(x),tail(x)))))
plus(0(),y) -> y
plus(s(x),y) -> s(plus(x,y))
isempty(nil()) -> true()
isempty(cons(n,x)) -> false()
head(nil()) -> error()
head(cons(n,x)) -> n
tail(nil()) -> nil()
tail(cons(n,x)) -> x
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 aprove03

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Secret 07 TRS aprove03

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  average(x, y) -> if(ge(x, y), x, y)
     , if(true(), x, y) -> averIter(y, x, y)
     , if(false(), x, y) -> averIter(x, y, x)
     , averIter(x, y, z) -> ifIter(ge(x, y), x, y, z)
     , ifIter(true(), x, y, z) -> z
     , ifIter(false(), x, y, z) ->
       averIter(plus(x, s(s(s(0())))), plus(y, s(0())), plus(z, s(0())))
     , append(nil(), y) -> y
     , append(cons(n, x), y) -> cons(n, app(x, y))
     , low(n, nil()) -> nil()
     , low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x))
     , if_low(false(), n, cons(m, x)) -> cons(m, low(n, x))
     , if_low(true(), n, cons(m, x)) -> low(n, x)
     , high(n, nil()) -> nil()
     , high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x))
     , if_high(false(), n, cons(m, x)) -> high(n, x)
     , if_high(true(), n, cons(m, x)) -> cons(average(m, m), high(n, x))
     , quicksort(x) -> ifquick(isempty(x), x)
     , ifquick(true(), x) -> nil()
     , ifquick(false(), x) ->
       append(quicksort(low(head(x), tail(x))),
              cons(tail(x), quicksort(high(head(x), tail(x)))))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , isempty(nil()) -> true()
     , isempty(cons(n, x)) -> false()
     , head(nil()) -> error()
     , head(cons(n, x)) -> n
     , tail(nil()) -> nil()
     , tail(cons(n, x)) -> x
     , 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 aprove03

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Secret 07 TRS aprove03

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  average(x, y) -> if(ge(x, y), x, y)
     , if(true(), x, y) -> averIter(y, x, y)
     , if(false(), x, y) -> averIter(x, y, x)
     , averIter(x, y, z) -> ifIter(ge(x, y), x, y, z)
     , ifIter(true(), x, y, z) -> z
     , ifIter(false(), x, y, z) ->
       averIter(plus(x, s(s(s(0())))), plus(y, s(0())), plus(z, s(0())))
     , append(nil(), y) -> y
     , append(cons(n, x), y) -> cons(n, app(x, y))
     , low(n, nil()) -> nil()
     , low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x))
     , if_low(false(), n, cons(m, x)) -> cons(m, low(n, x))
     , if_low(true(), n, cons(m, x)) -> low(n, x)
     , high(n, nil()) -> nil()
     , high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x))
     , if_high(false(), n, cons(m, x)) -> high(n, x)
     , if_high(true(), n, cons(m, x)) -> cons(average(m, m), high(n, x))
     , quicksort(x) -> ifquick(isempty(x), x)
     , ifquick(true(), x) -> nil()
     , ifquick(false(), x) ->
       append(quicksort(low(head(x), tail(x))),
              cons(tail(x), quicksort(high(head(x), tail(x)))))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , isempty(nil()) -> true()
     , isempty(cons(n, x)) -> false()
     , head(nil()) -> error()
     , head(cons(n, x)) -> n
     , tail(nil()) -> nil()
     , tail(cons(n, x)) -> x
     , 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