Problem Secret 07 TRS aprove06

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Secret 07 TRS aprove06

stdout:

MAYBE

Problem:
le(s(x),0()) -> false()
le(0(),y) -> true()
le(s(x),s(y)) -> le(x,y)
double(0()) -> 0()
double(s(x)) -> s(s(double(x)))
log(0()) -> logError()
log(s(x)) -> loop(s(x),s(0()),0())
loop(x,s(y),z) -> if(le(x,s(y)),x,s(y),z)
if(true(),x,y,z) -> z
if(false(),x,y,z) -> loop(x,double(y),s(z))
maplog(xs) -> mapIter(xs,nil())
mapIter(xs,ys) -> ifmap(isempty(xs),xs,ys)
ifmap(true(),xs,ys) -> ys
ifmap(false(),xs,ys) -> mapIter(droplast(xs),cons(log(last(xs)),ys))
isempty(nil()) -> true()
isempty(cons(x,xs)) -> false()
last(nil()) -> error()
last(cons(x,nil())) -> x
last(cons(x,cons(y,xs))) -> last(cons(y,xs))
droplast(nil()) -> nil()
droplast(cons(x,nil())) -> nil()
droplast(cons(x,cons(y,xs))) -> cons(x,droplast(cons(y,xs)))
a() -> b()
a() -> c()

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Secret 07 TRS aprove06

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Secret 07 TRS aprove06

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  le(s(x), 0()) -> false()
     , le(0(), y) -> true()
     , le(s(x), s(y)) -> le(x, y)
     , double(0()) -> 0()
     , double(s(x)) -> s(s(double(x)))
     , log(0()) -> logError()
     , log(s(x)) -> loop(s(x), s(0()), 0())
     , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z)
     , if(true(), x, y, z) -> z
     , if(false(), x, y, z) -> loop(x, double(y), s(z))
     , maplog(xs) -> mapIter(xs, nil())
     , mapIter(xs, ys) -> ifmap(isempty(xs), xs, ys)
     , ifmap(true(), xs, ys) -> ys
     , ifmap(false(), xs, ys) ->
       mapIter(droplast(xs), cons(log(last(xs)), ys))
     , isempty(nil()) -> true()
     , isempty(cons(x, xs)) -> false()
     , last(nil()) -> error()
     , last(cons(x, nil())) -> x
     , last(cons(x, cons(y, xs))) -> last(cons(y, xs))
     , droplast(nil()) -> nil()
     , droplast(cons(x, nil())) -> nil()
     , droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs)))
     , 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 aprove06

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Secret 07 TRS aprove06

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  le(s(x), 0()) -> false()
     , le(0(), y) -> true()
     , le(s(x), s(y)) -> le(x, y)
     , double(0()) -> 0()
     , double(s(x)) -> s(s(double(x)))
     , log(0()) -> logError()
     , log(s(x)) -> loop(s(x), s(0()), 0())
     , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z)
     , if(true(), x, y, z) -> z
     , if(false(), x, y, z) -> loop(x, double(y), s(z))
     , maplog(xs) -> mapIter(xs, nil())
     , mapIter(xs, ys) -> ifmap(isempty(xs), xs, ys)
     , ifmap(true(), xs, ys) -> ys
     , ifmap(false(), xs, ys) ->
       mapIter(droplast(xs), cons(log(last(xs)), ys))
     , isempty(nil()) -> true()
     , isempty(cons(x, xs)) -> false()
     , last(nil()) -> error()
     , last(cons(x, nil())) -> x
     , last(cons(x, cons(y, xs))) -> last(cons(y, xs))
     , droplast(nil()) -> nil()
     , droplast(cons(x, nil())) -> nil()
     , droplast(cons(x, cons(y, xs))) -> cons(x, droplast(cons(y, xs)))
     , a() -> b()
     , a() -> c()}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds