Problem Transformed CSR 04 ExAppendixB AEL03 GM

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 ExAppendixB AEL03 GM

stdout:

MAYBE

Problem:
a__from(X) -> cons(mark(X),from(s(X)))
a__2ndspos(0(),Z) -> rnil()
a__2ndspos(s(N),cons(X,Z)) -> a__2ndspos(s(mark(N)),cons2(X,mark(Z)))
a__2ndspos(s(N),cons2(X,cons(Y,Z))) -> rcons(posrecip(mark(Y)),a__2ndsneg(mark(N),mark(Z)))
a__2ndsneg(0(),Z) -> rnil()
a__2ndsneg(s(N),cons(X,Z)) -> a__2ndsneg(s(mark(N)),cons2(X,mark(Z)))
a__2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(mark(Y)),a__2ndspos(mark(N),mark(Z)))
a__pi(X) -> a__2ndspos(mark(X),a__from(0()))
a__plus(0(),Y) -> mark(Y)
a__plus(s(X),Y) -> s(a__plus(mark(X),mark(Y)))
a__times(0(),Y) -> 0()
a__times(s(X),Y) -> a__plus(mark(Y),a__times(mark(X),mark(Y)))
a__square(X) -> a__times(mark(X),mark(X))
mark(from(X)) -> a__from(mark(X))
mark(2ndspos(X1,X2)) -> a__2ndspos(mark(X1),mark(X2))
mark(2ndsneg(X1,X2)) -> a__2ndsneg(mark(X1),mark(X2))
mark(pi(X)) -> a__pi(mark(X))
mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
mark(times(X1,X2)) -> a__times(mark(X1),mark(X2))
mark(square(X)) -> a__square(mark(X))
mark(0()) -> 0()
mark(s(X)) -> s(mark(X))
mark(posrecip(X)) -> posrecip(mark(X))
mark(negrecip(X)) -> negrecip(mark(X))
mark(nil()) -> nil()
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(cons2(X1,X2)) -> cons2(X1,mark(X2))
mark(rnil()) -> rnil()
mark(rcons(X1,X2)) -> rcons(mark(X1),mark(X2))
a__from(X) -> from(X)
a__2ndspos(X1,X2) -> 2ndspos(X1,X2)
a__2ndsneg(X1,X2) -> 2ndsneg(X1,X2)
a__pi(X) -> pi(X)
a__plus(X1,X2) -> plus(X1,X2)
a__times(X1,X2) -> times(X1,X2)
a__square(X) -> square(X)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 ExAppendixB AEL03 GM

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 ExAppendixB AEL03 GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__2ndspos(0(), Z) -> rnil()
     , a__2ndspos(s(N), cons(X, Z)) ->
       a__2ndspos(s(mark(N)), cons2(X, mark(Z)))
     , a__2ndspos(s(N), cons2(X, cons(Y, Z))) ->
       rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
     , a__2ndsneg(0(), Z) -> rnil()
     , a__2ndsneg(s(N), cons(X, Z)) ->
       a__2ndsneg(s(mark(N)), cons2(X, mark(Z)))
     , a__2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
       rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
     , a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
     , a__plus(0(), Y) -> mark(Y)
     , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
     , a__times(0(), Y) -> 0()
     , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
     , a__square(X) -> a__times(mark(X), mark(X))
     , mark(from(X)) -> a__from(mark(X))
     , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
     , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
     , mark(pi(X)) -> a__pi(mark(X))
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
     , mark(square(X)) -> a__square(mark(X))
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(posrecip(X)) -> posrecip(mark(X))
     , mark(negrecip(X)) -> negrecip(mark(X))
     , mark(nil()) -> nil()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(cons2(X1, X2)) -> cons2(X1, mark(X2))
     , mark(rnil()) -> rnil()
     , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
     , a__from(X) -> from(X)
     , a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
     , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
     , a__pi(X) -> pi(X)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__times(X1, X2) -> times(X1, X2)
     , a__square(X) -> square(X)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 ExAppendixB AEL03 GM

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 ExAppendixB AEL03 GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__2ndspos(0(), Z) -> rnil()
     , a__2ndspos(s(N), cons(X, Z)) ->
       a__2ndspos(s(mark(N)), cons2(X, mark(Z)))
     , a__2ndspos(s(N), cons2(X, cons(Y, Z))) ->
       rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
     , a__2ndsneg(0(), Z) -> rnil()
     , a__2ndsneg(s(N), cons(X, Z)) ->
       a__2ndsneg(s(mark(N)), cons2(X, mark(Z)))
     , a__2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
       rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
     , a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
     , a__plus(0(), Y) -> mark(Y)
     , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
     , a__times(0(), Y) -> 0()
     , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
     , a__square(X) -> a__times(mark(X), mark(X))
     , mark(from(X)) -> a__from(mark(X))
     , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
     , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
     , mark(pi(X)) -> a__pi(mark(X))
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
     , mark(square(X)) -> a__square(mark(X))
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(posrecip(X)) -> posrecip(mark(X))
     , mark(negrecip(X)) -> negrecip(mark(X))
     , mark(nil()) -> nil()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(cons2(X1, X2)) -> cons2(X1, mark(X2))
     , mark(rnil()) -> rnil()
     , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
     , a__from(X) -> from(X)
     , a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
     , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
     , a__pi(X) -> pi(X)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__times(X1, X2) -> times(X1, X2)
     , a__square(X) -> square(X)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds