Problem Transformed CSR 04 Ex1 2 AEL03 C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex1 2 AEL03 C

stdout:

MAYBE

Problem:
active(from(X)) -> mark(cons(X,from(s(X))))
active(2ndspos(0(),Z)) -> mark(rnil())
active(2ndspos(s(N),cons(X,cons(Y,Z)))) -> mark(rcons(posrecip(Y),2ndsneg(N,Z)))
active(2ndsneg(0(),Z)) -> mark(rnil())
active(2ndsneg(s(N),cons(X,cons(Y,Z)))) -> mark(rcons(negrecip(Y),2ndspos(N,Z)))
active(pi(X)) -> mark(2ndspos(X,from(0())))
active(plus(0(),Y)) -> mark(Y)
active(plus(s(X),Y)) -> mark(s(plus(X,Y)))
active(times(0(),Y)) -> mark(0())
active(times(s(X),Y)) -> mark(plus(Y,times(X,Y)))
active(square(X)) -> mark(times(X,X))
active(s(X)) -> s(active(X))
active(posrecip(X)) -> posrecip(active(X))
active(negrecip(X)) -> negrecip(active(X))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(rcons(X1,X2)) -> rcons(active(X1),X2)
active(rcons(X1,X2)) -> rcons(X1,active(X2))
active(from(X)) -> from(active(X))
active(2ndspos(X1,X2)) -> 2ndspos(active(X1),X2)
active(2ndspos(X1,X2)) -> 2ndspos(X1,active(X2))
active(2ndsneg(X1,X2)) -> 2ndsneg(active(X1),X2)
active(2ndsneg(X1,X2)) -> 2ndsneg(X1,active(X2))
active(pi(X)) -> pi(active(X))
active(plus(X1,X2)) -> plus(active(X1),X2)
active(plus(X1,X2)) -> plus(X1,active(X2))
active(times(X1,X2)) -> times(active(X1),X2)
active(times(X1,X2)) -> times(X1,active(X2))
active(square(X)) -> square(active(X))
s(mark(X)) -> mark(s(X))
posrecip(mark(X)) -> mark(posrecip(X))
negrecip(mark(X)) -> mark(negrecip(X))
cons(mark(X1),X2) -> mark(cons(X1,X2))
rcons(mark(X1),X2) -> mark(rcons(X1,X2))
rcons(X1,mark(X2)) -> mark(rcons(X1,X2))
from(mark(X)) -> mark(from(X))
2ndspos(mark(X1),X2) -> mark(2ndspos(X1,X2))
2ndspos(X1,mark(X2)) -> mark(2ndspos(X1,X2))
2ndsneg(mark(X1),X2) -> mark(2ndsneg(X1,X2))
2ndsneg(X1,mark(X2)) -> mark(2ndsneg(X1,X2))
pi(mark(X)) -> mark(pi(X))
plus(mark(X1),X2) -> mark(plus(X1,X2))
plus(X1,mark(X2)) -> mark(plus(X1,X2))
times(mark(X1),X2) -> mark(times(X1,X2))
times(X1,mark(X2)) -> mark(times(X1,X2))
square(mark(X)) -> mark(square(X))
proper(0()) -> ok(0())
proper(s(X)) -> s(proper(X))
proper(posrecip(X)) -> posrecip(proper(X))
proper(negrecip(X)) -> negrecip(proper(X))
proper(nil()) -> ok(nil())
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(rnil()) -> ok(rnil())
proper(rcons(X1,X2)) -> rcons(proper(X1),proper(X2))
proper(from(X)) -> from(proper(X))
proper(2ndspos(X1,X2)) -> 2ndspos(proper(X1),proper(X2))
proper(2ndsneg(X1,X2)) -> 2ndsneg(proper(X1),proper(X2))
proper(pi(X)) -> pi(proper(X))
proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
proper(times(X1,X2)) -> times(proper(X1),proper(X2))
proper(square(X)) -> square(proper(X))
s(ok(X)) -> ok(s(X))
posrecip(ok(X)) -> ok(posrecip(X))
negrecip(ok(X)) -> ok(negrecip(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
rcons(ok(X1),ok(X2)) -> ok(rcons(X1,X2))
from(ok(X)) -> ok(from(X))
2ndspos(ok(X1),ok(X2)) -> ok(2ndspos(X1,X2))
2ndsneg(ok(X1),ok(X2)) -> ok(2ndsneg(X1,X2))
pi(ok(X)) -> ok(pi(X))
plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
times(ok(X1),ok(X2)) -> ok(times(X1,X2))
square(ok(X)) -> ok(square(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex1 2 AEL03 C

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex1 2 AEL03 C

stdout:

TIMEOUT

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

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex1 2 AEL03 C

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex1 2 AEL03 C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  active(from(X)) -> mark(cons(X, from(s(X))))
     , active(2ndspos(0(), Z)) -> mark(rnil())
     , active(2ndspos(s(N), cons(X, cons(Y, Z)))) ->
       mark(rcons(posrecip(Y), 2ndsneg(N, Z)))
     , active(2ndsneg(0(), Z)) -> mark(rnil())
     , active(2ndsneg(s(N), cons(X, cons(Y, Z)))) ->
       mark(rcons(negrecip(Y), 2ndspos(N, Z)))
     , active(pi(X)) -> mark(2ndspos(X, from(0())))
     , active(plus(0(), Y)) -> mark(Y)
     , active(plus(s(X), Y)) -> mark(s(plus(X, Y)))
     , active(times(0(), Y)) -> mark(0())
     , active(times(s(X), Y)) -> mark(plus(Y, times(X, Y)))
     , active(square(X)) -> mark(times(X, X))
     , active(s(X)) -> s(active(X))
     , active(posrecip(X)) -> posrecip(active(X))
     , active(negrecip(X)) -> negrecip(active(X))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(rcons(X1, X2)) -> rcons(active(X1), X2)
     , active(rcons(X1, X2)) -> rcons(X1, active(X2))
     , active(from(X)) -> from(active(X))
     , active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2)
     , active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2))
     , active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2)
     , active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2))
     , active(pi(X)) -> pi(active(X))
     , active(plus(X1, X2)) -> plus(active(X1), X2)
     , active(plus(X1, X2)) -> plus(X1, active(X2))
     , active(times(X1, X2)) -> times(active(X1), X2)
     , active(times(X1, X2)) -> times(X1, active(X2))
     , active(square(X)) -> square(active(X))
     , s(mark(X)) -> mark(s(X))
     , posrecip(mark(X)) -> mark(posrecip(X))
     , negrecip(mark(X)) -> mark(negrecip(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , rcons(mark(X1), X2) -> mark(rcons(X1, X2))
     , rcons(X1, mark(X2)) -> mark(rcons(X1, X2))
     , from(mark(X)) -> mark(from(X))
     , 2ndspos(mark(X1), X2) -> mark(2ndspos(X1, X2))
     , 2ndspos(X1, mark(X2)) -> mark(2ndspos(X1, X2))
     , 2ndsneg(mark(X1), X2) -> mark(2ndsneg(X1, X2))
     , 2ndsneg(X1, mark(X2)) -> mark(2ndsneg(X1, X2))
     , pi(mark(X)) -> mark(pi(X))
     , plus(mark(X1), X2) -> mark(plus(X1, X2))
     , plus(X1, mark(X2)) -> mark(plus(X1, X2))
     , times(mark(X1), X2) -> mark(times(X1, X2))
     , times(X1, mark(X2)) -> mark(times(X1, X2))
     , square(mark(X)) -> mark(square(X))
     , proper(0()) -> ok(0())
     , proper(s(X)) -> s(proper(X))
     , proper(posrecip(X)) -> posrecip(proper(X))
     , proper(negrecip(X)) -> negrecip(proper(X))
     , proper(nil()) -> ok(nil())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(rnil()) -> ok(rnil())
     , proper(rcons(X1, X2)) -> rcons(proper(X1), proper(X2))
     , proper(from(X)) -> from(proper(X))
     , proper(2ndspos(X1, X2)) -> 2ndspos(proper(X1), proper(X2))
     , proper(2ndsneg(X1, X2)) -> 2ndsneg(proper(X1), proper(X2))
     , proper(pi(X)) -> pi(proper(X))
     , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
     , proper(times(X1, X2)) -> times(proper(X1), proper(X2))
     , proper(square(X)) -> square(proper(X))
     , s(ok(X)) -> ok(s(X))
     , posrecip(ok(X)) -> ok(posrecip(X))
     , negrecip(ok(X)) -> ok(negrecip(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , rcons(ok(X1), ok(X2)) -> ok(rcons(X1, X2))
     , from(ok(X)) -> ok(from(X))
     , 2ndspos(ok(X1), ok(X2)) -> ok(2ndspos(X1, X2))
     , 2ndsneg(ok(X1), ok(X2)) -> ok(2ndsneg(X1, X2))
     , pi(ok(X)) -> ok(pi(X))
     , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
     , times(ok(X1), ok(X2)) -> ok(times(X1, X2))
     , square(ok(X)) -> ok(square(X))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds