Problem Transformed CSR 04 Ex1 Luc04b GM

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex1 Luc04b GM

stdout:

MAYBE

Problem:
a__nats() -> cons(0(),incr(nats()))
a__pairs() -> cons(0(),incr(odds()))
a__odds() -> a__incr(a__pairs())
a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
a__head(cons(X,XS)) -> mark(X)
a__tail(cons(X,XS)) -> mark(XS)
mark(nats()) -> a__nats()
mark(incr(X)) -> a__incr(mark(X))
mark(pairs()) -> a__pairs()
mark(odds()) -> a__odds()
mark(head(X)) -> a__head(mark(X))
mark(tail(X)) -> a__tail(mark(X))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(0()) -> 0()
mark(s(X)) -> s(mark(X))
a__nats() -> nats()
a__incr(X) -> incr(X)
a__pairs() -> pairs()
a__odds() -> odds()
a__head(X) -> head(X)
a__tail(X) -> tail(X)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex1 Luc04b GM

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex1 Luc04b GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  a__nats() -> cons(0(), incr(nats()))
     , a__pairs() -> cons(0(), incr(odds()))
     , a__odds() -> a__incr(a__pairs())
     , a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
     , a__head(cons(X, XS)) -> mark(X)
     , a__tail(cons(X, XS)) -> mark(XS)
     , mark(nats()) -> a__nats()
     , mark(incr(X)) -> a__incr(mark(X))
     , mark(pairs()) -> a__pairs()
     , mark(odds()) -> a__odds()
     , mark(head(X)) -> a__head(mark(X))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , a__nats() -> nats()
     , a__incr(X) -> incr(X)
     , a__pairs() -> pairs()
     , a__odds() -> odds()
     , a__head(X) -> head(X)
     , a__tail(X) -> tail(X)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex1 Luc04b GM

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex1 Luc04b GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  a__nats() -> cons(0(), incr(nats()))
     , a__pairs() -> cons(0(), incr(odds()))
     , a__odds() -> a__incr(a__pairs())
     , a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
     , a__head(cons(X, XS)) -> mark(X)
     , a__tail(cons(X, XS)) -> mark(XS)
     , mark(nats()) -> a__nats()
     , mark(incr(X)) -> a__incr(mark(X))
     , mark(pairs()) -> a__pairs()
     , mark(odds()) -> a__odds()
     , mark(head(X)) -> a__head(mark(X))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , a__nats() -> nats()
     , a__incr(X) -> incr(X)
     , a__pairs() -> pairs()
     , a__odds() -> odds()
     , a__head(X) -> head(X)
     , a__tail(X) -> tail(X)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds