/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


MAYBE
proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


H-Termination with start terms of the given HASKELL could not be shown:

(0) HASKELL
(1) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) Narrow [SOUND, 0 ms]
(6) QDP
    (7) NonTerminationLoopProof [COMPLETE, 0 ms]
    (8) NO
(9) Narrow [COMPLETE, 0 ms]
(10) QDP
    (11) PisEmptyProof [EQUIVALENT, 0 ms]
    (12) YES


----------------------------------------

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data List a = Cons a (List a)  | Nil ;

iterate :: (a  ->  a)  ->  a  ->  List a;
iterate f x = Cons x (iterate f (f x));

}

----------------------------------------

(1) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.
----------------------------------------

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data List a = Cons a (List a)  | Nil ;

iterate :: (a  ->  a)  ->  a  ->  List a;
iterate f x = Cons x (iterate f (f x));

}

----------------------------------------

(3) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"

----------------------------------------

(4)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data List a = Cons a (List a)  | Nil ;

iterate :: (a  ->  a)  ->  a  ->  List a;
iterate f x = Cons x (iterate f (f x));

}

----------------------------------------

(5) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="iterate",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="iterate vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="iterate vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="Cons vx4 (iterate vx3 (vx3 vx4))",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3];
6 -> 4[label="",style="dashed", color="red", weight=0];
6[label="iterate vx3 (vx3 vx4)",fontsize=16,color="magenta"];6 -> 7[label="",style="dashed", color="magenta", weight=3];
7[label="vx3 vx4",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3];
8[label="vx4",fontsize=16,color="green",shape="box"];}

----------------------------------------

(6)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_iterate(vx3, h) -> new_iterate(vx3, h)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(7) NonTerminationLoopProof (COMPLETE)
We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = new_iterate(vx3, h) evaluates to  t =new_iterate(vx3, h)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
* Matcher: [ ]
* Semiunifier: [ ]

--------------------------------------------------------------------------------
Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from new_iterate(vx3, h) to new_iterate(vx3, h).




----------------------------------------

(8)
NO

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(9) Narrow (COMPLETE)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="iterate",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="iterate vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="iterate vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="Cons vx4 (iterate vx3 (vx3 vx4))",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3];
6 -> 4[label="",style="dashed", color="red", weight=0];
6[label="iterate vx3 (vx3 vx4)",fontsize=16,color="magenta"];6 -> 7[label="",style="dashed", color="magenta", weight=3];
7[label="vx3 vx4",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3];
8[label="vx4",fontsize=16,color="green",shape="box"];}

----------------------------------------

(10)
Obligation:
Q DP problem:
P is empty.
R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.
----------------------------------------

(11) PisEmptyProof (EQUIVALENT)
The TRS P is empty. Hence, there is no (P,Q,R) chain.
----------------------------------------

(12)
YES