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


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NO
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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 be disproven:

(0) HASKELL
(1) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) Narrow [COMPLETE, 0 ms]
(6) QDP
(7) NonTerminationLoopProof [COMPLETE, 0 ms]
(8) NO


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(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

minBoundMyInt :: MyInt;
minBoundMyInt = primMinInt;

primMinInt :: MyInt;
primMinInt = primMinInt;

}

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

minBoundMyInt :: MyInt;
minBoundMyInt = primMinInt;

primMinInt :: MyInt;
primMinInt = primMinInt;

}

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(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 MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

minBoundMyInt :: MyInt;
minBoundMyInt = primMinInt;

primMinInt :: MyInt;
primMinInt = primMinInt;

}

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(5) Narrow (COMPLETE)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="minBoundMyInt",fontsize=16,color="black",shape="box"];1 -> 3[label="",style="solid", color="black", weight=3];
3[label="primMinInt",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4 -> 3[label="",style="dashed", color="red", weight=0];
4[label="primMinInt",fontsize=16,color="magenta"];}

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

   new_primMinInt([]) -> new_primMinInt([])

R is empty.
Q is empty.
We have to consider all (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_primMinInt([]) evaluates to  t =new_primMinInt([])

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

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Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from new_primMinInt([]) to new_primMinInt([]).




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(8)
NO