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


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


H-Termination with start terms of the given HASKELL could be proven:

(0) HASKELL
(1) LR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) Narrow [SOUND, 0 ms]
(8) QDP
(9) QDPSizeChangeProof [EQUIVALENT, 0 ms]
(10) YES


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(1) LR (EQUIVALENT)
Lambda Reductions:
The following Lambda expression
"\_->q"
is transformed to
"gtGt0 q _ = q;
"

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

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

(4)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(5) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"randomSelect (x : []) = x;
randomSelect (x : xs)|terminatorrandomSelect xs|otherwisex;
"
is transformed to
"randomSelect (x : []) = randomSelect3 (x : []);
randomSelect (x : xs) = randomSelect2 (x : xs);
"
"randomSelect0 x xs True = x;
"
"randomSelect1 x xs True = randomSelect xs;
randomSelect1 x xs False = randomSelect0 x xs otherwise;
"
"randomSelect2 (x : xs) = randomSelect1 x xs terminator;
"
"randomSelect3 (x : []) = x;
randomSelect3 wv = randomSelect2 wv;
"
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"

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

(6)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(7) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="putStr",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="putStr ww3",fontsize=16,color="burlywood",shape="triangle"];50[label="ww3/ww30 : ww31",fontsize=10,color="white",style="solid",shape="box"];3 -> 50[label="",style="solid", color="burlywood", weight=9];
50 -> 4[label="",style="solid", color="burlywood", weight=3];
51[label="ww3/[]",fontsize=10,color="white",style="solid",shape="box"];3 -> 51[label="",style="solid", color="burlywood", weight=9];
51 -> 5[label="",style="solid", color="burlywood", weight=3];
4[label="putStr (ww30 : ww31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3];
5[label="putStr []",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
6 -> 8[label="",style="dashed", color="red", weight=0];
6[label="putChar ww30 >> putStr ww31",fontsize=16,color="magenta"];6 -> 9[label="",style="dashed", color="magenta", weight=3];
7[label="output",fontsize=16,color="black",shape="triangle"];7 -> 10[label="",style="solid", color="black", weight=3];
9 -> 3[label="",style="dashed", color="red", weight=0];
9[label="putStr ww31",fontsize=16,color="magenta"];9 -> 11[label="",style="dashed", color="magenta", weight=3];
8[label="putChar ww30 >> ww4",fontsize=16,color="black",shape="triangle"];8 -> 12[label="",style="solid", color="black", weight=3];
10[label="randomSelect (aIOE IOError_FullError : aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3];
11[label="ww31",fontsize=16,color="green",shape="box"];12[label="putChar ww30 >>= gtGt0 ww4",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
13[label="randomSelect2 (aIOE IOError_FullError : aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
14[label="primbindIO (putChar ww30) (gtGt0 ww4)",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
15[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) terminator",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
16 -> 18[label="",style="dashed", color="red", weight=0];
16[label="primbindIO (seq ww30 output) (gtGt0 ww4)",fontsize=16,color="magenta"];16 -> 19[label="",style="dashed", color="magenta", weight=3];
17[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) ter0m",fontsize=16,color="burlywood",shape="box"];52[label="ter0m/False",fontsize=10,color="white",style="solid",shape="box"];17 -> 52[label="",style="solid", color="burlywood", weight=9];
52 -> 20[label="",style="solid", color="burlywood", weight=3];
53[label="ter0m/True",fontsize=10,color="white",style="solid",shape="box"];17 -> 53[label="",style="solid", color="burlywood", weight=9];
53 -> 21[label="",style="solid", color="burlywood", weight=3];
19 -> 7[label="",style="dashed", color="red", weight=0];
19[label="output",fontsize=16,color="magenta"];18[label="primbindIO (seq ww30 ww5) (gtGt0 ww4)",fontsize=16,color="black",shape="triangle"];18 -> 22[label="",style="solid", color="black", weight=3];
20[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) False",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3];
21[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];21 -> 24[label="",style="solid", color="black", weight=3];
22[label="primbindIO (enforceWHNF (WHNF ww30) ww5) (gtGt0 ww4)",fontsize=16,color="black",shape="box"];22 -> 25[label="",style="solid", color="black", weight=3];
23[label="randomSelect0 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) otherwise",fontsize=16,color="black",shape="box"];23 -> 26[label="",style="solid", color="black", weight=3];
24[label="randomSelect (aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];24 -> 27[label="",style="solid", color="black", weight=3];
25[label="primbindIO ww5 (gtGt0 ww4)",fontsize=16,color="burlywood",shape="box"];54[label="ww5/IO ww50",fontsize=10,color="white",style="solid",shape="box"];25 -> 54[label="",style="solid", color="burlywood", weight=9];
54 -> 28[label="",style="solid", color="burlywood", weight=3];
55[label="ww5/AProVE_IO ww50",fontsize=10,color="white",style="solid",shape="box"];25 -> 55[label="",style="solid", color="burlywood", weight=9];
55 -> 29[label="",style="solid", color="burlywood", weight=3];
56[label="ww5/AProVE_Exception ww50",fontsize=10,color="white",style="solid",shape="box"];25 -> 56[label="",style="solid", color="burlywood", weight=9];
56 -> 30[label="",style="solid", color="burlywood", weight=3];
57[label="ww5/AProVE_Error ww50",fontsize=10,color="white",style="solid",shape="box"];25 -> 57[label="",style="solid", color="burlywood", weight=9];
57 -> 31[label="",style="solid", color="burlywood", weight=3];
26[label="randomSelect0 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];26 -> 32[label="",style="solid", color="black", weight=3];
27[label="randomSelect2 (aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];27 -> 33[label="",style="solid", color="black", weight=3];
28[label="primbindIO (IO ww50) (gtGt0 ww4)",fontsize=16,color="black",shape="box"];28 -> 34[label="",style="solid", color="black", weight=3];
29[label="primbindIO (AProVE_IO ww50) (gtGt0 ww4)",fontsize=16,color="black",shape="box"];29 -> 35[label="",style="solid", color="black", weight=3];
30[label="primbindIO (AProVE_Exception ww50) (gtGt0 ww4)",fontsize=16,color="black",shape="box"];30 -> 36[label="",style="solid", color="black", weight=3];
31[label="primbindIO (AProVE_Error ww50) (gtGt0 ww4)",fontsize=16,color="black",shape="box"];31 -> 37[label="",style="solid", color="black", weight=3];
32[label="aIOE IOError_FullError",fontsize=16,color="black",shape="box"];32 -> 38[label="",style="solid", color="black", weight=3];
33[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) terminator",fontsize=16,color="black",shape="box"];33 -> 39[label="",style="solid", color="black", weight=3];
34[label="error []",fontsize=16,color="red",shape="box"];35[label="gtGt0 ww4 ww50",fontsize=16,color="black",shape="box"];35 -> 40[label="",style="solid", color="black", weight=3];
36[label="AProVE_Exception ww50",fontsize=16,color="green",shape="box"];37[label="AProVE_Error ww50",fontsize=16,color="green",shape="box"];38[label="AProVE_Exception (AET_IOError (IOError IOError_FullError [] [] Nothing))",fontsize=16,color="green",shape="box"];39[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) ter1m",fontsize=16,color="burlywood",shape="box"];58[label="ter1m/False",fontsize=10,color="white",style="solid",shape="box"];39 -> 58[label="",style="solid", color="burlywood", weight=9];
58 -> 41[label="",style="solid", color="burlywood", weight=3];
59[label="ter1m/True",fontsize=10,color="white",style="solid",shape="box"];39 -> 59[label="",style="solid", color="burlywood", weight=9];
59 -> 42[label="",style="solid", color="burlywood", weight=3];
40[label="ww4",fontsize=16,color="green",shape="box"];41[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) False",fontsize=16,color="black",shape="box"];41 -> 43[label="",style="solid", color="black", weight=3];
42[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];42 -> 44[label="",style="solid", color="black", weight=3];
43[label="randomSelect0 (aIOE IOError_PermDenied) (AProVE_IO () : []) otherwise",fontsize=16,color="black",shape="box"];43 -> 45[label="",style="solid", color="black", weight=3];
44[label="randomSelect (AProVE_IO () : [])",fontsize=16,color="black",shape="box"];44 -> 46[label="",style="solid", color="black", weight=3];
45[label="randomSelect0 (aIOE IOError_PermDenied) (AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];45 -> 47[label="",style="solid", color="black", weight=3];
46[label="randomSelect3 (AProVE_IO () : [])",fontsize=16,color="black",shape="box"];46 -> 48[label="",style="solid", color="black", weight=3];
47[label="aIOE IOError_PermDenied",fontsize=16,color="black",shape="box"];47 -> 49[label="",style="solid", color="black", weight=3];
48[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];49[label="AProVE_Exception (AET_IOError (IOError IOError_PermDenied [] [] Nothing))",fontsize=16,color="green",shape="box"];}

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

(8)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_putStr(:(ww30, ww31)) -> new_putStr(ww31)

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

(9) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*new_putStr(:(ww30, ww31)) -> new_putStr(ww31)
The graph contains the following edges 1 > 1


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

(10)
YES