/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) Narrow [SOUND, 0 ms]
(6) QDP
(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
(8) YES


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

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

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

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

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

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

(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;
}

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

(5) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="fmap",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="fmap vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="fmap vx3 vx4",fontsize=16,color="blue",shape="box"];38[label="fmap :: (a -> b) -> (IO a) -> IO b",fontsize=10,color="white",style="solid",shape="box"];4 -> 38[label="",style="solid", color="blue", weight=9];
38 -> 5[label="",style="solid", color="blue", weight=3];
39[label="fmap :: (a -> b) -> (Maybe a) -> Maybe b",fontsize=10,color="white",style="solid",shape="box"];4 -> 39[label="",style="solid", color="blue", weight=9];
39 -> 6[label="",style="solid", color="blue", weight=3];
40[label="fmap :: (a -> b) -> ([] a) -> [] b",fontsize=10,color="white",style="solid",shape="box"];4 -> 40[label="",style="solid", color="blue", weight=9];
40 -> 7[label="",style="solid", color="blue", weight=3];
5[label="fmap vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 8[label="",style="solid", color="black", weight=3];
6[label="fmap vx3 vx4",fontsize=16,color="burlywood",shape="box"];41[label="vx4/Nothing",fontsize=10,color="white",style="solid",shape="box"];6 -> 41[label="",style="solid", color="burlywood", weight=9];
41 -> 9[label="",style="solid", color="burlywood", weight=3];
42[label="vx4/Just vx40",fontsize=10,color="white",style="solid",shape="box"];6 -> 42[label="",style="solid", color="burlywood", weight=9];
42 -> 10[label="",style="solid", color="burlywood", weight=3];
7[label="fmap vx3 vx4",fontsize=16,color="black",shape="box"];7 -> 11[label="",style="solid", color="black", weight=3];
8[label="vx4 >>= return . vx3",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
9[label="fmap vx3 Nothing",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
10[label="fmap vx3 (Just vx40)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11[label="map vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];43[label="vx4/vx40 : vx41",fontsize=10,color="white",style="solid",shape="box"];11 -> 43[label="",style="solid", color="burlywood", weight=9];
43 -> 15[label="",style="solid", color="burlywood", weight=3];
44[label="vx4/[]",fontsize=10,color="white",style="solid",shape="box"];11 -> 44[label="",style="solid", color="burlywood", weight=9];
44 -> 16[label="",style="solid", color="burlywood", weight=3];
12[label="primbindIO vx4 (return . vx3)",fontsize=16,color="burlywood",shape="box"];45[label="vx4/IO vx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 45[label="",style="solid", color="burlywood", weight=9];
45 -> 17[label="",style="solid", color="burlywood", weight=3];
46[label="vx4/AProVE_IO vx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 46[label="",style="solid", color="burlywood", weight=9];
46 -> 18[label="",style="solid", color="burlywood", weight=3];
47[label="vx4/AProVE_Exception vx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 47[label="",style="solid", color="burlywood", weight=9];
47 -> 19[label="",style="solid", color="burlywood", weight=3];
48[label="vx4/AProVE_Error vx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 48[label="",style="solid", color="burlywood", weight=9];
48 -> 20[label="",style="solid", color="burlywood", weight=3];
13[label="Nothing",fontsize=16,color="green",shape="box"];14[label="Just (vx3 vx40)",fontsize=16,color="green",shape="box"];14 -> 21[label="",style="dashed", color="green", weight=3];
15[label="map vx3 (vx40 : vx41)",fontsize=16,color="black",shape="box"];15 -> 22[label="",style="solid", color="black", weight=3];
16[label="map vx3 []",fontsize=16,color="black",shape="box"];16 -> 23[label="",style="solid", color="black", weight=3];
17[label="primbindIO (IO vx40) (return . vx3)",fontsize=16,color="black",shape="box"];17 -> 24[label="",style="solid", color="black", weight=3];
18[label="primbindIO (AProVE_IO vx40) (return . vx3)",fontsize=16,color="black",shape="box"];18 -> 25[label="",style="solid", color="black", weight=3];
19[label="primbindIO (AProVE_Exception vx40) (return . vx3)",fontsize=16,color="black",shape="box"];19 -> 26[label="",style="solid", color="black", weight=3];
20[label="primbindIO (AProVE_Error vx40) (return . vx3)",fontsize=16,color="black",shape="box"];20 -> 27[label="",style="solid", color="black", weight=3];
21[label="vx3 vx40",fontsize=16,color="green",shape="box"];21 -> 28[label="",style="dashed", color="green", weight=3];
22[label="vx3 vx40 : map vx3 vx41",fontsize=16,color="green",shape="box"];22 -> 29[label="",style="dashed", color="green", weight=3];
22 -> 30[label="",style="dashed", color="green", weight=3];
23[label="[]",fontsize=16,color="green",shape="box"];24[label="error []",fontsize=16,color="red",shape="box"];25[label="return . vx3",fontsize=16,color="black",shape="box"];25 -> 31[label="",style="solid", color="black", weight=3];
26[label="AProVE_Exception vx40",fontsize=16,color="green",shape="box"];27[label="AProVE_Error vx40",fontsize=16,color="green",shape="box"];28[label="vx40",fontsize=16,color="green",shape="box"];29[label="vx3 vx40",fontsize=16,color="green",shape="box"];29 -> 32[label="",style="dashed", color="green", weight=3];
30 -> 11[label="",style="dashed", color="red", weight=0];
30[label="map vx3 vx41",fontsize=16,color="magenta"];30 -> 33[label="",style="dashed", color="magenta", weight=3];
31[label="return (vx3 vx40)",fontsize=16,color="black",shape="box"];31 -> 34[label="",style="solid", color="black", weight=3];
32[label="vx40",fontsize=16,color="green",shape="box"];33[label="vx41",fontsize=16,color="green",shape="box"];34[label="primretIO (vx3 vx40)",fontsize=16,color="black",shape="box"];34 -> 35[label="",style="solid", color="black", weight=3];
35[label="AProVE_IO (vx3 vx40)",fontsize=16,color="green",shape="box"];35 -> 36[label="",style="dashed", color="green", weight=3];
36[label="vx3 vx40",fontsize=16,color="green",shape="box"];36 -> 37[label="",style="dashed", color="green", weight=3];
37[label="vx40",fontsize=16,color="green",shape="box"];}

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

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

   new_map(vx3, :(vx40, vx41), h, ba) -> new_map(vx3, vx41, h, ba)

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

(7) 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_map(vx3, :(vx40, vx41), h, ba) -> new_map(vx3, vx41, h, ba)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4


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

(8)
YES