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


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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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) NumRed [SOUND, 0 ms]
(6) HASKELL
(7) Narrow [EQUIVALENT, 20 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) NumRed (SOUND)
Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
----------------------------------------

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

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

(7) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="fromIntegral",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="fromIntegral vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="fromInteger . toInteger",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="fromInteger (toInteger vx3)",fontsize=16,color="blue",shape="box"];51[label="fromInteger :: Integer -> Int",fontsize=10,color="white",style="solid",shape="box"];5 -> 51[label="",style="solid", color="blue", weight=9];
51 -> 6[label="",style="solid", color="blue", weight=3];
52[label="fromInteger :: Integer -> Double",fontsize=10,color="white",style="solid",shape="box"];5 -> 52[label="",style="solid", color="blue", weight=9];
52 -> 7[label="",style="solid", color="blue", weight=3];
53[label="fromInteger :: Integer -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];5 -> 53[label="",style="solid", color="blue", weight=9];
53 -> 8[label="",style="solid", color="blue", weight=3];
54[label="fromInteger :: Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];5 -> 54[label="",style="solid", color="blue", weight=9];
54 -> 9[label="",style="solid", color="blue", weight=3];
55[label="fromInteger :: Integer -> Float",fontsize=10,color="white",style="solid",shape="box"];5 -> 55[label="",style="solid", color="blue", weight=9];
55 -> 10[label="",style="solid", color="blue", weight=3];
6[label="fromInteger (toInteger vx3)",fontsize=16,color="black",shape="box"];6 -> 36[label="",style="solid", color="black", weight=3];
7[label="fromInteger (toInteger vx3)",fontsize=16,color="black",shape="box"];7 -> 12[label="",style="solid", color="black", weight=3];
8[label="fromInteger (toInteger vx3)",fontsize=16,color="black",shape="box"];8 -> 13[label="",style="solid", color="black", weight=3];
9[label="fromInteger (toInteger vx3)",fontsize=16,color="black",shape="box"];9 -> 40[label="",style="solid", color="black", weight=3];
10[label="fromInteger (toInteger vx3)",fontsize=16,color="black",shape="box"];10 -> 15[label="",style="solid", color="black", weight=3];
36 -> 30[label="",style="dashed", color="red", weight=0];
36[label="fromInteger (Integer vx3)",fontsize=16,color="magenta"];36 -> 46[label="",style="dashed", color="magenta", weight=3];
12[label="primIntegerToDouble (toInteger vx3)",fontsize=16,color="black",shape="box"];12 -> 17[label="",style="solid", color="black", weight=3];
13[label="fromInteger (toInteger vx3) :% fromInt (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];13 -> 18[label="",style="dashed", color="green", weight=3];
13 -> 19[label="",style="dashed", color="green", weight=3];
40 -> 25[label="",style="dashed", color="red", weight=0];
40[label="toInteger vx3",fontsize=16,color="magenta"];15 -> 21[label="",style="dashed", color="red", weight=0];
15[label="primIntegerToFloat (toInteger vx3)",fontsize=16,color="magenta"];15 -> 22[label="",style="dashed", color="magenta", weight=3];
46[label="Integer vx3",fontsize=16,color="green",shape="box"];30[label="fromInteger vx5",fontsize=16,color="burlywood",shape="triangle"];56[label="vx5/Integer vx50",fontsize=10,color="white",style="solid",shape="box"];30 -> 56[label="",style="solid", color="burlywood", weight=9];
56 -> 41[label="",style="solid", color="burlywood", weight=3];
17[label="primIntegerToDouble (Integer vx3)",fontsize=16,color="black",shape="box"];17 -> 23[label="",style="solid", color="black", weight=3];
18[label="fromInteger (toInteger vx3)",fontsize=16,color="blue",shape="box"];57[label="fromInteger :: Integer -> Int",fontsize=10,color="white",style="solid",shape="box"];18 -> 57[label="",style="solid", color="blue", weight=9];
57 -> 37[label="",style="solid", color="blue", weight=3];
58[label="fromInteger :: Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];18 -> 58[label="",style="solid", color="blue", weight=9];
58 -> 38[label="",style="solid", color="blue", weight=3];
19[label="fromInt (Pos (Succ Zero))",fontsize=16,color="blue",shape="box"];59[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];19 -> 59[label="",style="solid", color="blue", weight=9];
59 -> 32[label="",style="solid", color="blue", weight=3];
60[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];19 -> 60[label="",style="solid", color="blue", weight=9];
60 -> 33[label="",style="solid", color="blue", weight=3];
25[label="toInteger vx3",fontsize=16,color="black",shape="triangle"];25 -> 29[label="",style="solid", color="black", weight=3];
22 -> 25[label="",style="dashed", color="red", weight=0];
22[label="toInteger vx3",fontsize=16,color="magenta"];21[label="primIntegerToFloat vx4",fontsize=16,color="burlywood",shape="triangle"];61[label="vx4/Integer vx40",fontsize=10,color="white",style="solid",shape="box"];21 -> 61[label="",style="solid", color="burlywood", weight=9];
61 -> 34[label="",style="solid", color="burlywood", weight=3];
41[label="fromInteger (Integer vx50)",fontsize=16,color="black",shape="box"];41 -> 49[label="",style="solid", color="black", weight=3];
23[label="primIntToDouble vx3",fontsize=16,color="black",shape="box"];23 -> 35[label="",style="solid", color="black", weight=3];
37 -> 30[label="",style="dashed", color="red", weight=0];
37[label="fromInteger (toInteger vx3)",fontsize=16,color="magenta"];37 -> 47[label="",style="dashed", color="magenta", weight=3];
38 -> 31[label="",style="dashed", color="red", weight=0];
38[label="fromInteger (toInteger vx3)",fontsize=16,color="magenta"];38 -> 48[label="",style="dashed", color="magenta", weight=3];
32[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];32 -> 43[label="",style="solid", color="black", weight=3];
33[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];33 -> 44[label="",style="solid", color="black", weight=3];
29[label="Integer vx3",fontsize=16,color="green",shape="box"];34[label="primIntegerToFloat (Integer vx40)",fontsize=16,color="black",shape="box"];34 -> 45[label="",style="solid", color="black", weight=3];
49[label="vx50",fontsize=16,color="green",shape="box"];35[label="Double vx3 (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];47 -> 25[label="",style="dashed", color="red", weight=0];
47[label="toInteger vx3",fontsize=16,color="magenta"];48 -> 25[label="",style="dashed", color="red", weight=0];
48[label="toInteger vx3",fontsize=16,color="magenta"];31[label="fromInteger vx5",fontsize=16,color="black",shape="triangle"];31 -> 42[label="",style="solid", color="black", weight=3];
43[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];44[label="Integer (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];45[label="primIntToFloat vx40",fontsize=16,color="black",shape="box"];45 -> 50[label="",style="solid", color="black", weight=3];
42[label="vx5",fontsize=16,color="green",shape="box"];50[label="Float vx40 (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];}

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

(8)
YES