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


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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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) NumRed [SOUND, 0 ms]
(6) HASKELL
(7) Narrow [EQUIVALENT, 6 ms]
(8) YES


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(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="fromRational",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="fromRational vx3",fontsize=16,color="blue",shape="box"];32[label="fromRational :: (Ratio Integer) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];3 -> 32[label="",style="solid", color="blue", weight=9];
32 -> 4[label="",style="solid", color="blue", weight=3];
33[label="fromRational :: (Ratio Integer) -> Double",fontsize=10,color="white",style="solid",shape="box"];3 -> 33[label="",style="solid", color="blue", weight=9];
33 -> 5[label="",style="solid", color="blue", weight=3];
34[label="fromRational :: (Ratio Integer) -> Float",fontsize=10,color="white",style="solid",shape="box"];3 -> 34[label="",style="solid", color="blue", weight=9];
34 -> 6[label="",style="solid", color="blue", weight=3];
4[label="fromRational vx3",fontsize=16,color="burlywood",shape="box"];35[label="vx3/vx30 :% vx31",fontsize=10,color="white",style="solid",shape="box"];4 -> 35[label="",style="solid", color="burlywood", weight=9];
35 -> 7[label="",style="solid", color="burlywood", weight=3];
5[label="fromRational vx3",fontsize=16,color="black",shape="box"];5 -> 8[label="",style="solid", color="black", weight=3];
6[label="fromRational vx3",fontsize=16,color="black",shape="box"];6 -> 9[label="",style="solid", color="black", weight=3];
7[label="fromRational (vx30 :% vx31)",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3];
8[label="primRationalToDouble vx3",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9[label="primRationalToFloat vx3",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3];
10[label="fromInteger vx30 :% fromInteger vx31",fontsize=16,color="green",shape="box"];10 -> 13[label="",style="dashed", color="green", weight=3];
10 -> 14[label="",style="dashed", color="green", weight=3];
11[label="rationalToDouble vx3",fontsize=16,color="burlywood",shape="box"];36[label="vx3/vx30 :% vx31",fontsize=10,color="white",style="solid",shape="box"];11 -> 36[label="",style="solid", color="burlywood", weight=9];
36 -> 15[label="",style="solid", color="burlywood", weight=3];
12[label="rationalToFloat vx3",fontsize=16,color="burlywood",shape="box"];37[label="vx3/vx30 :% vx31",fontsize=10,color="white",style="solid",shape="box"];12 -> 37[label="",style="solid", color="burlywood", weight=9];
37 -> 16[label="",style="solid", color="burlywood", weight=3];
13[label="fromInteger vx30",fontsize=16,color="blue",shape="box"];38[label="fromInteger :: Integer -> Int",fontsize=10,color="white",style="solid",shape="box"];13 -> 38[label="",style="solid", color="blue", weight=9];
38 -> 17[label="",style="solid", color="blue", weight=3];
39[label="fromInteger :: Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];13 -> 39[label="",style="solid", color="blue", weight=9];
39 -> 18[label="",style="solid", color="blue", weight=3];
14[label="fromInteger vx31",fontsize=16,color="blue",shape="box"];40[label="fromInteger :: Integer -> Int",fontsize=10,color="white",style="solid",shape="box"];14 -> 40[label="",style="solid", color="blue", weight=9];
40 -> 19[label="",style="solid", color="blue", weight=3];
41[label="fromInteger :: Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];14 -> 41[label="",style="solid", color="blue", weight=9];
41 -> 20[label="",style="solid", color="blue", weight=3];
15[label="rationalToDouble (vx30 :% vx31)",fontsize=16,color="burlywood",shape="box"];42[label="vx30/Integer vx300",fontsize=10,color="white",style="solid",shape="box"];15 -> 42[label="",style="solid", color="burlywood", weight=9];
42 -> 21[label="",style="solid", color="burlywood", weight=3];
16[label="rationalToFloat (vx30 :% vx31)",fontsize=16,color="burlywood",shape="box"];43[label="vx30/Integer vx300",fontsize=10,color="white",style="solid",shape="box"];16 -> 43[label="",style="solid", color="burlywood", weight=9];
43 -> 22[label="",style="solid", color="burlywood", weight=3];
17[label="fromInteger vx30",fontsize=16,color="burlywood",shape="triangle"];44[label="vx30/Integer vx300",fontsize=10,color="white",style="solid",shape="box"];17 -> 44[label="",style="solid", color="burlywood", weight=9];
44 -> 23[label="",style="solid", color="burlywood", weight=3];
18[label="fromInteger vx30",fontsize=16,color="black",shape="triangle"];18 -> 24[label="",style="solid", color="black", weight=3];
19 -> 17[label="",style="dashed", color="red", weight=0];
19[label="fromInteger vx31",fontsize=16,color="magenta"];19 -> 25[label="",style="dashed", color="magenta", weight=3];
20 -> 18[label="",style="dashed", color="red", weight=0];
20[label="fromInteger vx31",fontsize=16,color="magenta"];20 -> 26[label="",style="dashed", color="magenta", weight=3];
21[label="rationalToDouble (Integer vx300 :% vx31)",fontsize=16,color="burlywood",shape="box"];45[label="vx31/Integer vx310",fontsize=10,color="white",style="solid",shape="box"];21 -> 45[label="",style="solid", color="burlywood", weight=9];
45 -> 27[label="",style="solid", color="burlywood", weight=3];
22[label="rationalToFloat (Integer vx300 :% vx31)",fontsize=16,color="burlywood",shape="box"];46[label="vx31/Integer vx310",fontsize=10,color="white",style="solid",shape="box"];22 -> 46[label="",style="solid", color="burlywood", weight=9];
46 -> 28[label="",style="solid", color="burlywood", weight=3];
23[label="fromInteger (Integer vx300)",fontsize=16,color="black",shape="box"];23 -> 29[label="",style="solid", color="black", weight=3];
24[label="vx30",fontsize=16,color="green",shape="box"];25[label="vx31",fontsize=16,color="green",shape="box"];26[label="vx31",fontsize=16,color="green",shape="box"];27[label="rationalToDouble (Integer vx300 :% Integer vx310)",fontsize=16,color="black",shape="box"];27 -> 30[label="",style="solid", color="black", weight=3];
28[label="rationalToFloat (Integer vx300 :% Integer vx310)",fontsize=16,color="black",shape="box"];28 -> 31[label="",style="solid", color="black", weight=3];
29[label="vx300",fontsize=16,color="green",shape="box"];30[label="Double vx300 vx310",fontsize=16,color="green",shape="box"];31[label="Float vx300 vx310",fontsize=16,color="green",shape="box"];}

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(8)
YES