/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 [EQUIVALENT, 28 ms]
(6) 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 (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="negate",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="negate vx3",fontsize=16,color="blue",shape="box"];35[label="negate :: Float -> Float",fontsize=10,color="white",style="solid",shape="box"];3 -> 35[label="",style="solid", color="blue", weight=9];
35 -> 4[label="",style="solid", color="blue", weight=3];
36[label="negate :: (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];3 -> 36[label="",style="solid", color="blue", weight=9];
36 -> 5[label="",style="solid", color="blue", weight=3];
37[label="negate :: Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];3 -> 37[label="",style="solid", color="blue", weight=9];
37 -> 6[label="",style="solid", color="blue", weight=3];
38[label="negate :: Double -> Double",fontsize=10,color="white",style="solid",shape="box"];3 -> 38[label="",style="solid", color="blue", weight=9];
38 -> 7[label="",style="solid", color="blue", weight=3];
39[label="negate :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];3 -> 39[label="",style="solid", color="blue", weight=9];
39 -> 8[label="",style="solid", color="blue", weight=3];
4[label="negate vx3",fontsize=16,color="black",shape="box"];4 -> 9[label="",style="solid", color="black", weight=3];
5[label="negate vx3",fontsize=16,color="burlywood",shape="box"];40[label="vx3/vx30 :% vx31",fontsize=10,color="white",style="solid",shape="box"];5 -> 40[label="",style="solid", color="burlywood", weight=9];
40 -> 10[label="",style="solid", color="burlywood", weight=3];
6[label="negate vx3",fontsize=16,color="burlywood",shape="triangle"];41[label="vx3/Integer vx30",fontsize=10,color="white",style="solid",shape="box"];6 -> 41[label="",style="solid", color="burlywood", weight=9];
41 -> 11[label="",style="solid", color="burlywood", weight=3];
7[label="negate vx3",fontsize=16,color="black",shape="box"];7 -> 12[label="",style="solid", color="black", weight=3];
8[label="negate vx3",fontsize=16,color="black",shape="triangle"];8 -> 13[label="",style="solid", color="black", weight=3];
9[label="primNegFloat vx3",fontsize=16,color="burlywood",shape="box"];42[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];9 -> 42[label="",style="solid", color="burlywood", weight=9];
42 -> 14[label="",style="solid", color="burlywood", weight=3];
10[label="negate vx30 :% vx31",fontsize=16,color="black",shape="box"];10 -> 15[label="",style="solid", color="black", weight=3];
11[label="negate Integer vx30",fontsize=16,color="black",shape="box"];11 -> 16[label="",style="solid", color="black", weight=3];
12[label="primNegDouble vx3",fontsize=16,color="burlywood",shape="box"];43[label="vx3/Double vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];12 -> 43[label="",style="solid", color="burlywood", weight=9];
43 -> 17[label="",style="solid", color="burlywood", weight=3];
13[label="primNegInt vx3",fontsize=16,color="burlywood",shape="triangle"];44[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];13 -> 44[label="",style="solid", color="burlywood", weight=9];
44 -> 18[label="",style="solid", color="burlywood", weight=3];
45[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];13 -> 45[label="",style="solid", color="burlywood", weight=9];
45 -> 19[label="",style="solid", color="burlywood", weight=3];
14[label="primNegFloat (Float vx30 vx31)",fontsize=16,color="black",shape="box"];14 -> 20[label="",style="solid", color="black", weight=3];
15[label="(negate vx30) :% vx31",fontsize=16,color="green",shape="box"];15 -> 21[label="",style="dashed", color="green", weight=3];
16[label="Integer (primNegInt vx30)",fontsize=16,color="green",shape="box"];16 -> 22[label="",style="dashed", color="green", weight=3];
17[label="primNegDouble (Double vx30 vx31)",fontsize=16,color="black",shape="box"];17 -> 23[label="",style="solid", color="black", weight=3];
18[label="primNegInt (Pos vx30)",fontsize=16,color="black",shape="box"];18 -> 24[label="",style="solid", color="black", weight=3];
19[label="primNegInt (Neg vx30)",fontsize=16,color="black",shape="box"];19 -> 25[label="",style="solid", color="black", weight=3];
20[label="Float (`negate` vx30) vx31",fontsize=16,color="green",shape="box"];20 -> 26[label="",style="dashed", color="green", weight=3];
21[label="negate vx30",fontsize=16,color="blue",shape="box"];46[label="negate :: Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];21 -> 46[label="",style="solid", color="blue", weight=9];
46 -> 27[label="",style="solid", color="blue", weight=3];
47[label="negate :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];21 -> 47[label="",style="solid", color="blue", weight=9];
47 -> 28[label="",style="solid", color="blue", weight=3];
22 -> 13[label="",style="dashed", color="red", weight=0];
22[label="primNegInt vx30",fontsize=16,color="magenta"];22 -> 29[label="",style="dashed", color="magenta", weight=3];
23[label="Double (`negate` vx30) vx31",fontsize=16,color="green",shape="box"];23 -> 30[label="",style="dashed", color="green", weight=3];
24[label="Neg vx30",fontsize=16,color="green",shape="box"];25[label="Pos vx30",fontsize=16,color="green",shape="box"];26 -> 8[label="",style="dashed", color="red", weight=0];
26[label="`negate` vx30",fontsize=16,color="magenta"];26 -> 31[label="",style="dashed", color="magenta", weight=3];
27 -> 6[label="",style="dashed", color="red", weight=0];
27[label="negate vx30",fontsize=16,color="magenta"];27 -> 32[label="",style="dashed", color="magenta", weight=3];
28 -> 8[label="",style="dashed", color="red", weight=0];
28[label="negate vx30",fontsize=16,color="magenta"];28 -> 33[label="",style="dashed", color="magenta", weight=3];
29[label="vx30",fontsize=16,color="green",shape="box"];30 -> 8[label="",style="dashed", color="red", weight=0];
30[label="`negate` vx30",fontsize=16,color="magenta"];30 -> 34[label="",style="dashed", color="magenta", weight=3];
31[label="vx30",fontsize=16,color="green",shape="box"];32[label="vx30",fontsize=16,color="green",shape="box"];33[label="vx30",fontsize=16,color="green",shape="box"];34[label="vx30",fontsize=16,color="green",shape="box"];}

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

(6)
YES