/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 24 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="fromInteger",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="fromInteger vx3",fontsize=16,color="blue",shape="box"];29[label="fromInteger :: Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];3 -> 29[label="",style="solid", color="blue", weight=9];
29 -> 4[label="",style="solid", color="blue", weight=3];
30[label="fromInteger :: Integer -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];3 -> 30[label="",style="solid", color="blue", weight=9];
30 -> 5[label="",style="solid", color="blue", weight=3];
31[label="fromInteger :: Integer -> Float",fontsize=10,color="white",style="solid",shape="box"];3 -> 31[label="",style="solid", color="blue", weight=9];
31 -> 6[label="",style="solid", color="blue", weight=3];
32[label="fromInteger :: Integer -> Int",fontsize=10,color="white",style="solid",shape="box"];3 -> 32[label="",style="solid", color="blue", weight=9];
32 -> 7[label="",style="solid", color="blue", weight=3];
33[label="fromInteger :: Integer -> Double",fontsize=10,color="white",style="solid",shape="box"];3 -> 33[label="",style="solid", color="blue", weight=9];
33 -> 8[label="",style="solid", color="blue", weight=3];
4[label="fromInteger vx3",fontsize=16,color="black",shape="triangle"];4 -> 9[label="",style="solid", color="black", weight=3];
5[label="fromInteger vx3",fontsize=16,color="black",shape="box"];5 -> 10[label="",style="solid", color="black", weight=3];
6[label="fromInteger vx3",fontsize=16,color="black",shape="box"];6 -> 11[label="",style="solid", color="black", weight=3];
7[label="fromInteger vx3",fontsize=16,color="burlywood",shape="triangle"];34[label="vx3/Integer vx30",fontsize=10,color="white",style="solid",shape="box"];7 -> 34[label="",style="solid", color="burlywood", weight=9];
34 -> 12[label="",style="solid", color="burlywood", weight=3];
8[label="fromInteger vx3",fontsize=16,color="black",shape="box"];8 -> 13[label="",style="solid", color="black", weight=3];
9[label="vx3",fontsize=16,color="green",shape="box"];10[label="fromInteger vx3 :% fromInt (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];10 -> 14[label="",style="dashed", color="green", weight=3];
10 -> 15[label="",style="dashed", color="green", weight=3];
11[label="primIntegerToFloat vx3",fontsize=16,color="burlywood",shape="box"];35[label="vx3/Integer vx30",fontsize=10,color="white",style="solid",shape="box"];11 -> 35[label="",style="solid", color="burlywood", weight=9];
35 -> 16[label="",style="solid", color="burlywood", weight=3];
12[label="fromInteger (Integer vx30)",fontsize=16,color="black",shape="box"];12 -> 17[label="",style="solid", color="black", weight=3];
13[label="primIntegerToDouble vx3",fontsize=16,color="burlywood",shape="box"];36[label="vx3/Integer vx30",fontsize=10,color="white",style="solid",shape="box"];13 -> 36[label="",style="solid", color="burlywood", weight=9];
36 -> 18[label="",style="solid", color="burlywood", weight=3];
14[label="fromInteger vx3",fontsize=16,color="blue",shape="box"];37[label="fromInteger :: Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];14 -> 37[label="",style="solid", color="blue", weight=9];
37 -> 19[label="",style="solid", color="blue", weight=3];
38[label="fromInteger :: Integer -> Int",fontsize=10,color="white",style="solid",shape="box"];14 -> 38[label="",style="solid", color="blue", weight=9];
38 -> 20[label="",style="solid", color="blue", weight=3];
15[label="fromInt (Pos (Succ Zero))",fontsize=16,color="blue",shape="box"];39[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];15 -> 39[label="",style="solid", color="blue", weight=9];
39 -> 21[label="",style="solid", color="blue", weight=3];
40[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];15 -> 40[label="",style="solid", color="blue", weight=9];
40 -> 22[label="",style="solid", color="blue", weight=3];
16[label="primIntegerToFloat (Integer vx30)",fontsize=16,color="black",shape="box"];16 -> 23[label="",style="solid", color="black", weight=3];
17[label="vx30",fontsize=16,color="green",shape="box"];18[label="primIntegerToDouble (Integer vx30)",fontsize=16,color="black",shape="box"];18 -> 24[label="",style="solid", color="black", weight=3];
19 -> 4[label="",style="dashed", color="red", weight=0];
19[label="fromInteger vx3",fontsize=16,color="magenta"];20 -> 7[label="",style="dashed", color="red", weight=0];
20[label="fromInteger vx3",fontsize=16,color="magenta"];21[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
22[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
23[label="primIntToFloat vx30",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
24[label="primIntToDouble vx30",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
25[label="Integer (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];26[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];27[label="Float vx30 (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];28[label="Double vx30 (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];}

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

(8)
YES