/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) Narrow [EQUIVALENT, 3 ms]
(6) 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;
"
The following Function with conditions
"compare x y|x == yEQ|x <= yLT|otherwiseGT;
"
is transformed to
"compare x y = compare3 x y;
"
"compare0 x y True = GT;
"
"compare2 x y True = EQ;
compare2 x y False = compare1 x y (x <= y);
"
"compare1 x y True = LT;
compare1 x y False = compare0 x y otherwise;
"
"compare3 x y = compare2 x y (x == y);
"

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(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="(<)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="(<) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="(<) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="compare vx3 vx4 == LT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="compare3 vx3 vx4 == LT",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="compare2 vx3 vx4 (vx3 == vx4) == LT",fontsize=16,color="burlywood",shape="box"];31[label="vx3/False",fontsize=10,color="white",style="solid",shape="box"];7 -> 31[label="",style="solid", color="burlywood", weight=9];
31 -> 8[label="",style="solid", color="burlywood", weight=3];
32[label="vx3/True",fontsize=10,color="white",style="solid",shape="box"];7 -> 32[label="",style="solid", color="burlywood", weight=9];
32 -> 9[label="",style="solid", color="burlywood", weight=3];
8[label="compare2 False vx4 (False == vx4) == LT",fontsize=16,color="burlywood",shape="box"];33[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];8 -> 33[label="",style="solid", color="burlywood", weight=9];
33 -> 10[label="",style="solid", color="burlywood", weight=3];
34[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];8 -> 34[label="",style="solid", color="burlywood", weight=9];
34 -> 11[label="",style="solid", color="burlywood", weight=3];
9[label="compare2 True vx4 (True == vx4) == LT",fontsize=16,color="burlywood",shape="box"];35[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];9 -> 35[label="",style="solid", color="burlywood", weight=9];
35 -> 12[label="",style="solid", color="burlywood", weight=3];
36[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];9 -> 36[label="",style="solid", color="burlywood", weight=9];
36 -> 13[label="",style="solid", color="burlywood", weight=3];
10[label="compare2 False False (False == False) == LT",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11[label="compare2 False True (False == True) == LT",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
12[label="compare2 True False (True == False) == LT",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13[label="compare2 True True (True == True) == LT",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="compare2 False False True == LT",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="compare2 False True False == LT",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="compare2 True False False == LT",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="compare2 True True True == LT",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18[label="EQ == LT",fontsize=16,color="black",shape="triangle"];18 -> 22[label="",style="solid", color="black", weight=3];
19[label="compare1 False True (False <= True) == LT",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
20[label="compare1 True False (True <= False) == LT",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
21 -> 18[label="",style="dashed", color="red", weight=0];
21[label="EQ == LT",fontsize=16,color="magenta"];22[label="False",fontsize=16,color="green",shape="box"];23[label="compare1 False True True == LT",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3];
24[label="compare1 True False False == LT",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
25[label="LT == LT",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
26[label="compare0 True False otherwise == LT",fontsize=16,color="black",shape="box"];26 -> 28[label="",style="solid", color="black", weight=3];
27[label="True",fontsize=16,color="green",shape="box"];28[label="compare0 True False True == LT",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3];
29[label="GT == LT",fontsize=16,color="black",shape="box"];29 -> 30[label="",style="solid", color="black", weight=3];
30[label="False",fontsize=16,color="green",shape="box"];}

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(6)
YES