/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) Narrow [EQUIVALENT, 0 ms]
(6) YES


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(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
ltEsMyBool MyFalse MyFalse = MyTrue;
ltEsMyBool MyFalse MyTrue = MyTrue;
ltEsMyBool MyTrue MyFalse = MyFalse;
ltEsMyBool MyTrue MyTrue = MyTrue;

}

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(1) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.
----------------------------------------

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
ltEsMyBool MyFalse MyFalse = MyTrue;
ltEsMyBool MyFalse MyTrue = MyTrue;
ltEsMyBool MyTrue MyFalse = MyFalse;
ltEsMyBool MyTrue MyTrue = MyTrue;

}

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

(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;
data MyBool = MyTrue  | MyFalse ;

ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
ltEsMyBool MyFalse MyFalse = MyTrue;
ltEsMyBool MyFalse MyTrue = MyTrue;
ltEsMyBool MyTrue MyFalse = MyFalse;
ltEsMyBool MyTrue MyTrue = MyTrue;

}

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(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="ltEsMyBool",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="ltEsMyBool vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="ltEsMyBool vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];15[label="vx3/MyTrue",fontsize=10,color="white",style="solid",shape="box"];4 -> 15[label="",style="solid", color="burlywood", weight=9];
15 -> 5[label="",style="solid", color="burlywood", weight=3];
16[label="vx3/MyFalse",fontsize=10,color="white",style="solid",shape="box"];4 -> 16[label="",style="solid", color="burlywood", weight=9];
16 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="ltEsMyBool MyTrue vx4",fontsize=16,color="burlywood",shape="box"];17[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];5 -> 17[label="",style="solid", color="burlywood", weight=9];
17 -> 7[label="",style="solid", color="burlywood", weight=3];
18[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
18 -> 8[label="",style="solid", color="burlywood", weight=3];
6[label="ltEsMyBool MyFalse vx4",fontsize=16,color="burlywood",shape="box"];19[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];6 -> 19[label="",style="solid", color="burlywood", weight=9];
19 -> 9[label="",style="solid", color="burlywood", weight=3];
20[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];6 -> 20[label="",style="solid", color="burlywood", weight=9];
20 -> 10[label="",style="solid", color="burlywood", weight=3];
7[label="ltEsMyBool MyTrue MyTrue",fontsize=16,color="black",shape="box"];7 -> 11[label="",style="solid", color="black", weight=3];
8[label="ltEsMyBool MyTrue MyFalse",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
9[label="ltEsMyBool MyFalse MyTrue",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
10[label="ltEsMyBool MyFalse MyFalse",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11[label="MyTrue",fontsize=16,color="green",shape="box"];12[label="MyFalse",fontsize=16,color="green",shape="box"];13[label="MyTrue",fontsize=16,color="green",shape="box"];14[label="MyTrue",fontsize=16,color="green",shape="box"];}

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(6)
YES