/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 5 ms]
(8) YES


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(0)
Obligation:
mainModule Main 
module FiniteMap where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;

instance (Eq a, Eq b) => Eq FiniteMap a b where { 
}
isEmptyFM :: FiniteMap b a  ->  Bool;
isEmptyFM fm = sizeFM fm == 0;

sizeFM :: FiniteMap a b  ->  Int;
sizeFM EmptyFM = 0;
sizeFM (Branch _ _ size _ _) = size;

}
module Maybe where {
import qualified FiniteMap;
import qualified Main;
import qualified Prelude;
}
module Main where {
import qualified FiniteMap;
import qualified Maybe;
import qualified Prelude;
}

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

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

(2)
Obligation:
mainModule Main 
module FiniteMap where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;

instance (Eq a, Eq b) => Eq FiniteMap a b where { 
}
isEmptyFM :: FiniteMap b a  ->  Bool;
isEmptyFM fm = sizeFM fm == 0;

sizeFM :: FiniteMap a b  ->  Int;
sizeFM EmptyFM = 0;
sizeFM (Branch wu wv size ww wx) = size;

}
module Maybe where {
import qualified FiniteMap;
import qualified Main;
import qualified Prelude;
}
module Main where {
import qualified FiniteMap;
import qualified Maybe;
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 FiniteMap where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;

instance (Eq a, Eq b) => Eq FiniteMap a b where { 
}
isEmptyFM :: FiniteMap b a  ->  Bool;
isEmptyFM fm = sizeFM fm == 0;

sizeFM :: FiniteMap a b  ->  Int;
sizeFM EmptyFM = 0;
sizeFM (Branch wu wv size ww wx) = size;

}
module Maybe where {
import qualified FiniteMap;
import qualified Main;
import qualified Prelude;
}
module Main where {
import qualified FiniteMap;
import qualified Maybe;
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 FiniteMap where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;

instance (Eq a, Eq b) => Eq FiniteMap a b where { 
}
isEmptyFM :: FiniteMap a b  ->  Bool;
isEmptyFM fm = sizeFM fm == Pos Zero;

sizeFM :: FiniteMap a b  ->  Int;
sizeFM EmptyFM = Pos Zero;
sizeFM (Branch wu wv size ww wx) = size;

}
module Maybe where {
import qualified FiniteMap;
import qualified Main;
import qualified Prelude;
}
module Main where {
import qualified FiniteMap;
import qualified Maybe;
import qualified Prelude;
}

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

(7) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="FiniteMap.isEmptyFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="FiniteMap.isEmptyFM wy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="FiniteMap.sizeFM wy3 == Pos Zero",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="primEqInt (FiniteMap.sizeFM wy3) (Pos Zero)",fontsize=16,color="burlywood",shape="box"];21[label="wy3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];5 -> 21[label="",style="solid", color="burlywood", weight=9];
21 -> 6[label="",style="solid", color="burlywood", weight=3];
22[label="wy3/FiniteMap.Branch wy30 wy31 wy32 wy33 wy34",fontsize=10,color="white",style="solid",shape="box"];5 -> 22[label="",style="solid", color="burlywood", weight=9];
22 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="primEqInt (FiniteMap.sizeFM FiniteMap.EmptyFM) (Pos Zero)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="primEqInt (FiniteMap.sizeFM (FiniteMap.Branch wy30 wy31 wy32 wy33 wy34)) (Pos Zero)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9[label="primEqInt wy32 (Pos Zero)",fontsize=16,color="burlywood",shape="box"];23[label="wy32/Pos wy320",fontsize=10,color="white",style="solid",shape="box"];9 -> 23[label="",style="solid", color="burlywood", weight=9];
23 -> 11[label="",style="solid", color="burlywood", weight=3];
24[label="wy32/Neg wy320",fontsize=10,color="white",style="solid",shape="box"];9 -> 24[label="",style="solid", color="burlywood", weight=9];
24 -> 12[label="",style="solid", color="burlywood", weight=3];
10[label="True",fontsize=16,color="green",shape="box"];11[label="primEqInt (Pos wy320) (Pos Zero)",fontsize=16,color="burlywood",shape="box"];25[label="wy320/Succ wy3200",fontsize=10,color="white",style="solid",shape="box"];11 -> 25[label="",style="solid", color="burlywood", weight=9];
25 -> 13[label="",style="solid", color="burlywood", weight=3];
26[label="wy320/Zero",fontsize=10,color="white",style="solid",shape="box"];11 -> 26[label="",style="solid", color="burlywood", weight=9];
26 -> 14[label="",style="solid", color="burlywood", weight=3];
12[label="primEqInt (Neg wy320) (Pos Zero)",fontsize=16,color="burlywood",shape="box"];27[label="wy320/Succ wy3200",fontsize=10,color="white",style="solid",shape="box"];12 -> 27[label="",style="solid", color="burlywood", weight=9];
27 -> 15[label="",style="solid", color="burlywood", weight=3];
28[label="wy320/Zero",fontsize=10,color="white",style="solid",shape="box"];12 -> 28[label="",style="solid", color="burlywood", weight=9];
28 -> 16[label="",style="solid", color="burlywood", weight=3];
13[label="primEqInt (Pos (Succ wy3200)) (Pos Zero)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="primEqInt (Neg (Succ wy3200)) (Pos Zero)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="False",fontsize=16,color="green",shape="box"];18[label="True",fontsize=16,color="green",shape="box"];19[label="False",fontsize=16,color="green",shape="box"];20[label="True",fontsize=16,color="green",shape="box"];}

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(8)
YES