/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 [SOUND, 0 ms]
(8) QDP
(9) QDPSizeChangeProof [EQUIVALENT, 0 ms]
(10) 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 (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="isAscii",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="isAscii vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4 -> 5[label="",style="dashed", color="red", weight=0];
4[label="fromEnum vx3 < Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="magenta"];4 -> 6[label="",style="dashed", color="magenta", weight=3];
4 -> 7[label="",style="dashed", color="magenta", weight=3];
6[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];7[label="vx3",fontsize=16,color="green",shape="box"];5[label="fromEnum vx5 < Pos (Succ vx6)",fontsize=16,color="black",shape="triangle"];5 -> 8[label="",style="solid", color="black", weight=3];
8[label="compare (fromEnum vx5) (Pos (Succ vx6)) == LT",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9 -> 10[label="",style="dashed", color="red", weight=0];
9[label="primCmpInt (fromEnum vx5) (Pos (Succ vx6)) == LT",fontsize=16,color="magenta"];9 -> 11[label="",style="dashed", color="magenta", weight=3];
9 -> 12[label="",style="dashed", color="magenta", weight=3];
11[label="vx6",fontsize=16,color="green",shape="box"];12[label="fromEnum vx5",fontsize=16,color="blue",shape="box"];60[label="fromEnum :: () -> Int",fontsize=10,color="white",style="solid",shape="box"];12 -> 60[label="",style="solid", color="blue", weight=9];
60 -> 13[label="",style="solid", color="blue", weight=3];
61[label="fromEnum :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];12 -> 61[label="",style="solid", color="blue", weight=9];
61 -> 14[label="",style="solid", color="blue", weight=3];
62[label="fromEnum :: (Ratio a) -> Int",fontsize=10,color="white",style="solid",shape="box"];12 -> 62[label="",style="solid", color="blue", weight=9];
62 -> 15[label="",style="solid", color="blue", weight=3];
63[label="fromEnum :: Char -> Int",fontsize=10,color="white",style="solid",shape="box"];12 -> 63[label="",style="solid", color="blue", weight=9];
63 -> 16[label="",style="solid", color="blue", weight=3];
64[label="fromEnum :: Float -> Int",fontsize=10,color="white",style="solid",shape="box"];12 -> 64[label="",style="solid", color="blue", weight=9];
64 -> 17[label="",style="solid", color="blue", weight=3];
65[label="fromEnum :: Bool -> Int",fontsize=10,color="white",style="solid",shape="box"];12 -> 65[label="",style="solid", color="blue", weight=9];
65 -> 18[label="",style="solid", color="blue", weight=3];
66[label="fromEnum :: Ordering -> Int",fontsize=10,color="white",style="solid",shape="box"];12 -> 66[label="",style="solid", color="blue", weight=9];
66 -> 19[label="",style="solid", color="blue", weight=3];
67[label="fromEnum :: Double -> Int",fontsize=10,color="white",style="solid",shape="box"];12 -> 67[label="",style="solid", color="blue", weight=9];
67 -> 20[label="",style="solid", color="blue", weight=3];
68[label="fromEnum :: Integer -> Int",fontsize=10,color="white",style="solid",shape="box"];12 -> 68[label="",style="solid", color="blue", weight=9];
68 -> 21[label="",style="solid", color="blue", weight=3];
10[label="primCmpInt vx10 (Pos (Succ vx11)) == LT",fontsize=16,color="burlywood",shape="triangle"];69[label="vx10/Pos vx100",fontsize=10,color="white",style="solid",shape="box"];10 -> 69[label="",style="solid", color="burlywood", weight=9];
69 -> 22[label="",style="solid", color="burlywood", weight=3];
70[label="vx10/Neg vx100",fontsize=10,color="white",style="solid",shape="box"];10 -> 70[label="",style="solid", color="burlywood", weight=9];
70 -> 23[label="",style="solid", color="burlywood", weight=3];
13[label="fromEnum vx5",fontsize=16,color="black",shape="box"];13 -> 24[label="",style="solid", color="black", weight=3];
14[label="fromEnum vx5",fontsize=16,color="black",shape="box"];14 -> 25[label="",style="solid", color="black", weight=3];
15[label="fromEnum vx5",fontsize=16,color="black",shape="box"];15 -> 26[label="",style="solid", color="black", weight=3];
16[label="fromEnum vx5",fontsize=16,color="black",shape="box"];16 -> 27[label="",style="solid", color="black", weight=3];
17[label="fromEnum vx5",fontsize=16,color="black",shape="box"];17 -> 28[label="",style="solid", color="black", weight=3];
18[label="fromEnum vx5",fontsize=16,color="black",shape="box"];18 -> 29[label="",style="solid", color="black", weight=3];
19[label="fromEnum vx5",fontsize=16,color="black",shape="box"];19 -> 30[label="",style="solid", color="black", weight=3];
20[label="fromEnum vx5",fontsize=16,color="black",shape="box"];20 -> 31[label="",style="solid", color="black", weight=3];
21[label="fromEnum vx5",fontsize=16,color="black",shape="box"];21 -> 32[label="",style="solid", color="black", weight=3];
22[label="primCmpInt (Pos vx100) (Pos (Succ vx11)) == LT",fontsize=16,color="burlywood",shape="box"];71[label="vx100/Succ vx1000",fontsize=10,color="white",style="solid",shape="box"];22 -> 71[label="",style="solid", color="burlywood", weight=9];
71 -> 33[label="",style="solid", color="burlywood", weight=3];
72[label="vx100/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 72[label="",style="solid", color="burlywood", weight=9];
72 -> 34[label="",style="solid", color="burlywood", weight=3];
23[label="primCmpInt (Neg vx100) (Pos (Succ vx11)) == LT",fontsize=16,color="burlywood",shape="box"];73[label="vx100/Succ vx1000",fontsize=10,color="white",style="solid",shape="box"];23 -> 73[label="",style="solid", color="burlywood", weight=9];
73 -> 35[label="",style="solid", color="burlywood", weight=3];
74[label="vx100/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 74[label="",style="solid", color="burlywood", weight=9];
74 -> 36[label="",style="solid", color="burlywood", weight=3];
24[label="error []",fontsize=16,color="red",shape="box"];25[label="error []",fontsize=16,color="red",shape="box"];26[label="error []",fontsize=16,color="red",shape="box"];27[label="primCharToInt vx5",fontsize=16,color="burlywood",shape="box"];75[label="vx5/Char vx50",fontsize=10,color="white",style="solid",shape="box"];27 -> 75[label="",style="solid", color="burlywood", weight=9];
75 -> 37[label="",style="solid", color="burlywood", weight=3];
28[label="error []",fontsize=16,color="red",shape="box"];29[label="error []",fontsize=16,color="red",shape="box"];30[label="error []",fontsize=16,color="red",shape="box"];31[label="error []",fontsize=16,color="red",shape="box"];32[label="error []",fontsize=16,color="red",shape="box"];33[label="primCmpInt (Pos (Succ vx1000)) (Pos (Succ vx11)) == LT",fontsize=16,color="black",shape="box"];33 -> 38[label="",style="solid", color="black", weight=3];
34[label="primCmpInt (Pos Zero) (Pos (Succ vx11)) == LT",fontsize=16,color="black",shape="box"];34 -> 39[label="",style="solid", color="black", weight=3];
35[label="primCmpInt (Neg (Succ vx1000)) (Pos (Succ vx11)) == LT",fontsize=16,color="black",shape="box"];35 -> 40[label="",style="solid", color="black", weight=3];
36[label="primCmpInt (Neg Zero) (Pos (Succ vx11)) == LT",fontsize=16,color="black",shape="box"];36 -> 41[label="",style="solid", color="black", weight=3];
37[label="primCharToInt (Char vx50)",fontsize=16,color="black",shape="box"];37 -> 42[label="",style="solid", color="black", weight=3];
38[label="primCmpNat (Succ vx1000) (Succ vx11) == LT",fontsize=16,color="black",shape="box"];38 -> 43[label="",style="solid", color="black", weight=3];
39[label="primCmpNat Zero (Succ vx11) == LT",fontsize=16,color="black",shape="box"];39 -> 44[label="",style="solid", color="black", weight=3];
40[label="LT == LT",fontsize=16,color="black",shape="triangle"];40 -> 45[label="",style="solid", color="black", weight=3];
41 -> 40[label="",style="dashed", color="red", weight=0];
41[label="LT == LT",fontsize=16,color="magenta"];42[label="Pos vx50",fontsize=16,color="green",shape="box"];43[label="primCmpNat vx1000 vx11 == LT",fontsize=16,color="burlywood",shape="triangle"];76[label="vx1000/Succ vx10000",fontsize=10,color="white",style="solid",shape="box"];43 -> 76[label="",style="solid", color="burlywood", weight=9];
76 -> 46[label="",style="solid", color="burlywood", weight=3];
77[label="vx1000/Zero",fontsize=10,color="white",style="solid",shape="box"];43 -> 77[label="",style="solid", color="burlywood", weight=9];
77 -> 47[label="",style="solid", color="burlywood", weight=3];
44 -> 40[label="",style="dashed", color="red", weight=0];
44[label="LT == LT",fontsize=16,color="magenta"];45[label="True",fontsize=16,color="green",shape="box"];46[label="primCmpNat (Succ vx10000) vx11 == LT",fontsize=16,color="burlywood",shape="box"];78[label="vx11/Succ vx110",fontsize=10,color="white",style="solid",shape="box"];46 -> 78[label="",style="solid", color="burlywood", weight=9];
78 -> 48[label="",style="solid", color="burlywood", weight=3];
79[label="vx11/Zero",fontsize=10,color="white",style="solid",shape="box"];46 -> 79[label="",style="solid", color="burlywood", weight=9];
79 -> 49[label="",style="solid", color="burlywood", weight=3];
47[label="primCmpNat Zero vx11 == LT",fontsize=16,color="burlywood",shape="box"];80[label="vx11/Succ vx110",fontsize=10,color="white",style="solid",shape="box"];47 -> 80[label="",style="solid", color="burlywood", weight=9];
80 -> 50[label="",style="solid", color="burlywood", weight=3];
81[label="vx11/Zero",fontsize=10,color="white",style="solid",shape="box"];47 -> 81[label="",style="solid", color="burlywood", weight=9];
81 -> 51[label="",style="solid", color="burlywood", weight=3];
48[label="primCmpNat (Succ vx10000) (Succ vx110) == LT",fontsize=16,color="black",shape="box"];48 -> 52[label="",style="solid", color="black", weight=3];
49[label="primCmpNat (Succ vx10000) Zero == LT",fontsize=16,color="black",shape="box"];49 -> 53[label="",style="solid", color="black", weight=3];
50[label="primCmpNat Zero (Succ vx110) == LT",fontsize=16,color="black",shape="box"];50 -> 54[label="",style="solid", color="black", weight=3];
51[label="primCmpNat Zero Zero == LT",fontsize=16,color="black",shape="box"];51 -> 55[label="",style="solid", color="black", weight=3];
52 -> 43[label="",style="dashed", color="red", weight=0];
52[label="primCmpNat vx10000 vx110 == LT",fontsize=16,color="magenta"];52 -> 56[label="",style="dashed", color="magenta", weight=3];
52 -> 57[label="",style="dashed", color="magenta", weight=3];
53[label="GT == LT",fontsize=16,color="black",shape="box"];53 -> 58[label="",style="solid", color="black", weight=3];
54 -> 40[label="",style="dashed", color="red", weight=0];
54[label="LT == LT",fontsize=16,color="magenta"];55[label="EQ == LT",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3];
56[label="vx110",fontsize=16,color="green",shape="box"];57[label="vx10000",fontsize=16,color="green",shape="box"];58[label="False",fontsize=16,color="green",shape="box"];59[label="False",fontsize=16,color="green",shape="box"];}

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

(8)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_esEs(Succ(vx10000), Succ(vx110)) -> new_esEs(vx10000, vx110)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(9) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*new_esEs(Succ(vx10000), Succ(vx110)) -> new_esEs(vx10000, vx110)
The graph contains the following edges 1 > 1, 2 > 2


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

(10)
YES