/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 [EQUIVALENT, 10 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.

Binding Reductions:
The bind variable of the following binding Pattern
"r@(vz,wu)"
is replaced by the following term
"(vz,wu)"

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

(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
"rangeSize (vz,wu)|null (range (vz,wu))0|otherwiseindex (vz,wu) wu + 1;
"
is transformed to
"rangeSize (vz,wu) = rangeSize2 (vz,wu);
"
"rangeSize1 vz wu True = 0;
rangeSize1 vz wu False = rangeSize0 vz wu otherwise;
"
"rangeSize0 vz wu True = index (vz,wu) wu + 1;
"
"rangeSize2 (vz,wu) = rangeSize1 vz wu (null (range (vz,wu)));
"

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

(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="rangeSize",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="rangeSize ww3",fontsize=16,color="burlywood",shape="triangle"];19[label="ww3/(ww30,ww31)",fontsize=10,color="white",style="solid",shape="box"];3 -> 19[label="",style="solid", color="burlywood", weight=9];
19 -> 4[label="",style="solid", color="burlywood", weight=3];
4[label="rangeSize (ww30,ww31)",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="rangeSize2 (ww30,ww31)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="rangeSize1 ww30 ww31 (null (range (ww30,ww31)))",fontsize=16,color="burlywood",shape="box"];20[label="ww30/()",fontsize=10,color="white",style="solid",shape="box"];6 -> 20[label="",style="solid", color="burlywood", weight=9];
20 -> 7[label="",style="solid", color="burlywood", weight=3];
7[label="rangeSize1 () ww31 (null (range ((),ww31)))",fontsize=16,color="burlywood",shape="box"];21[label="ww31/()",fontsize=10,color="white",style="solid",shape="box"];7 -> 21[label="",style="solid", color="burlywood", weight=9];
21 -> 8[label="",style="solid", color="burlywood", weight=3];
8[label="rangeSize1 () () (null (range ((),())))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="rangeSize1 () () (null (() : []))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="rangeSize1 () () False",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="rangeSize0 () () otherwise",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="rangeSize0 () () True",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13[label="index ((),()) () + Pos (Succ Zero)",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14[label="primPlusInt (index ((),()) ()) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
15[label="primPlusInt (Pos Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3];
16[label="Pos (primPlusNat Zero (Succ Zero))",fontsize=16,color="green",shape="box"];16 -> 17[label="",style="dashed", color="green", weight=3];
17[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3];
18[label="Succ Zero",fontsize=16,color="green",shape="box"];}

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

(8)
YES