/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) Narrow [SOUND, 0 ms]
(6) QDP
(7) QDPSizeChangeProof [EQUIVALENT, 0 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.
----------------------------------------

(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) Narrow (SOUND)
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="primCmpChar vx3 vx4 == LT",fontsize=16,color="burlywood",shape="box"];25[label="vx3/Char vx30",fontsize=10,color="white",style="solid",shape="box"];6 -> 25[label="",style="solid", color="burlywood", weight=9];
25 -> 7[label="",style="solid", color="burlywood", weight=3];
7[label="primCmpChar (Char vx30) vx4 == LT",fontsize=16,color="burlywood",shape="box"];26[label="vx4/Char vx40",fontsize=10,color="white",style="solid",shape="box"];7 -> 26[label="",style="solid", color="burlywood", weight=9];
26 -> 8[label="",style="solid", color="burlywood", weight=3];
8[label="primCmpChar (Char vx30) (Char vx40) == LT",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="primCmpNat vx30 vx40 == LT",fontsize=16,color="burlywood",shape="triangle"];27[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];9 -> 27[label="",style="solid", color="burlywood", weight=9];
27 -> 10[label="",style="solid", color="burlywood", weight=3];
28[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 28[label="",style="solid", color="burlywood", weight=9];
28 -> 11[label="",style="solid", color="burlywood", weight=3];
10[label="primCmpNat (Succ vx300) vx40 == LT",fontsize=16,color="burlywood",shape="box"];29[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];10 -> 29[label="",style="solid", color="burlywood", weight=9];
29 -> 12[label="",style="solid", color="burlywood", weight=3];
30[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 30[label="",style="solid", color="burlywood", weight=9];
30 -> 13[label="",style="solid", color="burlywood", weight=3];
11[label="primCmpNat Zero vx40 == LT",fontsize=16,color="burlywood",shape="box"];31[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];11 -> 31[label="",style="solid", color="burlywood", weight=9];
31 -> 14[label="",style="solid", color="burlywood", weight=3];
32[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];11 -> 32[label="",style="solid", color="burlywood", weight=9];
32 -> 15[label="",style="solid", color="burlywood", weight=3];
12[label="primCmpNat (Succ vx300) (Succ vx400) == LT",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13[label="primCmpNat (Succ vx300) Zero == LT",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="primCmpNat Zero (Succ vx400) == LT",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="primCmpNat Zero Zero == LT",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16 -> 9[label="",style="dashed", color="red", weight=0];
16[label="primCmpNat vx300 vx400 == LT",fontsize=16,color="magenta"];16 -> 20[label="",style="dashed", color="magenta", weight=3];
16 -> 21[label="",style="dashed", color="magenta", weight=3];
17[label="GT == LT",fontsize=16,color="black",shape="box"];17 -> 22[label="",style="solid", color="black", weight=3];
18[label="LT == LT",fontsize=16,color="black",shape="box"];18 -> 23[label="",style="solid", color="black", weight=3];
19[label="EQ == LT",fontsize=16,color="black",shape="box"];19 -> 24[label="",style="solid", color="black", weight=3];
20[label="vx300",fontsize=16,color="green",shape="box"];21[label="vx400",fontsize=16,color="green",shape="box"];22[label="False",fontsize=16,color="green",shape="box"];23[label="True",fontsize=16,color="green",shape="box"];24[label="False",fontsize=16,color="green",shape="box"];}

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

(6)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_esEs(Succ(vx300), Succ(vx400)) -> new_esEs(vx300, vx400)

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

(7) 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(vx300), Succ(vx400)) -> new_esEs(vx300, vx400)
The graph contains the following edges 1 > 1, 2 > 2


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

(8)
YES