/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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 [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="primEqChar vx3 vx4",fontsize=16,color="burlywood",shape="box"];21[label="vx3/Char vx30",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];
6[label="primEqChar (Char vx30) vx4",fontsize=16,color="burlywood",shape="box"];22[label="vx4/Char vx40",fontsize=10,color="white",style="solid",shape="box"];6 -> 22[label="",style="solid", color="burlywood", weight=9];
22 -> 7[label="",style="solid", color="burlywood", weight=3];
7[label="primEqChar (Char vx30) (Char vx40)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="primEqNat vx30 vx40",fontsize=16,color="burlywood",shape="triangle"];23[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];8 -> 23[label="",style="solid", color="burlywood", weight=9];
23 -> 9[label="",style="solid", color="burlywood", weight=3];
24[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 24[label="",style="solid", color="burlywood", weight=9];
24 -> 10[label="",style="solid", color="burlywood", weight=3];
9[label="primEqNat (Succ vx300) vx40",fontsize=16,color="burlywood",shape="box"];25[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];9 -> 25[label="",style="solid", color="burlywood", weight=9];
25 -> 11[label="",style="solid", color="burlywood", weight=3];
26[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 26[label="",style="solid", color="burlywood", weight=9];
26 -> 12[label="",style="solid", color="burlywood", weight=3];
10[label="primEqNat Zero vx40",fontsize=16,color="burlywood",shape="box"];27[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];10 -> 27[label="",style="solid", color="burlywood", weight=9];
27 -> 13[label="",style="solid", color="burlywood", weight=3];
28[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 28[label="",style="solid", color="burlywood", weight=9];
28 -> 14[label="",style="solid", color="burlywood", weight=3];
11[label="primEqNat (Succ vx300) (Succ vx400)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
12[label="primEqNat (Succ vx300) Zero",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13[label="primEqNat Zero (Succ vx400)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15 -> 8[label="",style="dashed", color="red", weight=0];
15[label="primEqNat vx300 vx400",fontsize=16,color="magenta"];15 -> 19[label="",style="dashed", color="magenta", weight=3];
15 -> 20[label="",style="dashed", color="magenta", weight=3];
16[label="False",fontsize=16,color="green",shape="box"];17[label="False",fontsize=16,color="green",shape="box"];18[label="True",fontsize=16,color="green",shape="box"];19[label="vx300",fontsize=16,color="green",shape="box"];20[label="vx400",fontsize=16,color="green",shape="box"];}

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

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

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


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

(8)
YES