/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) AND
    (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 1 ms]
        (11) YES
    (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) 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="pi",fontsize=16,color="black",shape="box"];1 -> 3[label="",style="solid", color="black", weight=3];
3[label="fromInt (Pos (Succ (Succ (Succ (Succ Zero))))) * atan (fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="primMulFloat (fromInt (Pos (Succ (Succ (Succ (Succ Zero)))))) (atan (fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="primMulFloat (primIntToFloat (Pos (Succ (Succ (Succ (Succ Zero)))))) (atan (fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6 -> 10[label="",style="dashed", color="red", weight=0];
6[label="primMulFloat (Float (Pos (Succ (Succ (Succ (Succ Zero))))) (Pos (Succ Zero))) (atan (fromInt (Pos (Succ Zero))))",fontsize=16,color="magenta"];6 -> 11[label="",style="dashed", color="magenta", weight=3];
11[label="atan (fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
10[label="primMulFloat (Float (Pos (Succ (Succ (Succ (Succ Zero))))) (Pos (Succ Zero))) vx3",fontsize=16,color="burlywood",shape="triangle"];197[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];10 -> 197[label="",style="solid", color="burlywood", weight=9];
197 -> 16[label="",style="solid", color="burlywood", weight=3];
15[label="primAtanFloat (fromInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3];
16[label="primMulFloat (Float (Pos (Succ (Succ (Succ (Succ Zero))))) (Pos (Succ Zero))) (Float vx30 vx31)",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3];
18 -> 21[label="",style="dashed", color="red", weight=0];
18[label="terminator (fromInt (Pos (Succ Zero)))",fontsize=16,color="magenta"];18 -> 22[label="",style="dashed", color="magenta", weight=3];
19[label="Float (Pos (Succ (Succ (Succ (Succ Zero)))) * vx30) (Pos (Succ Zero) * vx31)",fontsize=16,color="green",shape="box"];19 -> 23[label="",style="dashed", color="green", weight=3];
19 -> 24[label="",style="dashed", color="green", weight=3];
22[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];22 -> 25[label="",style="solid", color="black", weight=3];
21[label="terminator vx4",fontsize=16,color="black",shape="triangle"];21 -> 26[label="",style="solid", color="black", weight=3];
23[label="Pos (Succ (Succ (Succ (Succ Zero)))) * vx30",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
24[label="Pos (Succ Zero) * vx31",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
25[label="primIntToFloat (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
26[label="ter1m vx4",fontsize=16,color="green",shape="box"];26 -> 30[label="",style="dashed", color="green", weight=3];
27[label="primMulInt (Pos (Succ (Succ (Succ (Succ Zero))))) vx30",fontsize=16,color="burlywood",shape="box"];198[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];27 -> 198[label="",style="solid", color="burlywood", weight=9];
198 -> 31[label="",style="solid", color="burlywood", weight=3];
199[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];27 -> 199[label="",style="solid", color="burlywood", weight=9];
199 -> 32[label="",style="solid", color="burlywood", weight=3];
28[label="primMulInt (Pos (Succ Zero)) vx31",fontsize=16,color="burlywood",shape="box"];200[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];28 -> 200[label="",style="solid", color="burlywood", weight=9];
200 -> 33[label="",style="solid", color="burlywood", weight=3];
201[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];28 -> 201[label="",style="solid", color="burlywood", weight=9];
201 -> 34[label="",style="solid", color="burlywood", weight=3];
29[label="Float (Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];30[label="vx4",fontsize=16,color="green",shape="box"];31[label="primMulInt (Pos (Succ (Succ (Succ (Succ Zero))))) (Pos vx300)",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3];
32[label="primMulInt (Pos (Succ (Succ (Succ (Succ Zero))))) (Neg vx300)",fontsize=16,color="black",shape="box"];32 -> 36[label="",style="solid", color="black", weight=3];
33[label="primMulInt (Pos (Succ Zero)) (Pos vx310)",fontsize=16,color="black",shape="box"];33 -> 37[label="",style="solid", color="black", weight=3];
34[label="primMulInt (Pos (Succ Zero)) (Neg vx310)",fontsize=16,color="black",shape="box"];34 -> 38[label="",style="solid", color="black", weight=3];
35[label="Pos (primMulNat (Succ (Succ (Succ (Succ Zero)))) vx300)",fontsize=16,color="green",shape="box"];35 -> 39[label="",style="dashed", color="green", weight=3];
36[label="Neg (primMulNat (Succ (Succ (Succ (Succ Zero)))) vx300)",fontsize=16,color="green",shape="box"];36 -> 40[label="",style="dashed", color="green", weight=3];
37[label="Pos (primMulNat (Succ Zero) vx310)",fontsize=16,color="green",shape="box"];37 -> 41[label="",style="dashed", color="green", weight=3];
38[label="Neg (primMulNat (Succ Zero) vx310)",fontsize=16,color="green",shape="box"];38 -> 42[label="",style="dashed", color="green", weight=3];
39[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) vx300",fontsize=16,color="burlywood",shape="triangle"];202[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];39 -> 202[label="",style="solid", color="burlywood", weight=9];
202 -> 43[label="",style="solid", color="burlywood", weight=3];
203[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];39 -> 203[label="",style="solid", color="burlywood", weight=9];
203 -> 44[label="",style="solid", color="burlywood", weight=3];
40 -> 39[label="",style="dashed", color="red", weight=0];
40[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) vx300",fontsize=16,color="magenta"];40 -> 45[label="",style="dashed", color="magenta", weight=3];
41[label="primMulNat (Succ Zero) vx310",fontsize=16,color="burlywood",shape="triangle"];204[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];41 -> 204[label="",style="solid", color="burlywood", weight=9];
204 -> 46[label="",style="solid", color="burlywood", weight=3];
205[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];41 -> 205[label="",style="solid", color="burlywood", weight=9];
205 -> 47[label="",style="solid", color="burlywood", weight=3];
42 -> 41[label="",style="dashed", color="red", weight=0];
42[label="primMulNat (Succ Zero) vx310",fontsize=16,color="magenta"];42 -> 48[label="",style="dashed", color="magenta", weight=3];
43[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ vx3000)",fontsize=16,color="black",shape="box"];43 -> 49[label="",style="solid", color="black", weight=3];
44[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) Zero",fontsize=16,color="black",shape="box"];44 -> 50[label="",style="solid", color="black", weight=3];
45[label="vx300",fontsize=16,color="green",shape="box"];46[label="primMulNat (Succ Zero) (Succ vx3100)",fontsize=16,color="black",shape="box"];46 -> 51[label="",style="solid", color="black", weight=3];
47[label="primMulNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];47 -> 52[label="",style="solid", color="black", weight=3];
48[label="vx310",fontsize=16,color="green",shape="box"];49[label="primPlusNat (primMulNat (Succ (Succ (Succ Zero))) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="black",shape="box"];49 -> 53[label="",style="solid", color="black", weight=3];
50[label="Zero",fontsize=16,color="green",shape="box"];51[label="primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100)",fontsize=16,color="black",shape="box"];51 -> 54[label="",style="solid", color="black", weight=3];
52[label="Zero",fontsize=16,color="green",shape="box"];53[label="primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ vx3000)) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="black",shape="box"];53 -> 55[label="",style="solid", color="black", weight=3];
54[label="primPlusNat Zero (Succ vx3100)",fontsize=16,color="black",shape="box"];54 -> 56[label="",style="solid", color="black", weight=3];
55 -> 57[label="",style="dashed", color="red", weight=0];
55[label="primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ Zero) (Succ vx3000)) (Succ vx3000)) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="magenta"];55 -> 58[label="",style="dashed", color="magenta", weight=3];
56[label="Succ vx3100",fontsize=16,color="green",shape="box"];58 -> 41[label="",style="dashed", color="red", weight=0];
58[label="primMulNat (Succ Zero) (Succ vx3000)",fontsize=16,color="magenta"];58 -> 59[label="",style="dashed", color="magenta", weight=3];
57[label="primPlusNat (primPlusNat (primPlusNat vx5 (Succ vx3000)) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="burlywood",shape="triangle"];206[label="vx5/Succ vx50",fontsize=10,color="white",style="solid",shape="box"];57 -> 206[label="",style="solid", color="burlywood", weight=9];
206 -> 60[label="",style="solid", color="burlywood", weight=3];
207[label="vx5/Zero",fontsize=10,color="white",style="solid",shape="box"];57 -> 207[label="",style="solid", color="burlywood", weight=9];
207 -> 61[label="",style="solid", color="burlywood", weight=3];
59[label="Succ vx3000",fontsize=16,color="green",shape="box"];60[label="primPlusNat (primPlusNat (primPlusNat (Succ vx50) (Succ vx3000)) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="black",shape="box"];60 -> 62[label="",style="solid", color="black", weight=3];
61[label="primPlusNat (primPlusNat (primPlusNat Zero (Succ vx3000)) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="black",shape="box"];61 -> 63[label="",style="solid", color="black", weight=3];
62[label="primPlusNat (primPlusNat (Succ (Succ (primPlusNat vx50 vx3000))) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="black",shape="box"];62 -> 64[label="",style="solid", color="black", weight=3];
63[label="primPlusNat (primPlusNat (Succ vx3000) (Succ vx3000)) (Succ vx3000)",fontsize=16,color="black",shape="box"];63 -> 65[label="",style="solid", color="black", weight=3];
64 -> 140[label="",style="dashed", color="red", weight=0];
64[label="primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat vx50 vx3000)) vx3000))) (Succ vx3000)",fontsize=16,color="magenta"];64 -> 141[label="",style="dashed", color="magenta", weight=3];
64 -> 142[label="",style="dashed", color="magenta", weight=3];
65 -> 140[label="",style="dashed", color="red", weight=0];
65[label="primPlusNat (Succ (Succ (primPlusNat vx3000 vx3000))) (Succ vx3000)",fontsize=16,color="magenta"];65 -> 143[label="",style="dashed", color="magenta", weight=3];
65 -> 144[label="",style="dashed", color="magenta", weight=3];
141[label="Succ vx3000",fontsize=16,color="green",shape="box"];142[label="Succ (primPlusNat (Succ (primPlusNat vx50 vx3000)) vx3000)",fontsize=16,color="green",shape="box"];142 -> 167[label="",style="dashed", color="green", weight=3];
140[label="primPlusNat (Succ vx7) vx8",fontsize=16,color="burlywood",shape="triangle"];208[label="vx8/Succ vx80",fontsize=10,color="white",style="solid",shape="box"];140 -> 208[label="",style="solid", color="burlywood", weight=9];
208 -> 168[label="",style="solid", color="burlywood", weight=3];
209[label="vx8/Zero",fontsize=10,color="white",style="solid",shape="box"];140 -> 209[label="",style="solid", color="burlywood", weight=9];
209 -> 169[label="",style="solid", color="burlywood", weight=3];
143[label="Succ vx3000",fontsize=16,color="green",shape="box"];144[label="Succ (primPlusNat vx3000 vx3000)",fontsize=16,color="green",shape="box"];144 -> 170[label="",style="dashed", color="green", weight=3];
167 -> 140[label="",style="dashed", color="red", weight=0];
167[label="primPlusNat (Succ (primPlusNat vx50 vx3000)) vx3000",fontsize=16,color="magenta"];167 -> 171[label="",style="dashed", color="magenta", weight=3];
167 -> 172[label="",style="dashed", color="magenta", weight=3];
168[label="primPlusNat (Succ vx7) (Succ vx80)",fontsize=16,color="black",shape="box"];168 -> 173[label="",style="solid", color="black", weight=3];
169[label="primPlusNat (Succ vx7) Zero",fontsize=16,color="black",shape="box"];169 -> 174[label="",style="solid", color="black", weight=3];
170[label="primPlusNat vx3000 vx3000",fontsize=16,color="burlywood",shape="triangle"];210[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];170 -> 210[label="",style="solid", color="burlywood", weight=9];
210 -> 175[label="",style="solid", color="burlywood", weight=3];
211[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];170 -> 211[label="",style="solid", color="burlywood", weight=9];
211 -> 176[label="",style="solid", color="burlywood", weight=3];
171[label="vx3000",fontsize=16,color="green",shape="box"];172[label="primPlusNat vx50 vx3000",fontsize=16,color="burlywood",shape="triangle"];212[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];172 -> 212[label="",style="solid", color="burlywood", weight=9];
212 -> 177[label="",style="solid", color="burlywood", weight=3];
213[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];172 -> 213[label="",style="solid", color="burlywood", weight=9];
213 -> 178[label="",style="solid", color="burlywood", weight=3];
173[label="Succ (Succ (primPlusNat vx7 vx80))",fontsize=16,color="green",shape="box"];173 -> 179[label="",style="dashed", color="green", weight=3];
174[label="Succ vx7",fontsize=16,color="green",shape="box"];175[label="primPlusNat (Succ vx30000) (Succ vx30000)",fontsize=16,color="black",shape="box"];175 -> 180[label="",style="solid", color="black", weight=3];
176[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];176 -> 181[label="",style="solid", color="black", weight=3];
177[label="primPlusNat (Succ vx500) vx3000",fontsize=16,color="burlywood",shape="box"];214[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];177 -> 214[label="",style="solid", color="burlywood", weight=9];
214 -> 182[label="",style="solid", color="burlywood", weight=3];
215[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];177 -> 215[label="",style="solid", color="burlywood", weight=9];
215 -> 183[label="",style="solid", color="burlywood", weight=3];
178[label="primPlusNat Zero vx3000",fontsize=16,color="burlywood",shape="box"];216[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];178 -> 216[label="",style="solid", color="burlywood", weight=9];
216 -> 184[label="",style="solid", color="burlywood", weight=3];
217[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];178 -> 217[label="",style="solid", color="burlywood", weight=9];
217 -> 185[label="",style="solid", color="burlywood", weight=3];
179 -> 172[label="",style="dashed", color="red", weight=0];
179[label="primPlusNat vx7 vx80",fontsize=16,color="magenta"];179 -> 186[label="",style="dashed", color="magenta", weight=3];
179 -> 187[label="",style="dashed", color="magenta", weight=3];
180[label="Succ (Succ (primPlusNat vx30000 vx30000))",fontsize=16,color="green",shape="box"];180 -> 188[label="",style="dashed", color="green", weight=3];
181[label="Zero",fontsize=16,color="green",shape="box"];182[label="primPlusNat (Succ vx500) (Succ vx30000)",fontsize=16,color="black",shape="box"];182 -> 189[label="",style="solid", color="black", weight=3];
183[label="primPlusNat (Succ vx500) Zero",fontsize=16,color="black",shape="box"];183 -> 190[label="",style="solid", color="black", weight=3];
184[label="primPlusNat Zero (Succ vx30000)",fontsize=16,color="black",shape="box"];184 -> 191[label="",style="solid", color="black", weight=3];
185[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];185 -> 192[label="",style="solid", color="black", weight=3];
186[label="vx80",fontsize=16,color="green",shape="box"];187[label="vx7",fontsize=16,color="green",shape="box"];188 -> 170[label="",style="dashed", color="red", weight=0];
188[label="primPlusNat vx30000 vx30000",fontsize=16,color="magenta"];188 -> 193[label="",style="dashed", color="magenta", weight=3];
189[label="Succ (Succ (primPlusNat vx500 vx30000))",fontsize=16,color="green",shape="box"];189 -> 194[label="",style="dashed", color="green", weight=3];
190[label="Succ vx500",fontsize=16,color="green",shape="box"];191[label="Succ vx30000",fontsize=16,color="green",shape="box"];192[label="Zero",fontsize=16,color="green",shape="box"];193[label="vx30000",fontsize=16,color="green",shape="box"];194 -> 172[label="",style="dashed", color="red", weight=0];
194[label="primPlusNat vx500 vx30000",fontsize=16,color="magenta"];194 -> 195[label="",style="dashed", color="magenta", weight=3];
194 -> 196[label="",style="dashed", color="magenta", weight=3];
195[label="vx30000",fontsize=16,color="green",shape="box"];196[label="vx500",fontsize=16,color="green",shape="box"];}

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

(8)
Complex Obligation (AND)

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

(9)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primPlusNat(Succ(vx30000)) -> new_primPlusNat(vx30000)

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

(10) 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_primPlusNat(Succ(vx30000)) -> new_primPlusNat(vx30000)
The graph contains the following edges 1 > 1


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

(11)
YES

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

(12)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primPlusNat0(Succ(vx500), Succ(vx30000)) -> new_primPlusNat0(vx500, vx30000)

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

(13) 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_primPlusNat0(Succ(vx500), Succ(vx30000)) -> new_primPlusNat0(vx500, vx30000)
The graph contains the following edges 1 > 1, 2 > 2


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

(14)
YES