/export/starexec/sandbox/solver/bin/starexec_run_c /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.c
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given C Problem could be proven:

(0) C Problem
(1) CToIRSProof [EQUIVALENT, 0 ms]
(2) IntTRS
(3) IRS2T2 [EQUIVALENT, 0 ms]
(4) T2IntSys
(5) T2 [EQUIVALENT, 1328 ms]
(6) YES


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

(0)
Obligation:
c file /export/starexec/sandbox/benchmark/theBenchmark.c
----------------------------------------

(1) CToIRSProof (EQUIVALENT)
Parsed C Integer Program as IRS.
----------------------------------------

(2)
Obligation:
Rules:
f1(a, x, max) -> f2(x_1, x, max) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE
f5(x9, x10, x11) -> f8(0, x10, x11) :|: TRUE
f8(x12, x13, x14) -> f9(x12, 1, x14) :|: TRUE
f11(x15, x16, x17) -> f14(arith, x16, x17) :|: TRUE && arith = x15 + 1
f12(x59, x60, x61) -> f15(x62, x60, x61) :|: TRUE && x62 = x59 - 1
f10(x21, x22, x23) -> f11(x21, x22, x23) :|: x24 < 0
f10(x63, x64, x65) -> f11(x63, x64, x65) :|: x66 > 0
f10(x25, x26, x27) -> f12(x25, x26, x27) :|: x28 = 0
f14(x29, x30, x31) -> f13(x29, x30, x31) :|: TRUE
f15(x32, x33, x34) -> f13(x32, x33, x34) :|: TRUE
f13(x67, x68, x69) -> f16(x67, x70, x69) :|: TRUE && x70 = x68 + 1
f9(x38, x39, x40) -> f10(x38, x39, x40) :|: x39 <= x40
f16(x41, x42, x43) -> f9(x41, x42, x43) :|: TRUE
f9(x44, x45, x46) -> f17(x44, x45, x46) :|: x45 > x46
f4(x47, x48, x49) -> f5(x47, x48, x49) :|: x49 > 0
f4(x50, x51, x52) -> f6(x50, x51, x52) :|: x52 <= 0
f17(x53, x54, x55) -> f7(x53, x54, x55) :|: TRUE
f6(x56, x57, x58) -> f7(x56, x57, x58) :|: TRUE
Start term: f1(a, x, max)

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

(3) IRS2T2 (EQUIVALENT)
Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs:

   (f1_3,1)
   (f2_3,2)
   (f3_3,3)
   (f4_3,4)
   (f5_3,5)
   (f8_3,6)
   (f9_3,7)
   (f11_3,8)
   (f14_3,9)
   (f12_3,10)
   (f15_3,11)
   (f10_3,12)
   (f13_3,13)
   (f16_3,14)
   (f17_3,15)
   (f6_3,16)
   (f7_3,17)

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

(4)
Obligation:
START: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(0 = 0);
x0 := oldX3;
x1 := oldX1;
x2 := oldX2;
TO: 2;

FROM: 2;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX3;
x2 := oldX2;
TO: 3;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX3;
TO: 4;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := 0;
x1 := oldX1;
x2 := oldX2;
TO: 6;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := 1;
x2 := oldX2;
TO: 7;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(-(oldX0 + 1));
assume(0 = 0 && oldX3 = oldX0 + 1);
x0 := -(-(oldX0 + 1));
x1 := oldX1;
x2 := oldX2;
TO: 9;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(1 - oldX0);
assume(0 = 0 && oldX3 = oldX0 - 1);
x0 := -(1 - oldX0);
x1 := oldX1;
x2 := oldX2;
TO: 11;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX3 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 8;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX3 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 8;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(0);
assume(oldX3 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 10;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 13;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 13;

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(-(oldX1 + 1));
assume(0 = 0 && oldX3 = oldX1 + 1);
x0 := oldX0;
x1 := -(-(oldX1 + 1));
x2 := oldX2;
TO: 14;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 <= oldX2);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 12;

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 7;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 > oldX2);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 15;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX2 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 5;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX2 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 16;

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 17;

FROM: 16;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 17;


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

(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 11, 12, 13, 14, 15, 16, 19, 20 using the following rank functions:
    - Rank function 1:
      RF for loc. 10: -1-4*x1+4*x2
      RF for loc. 11: -2-4*x1+4*x2
      RF for loc. 12: -4*x1+4*x2
      RF for loc. 14: 1-4*x1+4*x2
      Bound for (chained) transitions 19: 1
      Bound for (chained) transitions 20: 1
    - Rank function 2:
      RF for loc. 10: -1+2*x2
      RF for loc. 11: 0
      RF for loc. 12: 2*x2
      RF for loc. 14: -1
      Bound for (chained) transitions 11: 1
      Bound for (chained) transitions 12: 2
      Bound for (chained) transitions 13: 2
      Bound for (chained) transitions 14: 2
      Bound for (chained) transitions 15, 16: 0

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

(6)
YES