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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 2733 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(x, y, z, tx) -> f2(x_1, y, z, tx) :|: TRUE
f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE
f3(x6, x7, x8, x9) -> f4(x6, x7, x10, x9) :|: TRUE
f4(x11, x12, x13, x14) -> f5(x11, x12, x13, x15) :|: TRUE
f7(x16, x17, x18, x19) -> f10(x16, x17, arith, x19) :|: TRUE && arith = x18 - 1
f10(x20, x21, x22, x23) -> f11(x20, x21, x22, x20) :|: TRUE
f11(x24, x25, x26, x27) -> f12(x28, x25, x26, x27) :|: TRUE
f8(x63, x64, x65, x66) -> f13(x63, x67, x65, x66) :|: TRUE && x67 = x64 + 1
f6(x33, x34, x35, x36) -> f7(x33, x34, x35, x36) :|: x37 < 0
f6(x68, x69, x70, x71) -> f7(x68, x69, x70, x71) :|: x72 > 0
f6(x38, x39, x40, x41) -> f8(x38, x39, x40, x41) :|: x42 = 0
f12(x43, x44, x45, x46) -> f9(x43, x44, x45, x46) :|: TRUE
f13(x47, x48, x49, x50) -> f9(x47, x48, x49, x50) :|: TRUE
f5(x51, x52, x53, x54) -> f6(x51, x52, x53, x54) :|: x51 >= x52 && x51 <= x54 + x53
f9(x55, x56, x57, x58) -> f5(x55, x56, x57, x58) :|: TRUE
f5(x59, x60, x61, x62) -> f14(x59, x60, x61, x62) :|: x59 < x60
f5(x73, x74, x75, x76) -> f14(x73, x74, x75, x76) :|: x73 > x76 + x75
Start term: f1(x, y, z, tx)

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

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

   (f1_4,1)
   (f2_4,2)
   (f3_4,3)
   (f4_4,4)
   (f5_4,5)
   (f7_4,6)
   (f10_4,7)
   (f11_4,8)
   (f12_4,9)
   (f8_4,10)
   (f13_4,11)
   (f6_4,12)
   (f9_4,13)
   (f14_4,14)

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

(4)
Obligation:
START: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(0 = 0);
x0 := oldX4;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 2;

FROM: 2;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX4;
x2 := oldX2;
x3 := oldX3;
TO: 3;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX4;
x3 := oldX3;
TO: 4;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX4;
TO: 5;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(1 - oldX2);
assume(0 = 0 && oldX4 = oldX2 - 1);
x0 := oldX0;
x1 := oldX1;
x2 := -(1 - oldX2);
x3 := oldX3;
TO: 7;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX0;
TO: 8;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(0 = 0);
x0 := oldX4;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 9;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(-(oldX1 + 1));
assume(0 = 0 && oldX4 = oldX1 + 1);
x0 := oldX0;
x1 := -(-(oldX1 + 1));
x2 := oldX2;
x3 := oldX3;
TO: 11;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(oldX4 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 6;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(oldX4 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 6;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(0);
assume(oldX4 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 10;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 13;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 13;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX0 >= oldX1 && oldX0 <= oldX3 + oldX2);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 12;

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 5;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX0 < oldX1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 14;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX0 > oldX3 + oldX2);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 14;


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

(5) T2 (EQUIVALENT)
Used the following cutpoint-specific lexicographic rank functions:
 * For cutpoint 9, used the following rank functions/bounds (in descending priority order):
    - RF -x1+x0, bound 0

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

(6)
YES