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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 2 ms]
(4) T2IntSys
(5) T2 [EQUIVALENT, 1958 ms]
(6) YES


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(0)
Obligation:
c file /export/starexec/sandbox/benchmark/theBenchmark.c
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(1) CToIRSProof (EQUIVALENT)
Parsed C Integer Program as IRS.
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(2)
Obligation:
Rules:
f1(i, x, n, b, t) -> f2(x_1, x, n, b, t) :|: TRUE
f2(x1, x2, x3, x4, x5) -> f3(x1, x6, x3, x4, x5) :|: TRUE
f3(x7, x8, x9, x10, x11) -> f4(x7, x8, x12, x10, x11) :|: TRUE
f4(x13, x14, x15, x16, x17) -> f5(x13, x14, x15, x18, x17) :|: TRUE
f6(x19, x20, x21, x22, x23) -> f9(x19, x20, x21, x22, 1) :|: TRUE
f7(x24, x25, x26, x27, x28) -> f10(x24, x25, x26, x27, arith) :|: TRUE && arith = 0 - 1
f5(x29, x30, x31, x32, x33) -> f6(x29, x30, x31, x32, x33) :|: x32 >= 1
f5(x34, x35, x36, x37, x38) -> f7(x34, x35, x36, x37, x38) :|: x37 < 1
f9(x39, x40, x41, x42, x43) -> f8(x39, x40, x41, x42, x43) :|: TRUE
f10(x44, x45, x46, x47, x48) -> f8(x44, x45, x46, x47, x48) :|: TRUE
f12(x94, x95, x96, x97, x98) -> f15(x94, x99, x96, x97, x98) :|: TRUE && x99 = x95 + x98
f13(x100, x101, x102, x103, x104) -> f16(x100, x105, x102, x103, x104) :|: TRUE && x105 = x101 - x104
f11(x59, x60, x61, x62, x63) -> f12(x59, x60, x61, x62, x63) :|: x62 >= 1
f11(x64, x65, x66, x67, x68) -> f13(x64, x65, x66, x67, x68) :|: x67 < 1
f15(x69, x70, x71, x72, x73) -> f14(x69, x70, x71, x72, x73) :|: TRUE
f16(x74, x75, x76, x77, x78) -> f14(x74, x75, x76, x77, x78) :|: TRUE
f8(x79, x80, x81, x82, x83) -> f11(x79, x80, x81, x82, x83) :|: x80 <= x81
f14(x84, x85, x86, x87, x88) -> f8(x84, x85, x86, x87, x88) :|: TRUE
f8(x89, x90, x91, x92, x93) -> f17(x89, x90, x91, x92, x93) :|: x90 > x91
Start term: f1(i, x, n, b, t)

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

   (f1_5,1)
   (f2_5,2)
   (f3_5,3)
   (f4_5,4)
   (f5_5,5)
   (f6_5,6)
   (f9_5,7)
   (f7_5,8)
   (f10_5,9)
   (f8_5,10)
   (f12_5,11)
   (f15_5,12)
   (f13_5,13)
   (f16_5,14)
   (f11_5,15)
   (f14_5,16)
   (f17_5,17)

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(4)
Obligation:
START: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := nondet();
assume(0 = 0);
x0 := oldX5;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 2;

FROM: 2;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX5;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 3;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX5;
x3 := oldX3;
x4 := oldX4;
TO: 4;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX5;
x4 := oldX4;
TO: 5;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := 1;
TO: 7;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := -(1);
assume(0 = 0 && oldX5 = 0 - 1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := -(1);
TO: 9;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(oldX3 >= 1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 6;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(oldX3 < 1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 8;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 10;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 10;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := -(-(oldX1 + oldX4));
assume(0 = 0 && oldX5 = oldX1 + oldX4);
x0 := oldX0;
x1 := -(-(oldX1 + oldX4));
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 12;

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := -(oldX4 - oldX1);
assume(0 = 0 && oldX5 = oldX1 - oldX4);
x0 := oldX0;
x1 := -(oldX4 - oldX1);
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 14;

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(oldX3 >= 1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 11;

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(oldX3 < 1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 13;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 16;

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 16;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(oldX1 <= oldX2);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 15;

FROM: 16;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 10;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(oldX1 > oldX2);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 17;


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(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 x2-x1, bound 0

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(6)
YES