YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) TerminationGraphProcessor [SOUND, 51 ms]
(4) AND
    (5) IntTRS
        (6) IntTRSCompressionProof [EQUIVALENT, 9 ms]
        (7) IntTRS
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (11) YES
    (12) IntTRS
        (13) IntTRSCompressionProof [EQUIVALENT, 25 ms]
        (14) IntTRS
        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (16) IntTRS
        (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (18) YES


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

(0)
Obligation:
c file /export/starexec/sandbox2/benchmark/theBenchmark.c
----------------------------------------

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

(2)
Obligation:
Rules:
f1(x, i, n, m) -> f2(x_1, i, n, m) :|: 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
f6(x16, x17, x18, x19) -> f7(x16, arith, x18, x19) :|: TRUE && arith = x17 + 1
f7(x56, x57, x58, x59) -> f8(x60, x57, x58, x59) :|: TRUE && x60 = x56 + 1
f5(x24, x25, x26, x27) -> f6(x24, x25, x26, x27) :|: x24 < x26
f8(x28, x29, x30, x31) -> f5(x28, x29, x30, x31) :|: TRUE
f5(x32, x33, x34, x35) -> f9(x32, x33, x34, x35) :|: x32 >= x34
f10(x61, x62, x63, x64) -> f11(x61, x65, x63, x64) :|: TRUE && x65 = x62 + 1
f11(x66, x67, x68, x69) -> f12(x70, x67, x68, x69) :|: TRUE && x70 = x66 + 1
f9(x44, x45, x46, x47) -> f10(x44, x45, x46, x47) :|: x44 < x47
f12(x48, x49, x50, x51) -> f9(x48, x49, x50, x51) :|: TRUE
f9(x52, x53, x54, x55) -> f13(x52, x53, x54, x55) :|: x52 >= x55
Start term: f1(x, i, n, m)

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

(3) TerminationGraphProcessor (SOUND)
Constructed the termination graph and obtained 2 non-trivial SCCs.

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:
Rules:
f5(x24, x25, x26, x27) -> f6(x24, x25, x26, x27) :|: x24 < x26
f8(x28, x29, x30, x31) -> f5(x28, x29, x30, x31) :|: TRUE
f7(x56, x57, x58, x59) -> f8(x60, x57, x58, x59) :|: TRUE && x60 = x56 + 1
f6(x16, x17, x18, x19) -> f7(x16, arith, x18, x19) :|: TRUE && arith = x17 + 1

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

(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(7)
Obligation:
Rules:
f7(x56:0, x57:0, x58:0, x59:0) -> f7(x56:0 + 1, x57:0 + 1, x58:0, x59:0) :|: x58:0 > x56:0 + 1

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

(8) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f7(x1, x2, x3, x4) -> f7(x1, x3)

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

(9)
Obligation:
Rules:
f7(x56:0, x58:0) -> f7(x56:0 + 1, x58:0) :|: x58:0 > x56:0 + 1

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

(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f7(x, x1)] = -x + x1

The following rules are decreasing:
f7(x56:0, x58:0) -> f7(x56:0 + 1, x58:0) :|: x58:0 > x56:0 + 1
The following rules are bounded:
f7(x56:0, x58:0) -> f7(x56:0 + 1, x58:0) :|: x58:0 > x56:0 + 1

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

(11)
YES

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

(12)
Obligation:
Rules:
f9(x44, x45, x46, x47) -> f10(x44, x45, x46, x47) :|: x44 < x47
f12(x48, x49, x50, x51) -> f9(x48, x49, x50, x51) :|: TRUE
f11(x66, x67, x68, x69) -> f12(x70, x67, x68, x69) :|: TRUE && x70 = x66 + 1
f10(x61, x62, x63, x64) -> f11(x61, x65, x63, x64) :|: TRUE && x65 = x62 + 1

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

(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(14)
Obligation:
Rules:
f11(x66:0, x67:0, x68:0, x69:0) -> f11(x66:0 + 1, x67:0 + 1, x68:0, x69:0) :|: x69:0 > x66:0 + 1

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

(15) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f11(x1, x2, x3, x4) -> f11(x1, x4)

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

(16)
Obligation:
Rules:
f11(x66:0, x69:0) -> f11(x66:0 + 1, x69:0) :|: x69:0 > x66:0 + 1

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

(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f11(x, x1)] = -x + x1

The following rules are decreasing:
f11(x66:0, x69:0) -> f11(x66:0 + 1, x69:0) :|: x69:0 > x66:0 + 1
The following rules are bounded:
f11(x66:0, x69:0) -> f11(x66:0 + 1, x69:0) :|: x69:0 > x66:0 + 1

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

(18)
YES