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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 68 ms]
(2) IntTRS
(3) TerminationGraphProcessor [SOUND, 105 ms]
(4) AND
    (5) IntTRS
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IntTRS
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 3 ms]
        (11) YES
    (12) IntTRS
        (13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (14) IntTRS
        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (16) IntTRS
        (17) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (20) 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(x, y, res) -> f2(x_1, y, res) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
f3(x5, x6, x7) -> f4(x5, x6, 0) :|: TRUE
f5(x8, x9, x10) -> f6(arith, x9, x10) :|: TRUE && arith = x8 - 1
f6(x53, x54, x55) -> f7(x53, x56, x55) :|: TRUE && x56 = x54 - 1
f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x14 > 0 && x15 > 0
f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
f4(x20, x21, x22) -> f8(x20, x21, x22) :|: x20 <= 0
f4(x57, x58, x59) -> f8(x57, x58, x59) :|: x58 <= 0
f9(x60, x61, x62) -> f10(x60, x63, x62) :|: TRUE && x63 = x61 + 1
f10(x64, x65, x66) -> f11(x64, x65, x67) :|: TRUE && x67 = x66 + 1
f12(x68, x69, x70) -> f13(x71, x69, x70) :|: TRUE && x71 = x68 - 1
f13(x72, x73, x74) -> f14(x72, x75, x74) :|: TRUE && x75 = x73 - 1
f11(x35, x36, x37) -> f12(x35, x36, x37) :|: x35 > 0 && x36 > 0
f14(x38, x39, x40) -> f11(x38, x39, x40) :|: TRUE
f11(x41, x42, x43) -> f15(x41, x42, x43) :|: x41 <= 0
f11(x76, x77, x78) -> f15(x76, x77, x78) :|: x77 <= 0
f8(x44, x45, x46) -> f9(x44, x45, x46) :|: x44 > 0
f15(x47, x48, x49) -> f8(x47, x48, x49) :|: TRUE
f8(x50, x51, x52) -> f16(x50, x51, x52) :|: x50 <= 0
Start term: f1(x, y, res)

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

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(4)
Complex Obligation (AND)

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(5)
Obligation:
Rules:
f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x14 > 0 && x15 > 0
f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
f6(x53, x54, x55) -> f7(x53, x56, x55) :|: TRUE && x56 = x54 - 1
f5(x8, x9, x10) -> f6(arith, x9, x10) :|: TRUE && arith = x8 - 1

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
f6(x53:0, x54:0, x55:0) -> f6(x53:0 - 1, x54:0 - 1, x55:0) :|: x53:0 > 0 && x54:0 > 1

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

   f6(x1, x2, x3) -> f6(x1, x2)

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(9)
Obligation:
Rules:
f6(x53:0, x54:0) -> f6(x53:0 - 1, x54:0 - 1) :|: x53:0 > 0 && x54:0 > 1

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x, x1)] = x1

The following rules are decreasing:
f6(x53:0, x54:0) -> f6(x53:0 - 1, x54:0 - 1) :|: x53:0 > 0 && x54:0 > 1
The following rules are bounded:
f6(x53:0, x54:0) -> f6(x53:0 - 1, x54:0 - 1) :|: x53:0 > 0 && x54:0 > 1

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(11)
YES

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(12)
Obligation:
Rules:
f8(x44, x45, x46) -> f9(x44, x45, x46) :|: x44 > 0
f15(x47, x48, x49) -> f8(x47, x48, x49) :|: TRUE
f11(x41, x42, x43) -> f15(x41, x42, x43) :|: x41 <= 0
f10(x64, x65, x66) -> f11(x64, x65, x67) :|: TRUE && x67 = x66 + 1
f9(x60, x61, x62) -> f10(x60, x63, x62) :|: TRUE && x63 = x61 + 1
f14(x38, x39, x40) -> f11(x38, x39, x40) :|: TRUE
f13(x72, x73, x74) -> f14(x72, x75, x74) :|: TRUE && x75 = x73 - 1
f12(x68, x69, x70) -> f13(x71, x69, x70) :|: TRUE && x71 = x68 - 1
f11(x35, x36, x37) -> f12(x35, x36, x37) :|: x35 > 0 && x36 > 0
f11(x76, x77, x78) -> f15(x76, x77, x78) :|: x77 <= 0

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(14)
Obligation:
Rules:
f11(x76:0, x77:0, x78:0) -> f11(x76:0, x77:0 + 1, x78:0 + 1) :|: x77:0 < 1 && x76:0 > 0
f11(x41:0, x42:0, x43:0) -> f11(x41:0, x42:0 + 1, x43:0 + 1) :|: x41:0 < 1 && x41:0 > 0
f11(x35:0, x36:0, x37:0) -> f11(x35:0 - 1, x36:0 - 1, x37:0) :|: x35:0 > 0 && x36:0 > 0

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

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

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(16)
Obligation:
Rules:
f11(x76:0, x77:0) -> f11(x76:0, x77:0 + 1) :|: x77:0 < 1 && x76:0 > 0
f11(x41:0, x42:0) -> f11(x41:0, x42:0 + 1) :|: x41:0 < 1 && x41:0 > 0
f11(x35:0, x36:0) -> f11(x35:0 - 1, x36:0 - 1) :|: x35:0 > 0 && x36:0 > 0

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(17) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f11 ] = f11_1

The following rules are decreasing:
f11(x41:0, x42:0) -> f11(x41:0, x42:0 + 1) :|: x41:0 < 1 && x41:0 > 0
f11(x35:0, x36:0) -> f11(x35:0 - 1, x36:0 - 1) :|: x35:0 > 0 && x36:0 > 0

The following rules are bounded:
f11(x76:0, x77:0) -> f11(x76:0, x77:0 + 1) :|: x77:0 < 1 && x76:0 > 0
f11(x41:0, x42:0) -> f11(x41:0, x42:0 + 1) :|: x41:0 < 1 && x41:0 > 0
f11(x35:0, x36:0) -> f11(x35:0 - 1, x36:0 - 1) :|: x35:0 > 0 && x36:0 > 0


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(18)
Obligation:
Rules:
f11(x76:0, x77:0) -> f11(x76:0, x77:0 + 1) :|: x77:0 < 1 && x76:0 > 0

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(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f11 ] = -1*f11_2

The following rules are decreasing:
f11(x76:0, x77:0) -> f11(x76:0, x77:0 + 1) :|: x77:0 < 1 && x76:0 > 0

The following rules are bounded:
f11(x76:0, x77:0) -> f11(x76:0, x77:0 + 1) :|: x77:0 < 1 && x76:0 > 0


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(20)
YES