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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) TerminationGraphProcessor [SOUND, 78 ms]
(4) AND
    (5) IntTRS
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IntTRS
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 2 ms]
        (11) YES
    (12) IntTRS
        (13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (14) IntTRS
        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (16) IntTRS
        (17) RankingReductionPairProof [EQUIVALENT, 5 ms]
        (18) 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, z, i) -> f2(x_1, y, z, i) :|: TRUE
f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE
f3(x6, x7, x8, x9) -> f4(x6, x7, 0, x9) :|: TRUE
f4(x10, x11, x12, x13) -> f5(x10, x11, x12, x10) :|: TRUE
f9(x14, x15, x16, x17) -> f10(x14, x15, x16, arith) :|: TRUE && arith = x17 - 1
f10(x70, x71, x72, x73) -> f11(x70, x71, x74, x73) :|: TRUE && x74 = x72 + 1
f6(x22, x23, x24, x25) -> f9(x22, x23, x24, x25) :|: x25 > 0
f11(x26, x27, x28, x29) -> f6(x26, x27, x28, x29) :|: TRUE
f6(x30, x31, x32, x33) -> f12(x30, x31, x32, x33) :|: x33 <= 0
f13(x75, x76, x77, x78) -> f14(x75, x76, x77, x79) :|: TRUE && x79 = x78 + 1
f14(x80, x81, x82, x83) -> f15(x80, x81, x84, x83) :|: TRUE && x84 = x82 - 1
f12(x42, x43, x44, x45) -> f13(x42, x43, x44, x45) :|: x45 < x43
f15(x46, x47, x48, x49) -> f12(x46, x47, x48, x49) :|: TRUE
f12(x50, x51, x52, x53) -> f16(x50, x51, x52, x53) :|: x53 >= x51
f5(x54, x55, x56, x57) -> f6(x54, x55, x56, x57) :|: x55 > 0 && x54 > 0
f5(x58, x59, x60, x61) -> f7(x58, x59, x60, x61) :|: x59 <= 0
f5(x85, x86, x87, x88) -> f7(x85, x86, x87, x88) :|: x85 <= 0
f16(x62, x63, x64, x65) -> f8(x62, x63, x64, x65) :|: TRUE
f7(x66, x67, x68, x69) -> f8(x66, x67, x68, x69) :|: TRUE
Start term: f1(x, y, z, i)

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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:
f6(x22, x23, x24, x25) -> f9(x22, x23, x24, x25) :|: x25 > 0
f11(x26, x27, x28, x29) -> f6(x26, x27, x28, x29) :|: TRUE
f10(x70, x71, x72, x73) -> f11(x70, x71, x74, x73) :|: TRUE && x74 = x72 + 1
f9(x14, x15, x16, x17) -> f10(x14, x15, x16, arith) :|: TRUE && arith = x17 - 1

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
f10(x70:0, x71:0, x72:0, x73:0) -> f10(x70:0, x71:0, x72:0 + 1, x73:0 - 1) :|: x73:0 > 0

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

   f10(x1, x2, x3, x4) -> f10(x4)

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(9)
Obligation:
Rules:
f10(x73:0) -> f10(x73:0 - 1) :|: x73:0 > 0

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f10(x)] = x

The following rules are decreasing:
f10(x73:0) -> f10(x73:0 - 1) :|: x73:0 > 0
The following rules are bounded:
f10(x73:0) -> f10(x73:0 - 1) :|: x73:0 > 0

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(11)
YES

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(12)
Obligation:
Rules:
f12(x42, x43, x44, x45) -> f13(x42, x43, x44, x45) :|: x45 < x43
f15(x46, x47, x48, x49) -> f12(x46, x47, x48, x49) :|: TRUE
f14(x80, x81, x82, x83) -> f15(x80, x81, x84, x83) :|: TRUE && x84 = x82 - 1
f13(x75, x76, x77, x78) -> f14(x75, x76, x77, x79) :|: TRUE && x79 = x78 + 1

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(14)
Obligation:
Rules:
f14(x80:0, x81:0, x82:0, x83:0) -> f14(x80:0, x81:0, x82:0 - 1, x83:0 + 1) :|: x83:0 < x81:0

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

   f14(x1, x2, x3, x4) -> f14(x2, x4)

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(16)
Obligation:
Rules:
f14(x81:0, x83:0) -> f14(x81:0, x83:0 + 1) :|: x83:0 < x81:0

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(17) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f14 ] = -1*f14_2 + f14_1

The following rules are decreasing:
f14(x81:0, x83:0) -> f14(x81:0, x83:0 + 1) :|: x83:0 < x81:0

The following rules are bounded:
f14(x81:0, x83:0) -> f14(x81:0, x83:0 + 1) :|: x83:0 < x81:0


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(18)
YES