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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 77 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 25 ms]
(6) IntTRS
(7) CaseAnalysis [EQUIVALENT, 20 ms]
(8) AND
    (9) IntTRS
        (10) TerminationGraphProcessor [EQUIVALENT, 15 ms]
        (11) IntTRS
        (12) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (13) IntTRS
        (14) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (15) AND
            (16) IntTRS
                (17) TerminationGraphProcessor [EQUIVALENT, 2 ms]
                (18) YES
            (19) IntTRS
                (20) IntTRSCompressionProof [EQUIVALENT, 0 ms]
                (21) IntTRS
                (22) RankingReductionPairProof [EQUIVALENT, 0 ms]
                (23) YES
    (24) IntTRS
        (25) TerminationGraphProcessor [EQUIVALENT, 12 ms]
        (26) IntTRS
        (27) IntTRSCompressionProof [EQUIVALENT, 1 ms]
        (28) IntTRS
        (29) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (30) 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) -> f2(x_1, y) :|: TRUE
f2(x1, x2) -> f3(x1, x3) :|: TRUE
f8(x4, x5) -> f11(arith, x5) :|: TRUE && arith = x4 + 1
f9(x30, x31) -> f12(x30, x32) :|: TRUE && x32 = x31 + 1
f7(x8, x9) -> f8(x8, x9) :|: x8 < x9
f7(x10, x11) -> f9(x10, x11) :|: x10 >= x11
f11(x12, x13) -> f10(x12, x13) :|: TRUE
f12(x14, x15) -> f10(x14, x15) :|: TRUE
f4(x16, x17) -> f7(x16, x17) :|: x16 - x17 > 2
f4(x33, x34) -> f7(x33, x34) :|: x34 - x33 > 2
f10(x18, x19) -> f4(x18, x19) :|: TRUE
f4(x20, x21) -> f13(x20, x21) :|: x20 - x21 <= 2 && x21 - x20 <= 2
f3(x22, x23) -> f4(x22, x23) :|: x22 >= 0 && x23 >= 0
f3(x24, x25) -> f5(x24, x25) :|: x24 < 0
f3(x35, x36) -> f5(x35, x36) :|: x36 < 0
f13(x26, x27) -> f6(x26, x27) :|: TRUE
f5(x28, x29) -> f6(x28, x29) :|: TRUE
Start term: f1(x, y)

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(3) TerminationGraphProcessor (SOUND)
Constructed the termination graph and obtained one non-trivial SCC.

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(4)
Obligation:
Rules:
f4(x16, x17) -> f7(x16, x17) :|: x16 - x17 > 2
f10(x18, x19) -> f4(x18, x19) :|: TRUE
f11(x12, x13) -> f10(x12, x13) :|: TRUE
f8(x4, x5) -> f11(arith, x5) :|: TRUE && arith = x4 + 1
f7(x8, x9) -> f8(x8, x9) :|: x8 < x9
f4(x33, x34) -> f7(x33, x34) :|: x34 - x33 > 2
f12(x14, x15) -> f10(x14, x15) :|: TRUE
f9(x30, x31) -> f12(x30, x32) :|: TRUE && x32 = x31 + 1
f7(x10, x11) -> f9(x10, x11) :|: x10 >= x11

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f10(x18:0, x19:0) -> f7(x18:0, x19:0) :|: x18:0 - x19:0 > 2
f10(x, x1) -> f7(x, x1) :|: x1 - x > 2
f7(x10:0, x11:0) -> f10(x10:0, x11:0 + 1) :|: x11:0 <= x10:0
f7(x8:0, x9:0) -> f10(x8:0 + 1, x9:0) :|: x9:0 > x8:0

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(7) CaseAnalysis (EQUIVALENT)
Found the following inductive condition: 
f10(x, x1): 3 + 3*x - 3*x1>=0
f7(x2, x3): 3 + 3*x2 - 3*x3>=0

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(8)
Complex Obligation (AND)

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(9)
Obligation:
Rules:
f10(x18:0, x19:0) -> f7(x18:0, x19:0) :|: x18:0 - x19:0 > 2 && 3 + 3 * x18:0 + -3 * x19:0 >= 0
f10(x, x1) -> f7(x, x1) :|: x1 - x > 2 && 3 + 3 * x + -3 * x1 >= 0
f7(x10:0, x11:0) -> f10(x10:0, x11:0 + 1) :|: x11:0 <= x10:0 && 3 + 3 * x10:0 + -3 * x11:0 >= 0
f7(x8:0, x9:0) -> f10(x8:0 + 1, x9:0) :|: x9:0 > x8:0 && 3 + 3 * x8:0 + -3 * x9:0 >= 0

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(10) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained one non-trivial SCC.

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(11)
Obligation:
Rules:
f10(x18:0, x19:0) -> f7(x18:0, x19:0) :|: x18:0 - x19:0 > 2 && 3 + 3 * x18:0 + -3 * x19:0 >= 0
f7(x10:0, x11:0) -> f10(x10:0, x11:0 + 1) :|: x11:0 <= x10:0 && 3 + 3 * x10:0 + -3 * x11:0 >= 0
f7(x8:0, x9:0) -> f10(x8:0 + 1, x9:0) :|: x9:0 > x8:0 && 3 + 3 * x8:0 + -3 * x9:0 >= 0

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(12) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(13)
Obligation:
Rules:
f10(x18:0:0, x19:0:0) -> f10(x18:0:0, x19:0:0 + 1) :|: x18:0:0 - x19:0:0 > 2 && 3 + 3 * x18:0:0 + -3 * x19:0:0 >= 0 && x19:0:0 <= x18:0:0
f10(x, x1) -> f10(x + 1, x1) :|: x - x1 > 2 && 3 + 3 * x + -3 * x1 >= 0 && x1 > x

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(14) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f10(x, x1)] = d - x1

The following rules are decreasing:
f10(x18:0:0, x19:0:0) -> f10(x18:0:0, x19:0:0 + 1) :|: x18:0:0 - x19:0:0 > 2 && 3 + 3 * x18:0:0 + -3 * x19:0:0 >= 0 && x19:0:0 <= x18:0:0
The following rules are bounded:
f10(x, x1) -> f10(x + 1, x1) :|: x - x1 > 2 && 3 + 3 * x + -3 * x1 >= 0 && x1 > x

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(15)
Complex Obligation (AND)

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(16)
Obligation:
Rules:
f10(x, x1) -> f10(x + 1, x1) :|: x - x1 > 2 && 3 + 3 * x + -3 * x1 >= 0 && x1 > x

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(17) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained no non-trivial SCC(s).

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(18)
YES

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(19)
Obligation:
Rules:
f10(x18:0:0, x19:0:0) -> f10(x18:0:0, x19:0:0 + 1) :|: x18:0:0 - x19:0:0 > 2 && 3 + 3 * x18:0:0 + -3 * x19:0:0 >= 0 && x19:0:0 <= x18:0:0

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(20) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(21)
Obligation:
Rules:
f10(x18:0:0:0, x19:0:0:0) -> f10(x18:0:0:0, x19:0:0:0 + 1) :|: x18:0:0:0 - x19:0:0:0 > 2 && 3 + 3 * x18:0:0:0 + -3 * x19:0:0:0 >= 0 && x19:0:0:0 <= x18:0:0:0

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(22) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f10 ] = f10_1 + -1*f10_2

The following rules are decreasing:
f10(x18:0:0:0, x19:0:0:0) -> f10(x18:0:0:0, x19:0:0:0 + 1) :|: x18:0:0:0 - x19:0:0:0 > 2 && 3 + 3 * x18:0:0:0 + -3 * x19:0:0:0 >= 0 && x19:0:0:0 <= x18:0:0:0

The following rules are bounded:
f10(x18:0:0:0, x19:0:0:0) -> f10(x18:0:0:0, x19:0:0:0 + 1) :|: x18:0:0:0 - x19:0:0:0 > 2 && 3 + 3 * x18:0:0:0 + -3 * x19:0:0:0 >= 0 && x19:0:0:0 <= x18:0:0:0


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(23)
YES

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(24)
Obligation:
Rules:
f10(x18:0, x19:0) -> f7(x18:0, x19:0) :|: x18:0 - x19:0 > 2 && 3 + 3 * x18:0 + -3 * x19:0 < 0
f10(x, x1) -> f7(x, x1) :|: x1 - x > 2 && 3 + 3 * x + -3 * x1 < 0
f7(x10:0, x11:0) -> f10(x10:0, x11:0 + 1) :|: x11:0 <= x10:0 && 3 + 3 * x10:0 + -3 * x11:0 < 0
f7(x8:0, x9:0) -> f10(x8:0 + 1, x9:0) :|: x9:0 > x8:0 && 3 + 3 * x8:0 + -3 * x9:0 < 0

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(25) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained one non-trivial SCC.

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(26)
Obligation:
Rules:
f10(x, x1) -> f7(x, x1) :|: x1 - x > 2 && 3 + 3 * x + -3 * x1 < 0
f7(x8:0, x9:0) -> f10(x8:0 + 1, x9:0) :|: x9:0 > x8:0 && 3 + 3 * x8:0 + -3 * x9:0 < 0

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(27) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(28)
Obligation:
Rules:
f10(x:0, x1:0) -> f10(x:0 + 1, x1:0) :|: x1:0 - x:0 > 2 && 3 + 3 * x:0 + -3 * x1:0 < 0 && x:0 < x1:0

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(29) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f10(x, x1)] = -x + x1

The following rules are decreasing:
f10(x:0, x1:0) -> f10(x:0 + 1, x1:0) :|: x1:0 - x:0 > 2 && 3 + 3 * x:0 + -3 * x1:0 < 0 && x:0 < x1:0
The following rules are bounded:
f10(x:0, x1:0) -> f10(x:0 + 1, x1:0) :|: x1:0 - x:0 > 2 && 3 + 3 * x:0 + -3 * x1:0 < 0 && x:0 < x1:0

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(30)
YES