YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.c
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given C Problem could be proven:

(0) C Problem
(1) CToIRSProof [EQUIVALENT, 0 ms]
(2) IntTRS
(3) TerminationGraphProcessor [SOUND, 93 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 44 ms]
(6) IntTRS
(7) RankingReductionPairProof [EQUIVALENT, 36 ms]
(8) AND
    (9) IntTRS
        (10) TerminationGraphProcessor [EQUIVALENT, 8 ms]
        (11) YES
    (12) IntTRS
        (13) TerminationGraphProcessor [EQUIVALENT, 10 ms]
        (14) IntTRS
        (15) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (16) IntTRS
        (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (22) 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(p, q) -> f2(p, x_1) :|: TRUE
f2(x, x1) -> f3(x2, x1) :|: TRUE
f5(x3, x4) -> f8(x3, arith) :|: TRUE && arith = x4 - 1
f9(x29, x30) -> f12(x31, x30) :|: TRUE && x31 = x29 - 1
f6(x7, x8) -> f9(x7, x8) :|: x7 < x8
f6(x9, x10) -> f10(x9, x10) :|: x9 >= x10
f12(x11, x12) -> f11(x11, x12) :|: TRUE
f10(x13, x14) -> f11(x13, x14) :|: TRUE
f4(x15, x16) -> f5(x15, x16) :|: x16 < x15
f4(x17, x18) -> f6(x17, x18) :|: x18 >= x17
f8(x19, x20) -> f7(x19, x20) :|: TRUE
f11(x21, x22) -> f7(x21, x22) :|: TRUE
f3(x23, x24) -> f4(x23, x24) :|: x24 > 0 && x23 > 0 && x23 < x24
f3(x32, x33) -> f4(x32, x33) :|: x33 > 0 && x32 > 0 && x32 > x33
f7(x25, x26) -> f3(x25, x26) :|: TRUE
f3(x27, x28) -> f13(x27, x28) :|: x27 = x28
f3(x34, x35) -> f13(x34, x35) :|: x35 <= 0
f3(x36, x37) -> f13(x36, x37) :|: x36 <= 0
Start term: f1(p, q)

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

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(4)
Obligation:
Rules:
f3(x23, x24) -> f4(x23, x24) :|: x24 > 0 && x23 > 0 && x23 < x24
f7(x25, x26) -> f3(x25, x26) :|: TRUE
f8(x19, x20) -> f7(x19, x20) :|: TRUE
f5(x3, x4) -> f8(x3, arith) :|: TRUE && arith = x4 - 1
f4(x15, x16) -> f5(x15, x16) :|: x16 < x15
f3(x32, x33) -> f4(x32, x33) :|: x33 > 0 && x32 > 0 && x32 > x33
f11(x21, x22) -> f7(x21, x22) :|: TRUE
f12(x11, x12) -> f11(x11, x12) :|: TRUE
f9(x29, x30) -> f12(x31, x30) :|: TRUE && x31 = x29 - 1
f6(x7, x8) -> f9(x7, x8) :|: x7 < x8
f4(x17, x18) -> f6(x17, x18) :|: x18 >= x17
f10(x13, x14) -> f11(x13, x14) :|: TRUE
f6(x9, x10) -> f10(x9, x10) :|: x9 >= x10

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f7(x25:0, x26:0) -> f4(x25:0, x26:0) :|: x26:0 > 0 && x25:0 > 0 && x26:0 < x25:0
f4(x15:0, x16:0) -> f7(x15:0, x16:0 - 1) :|: x16:0 < x15:0
f4(x17:0, x17:01) -> f7(x17:0, x17:0) :|: TRUE && x17:0 = x17:01
f4(x, x1) -> f7(x - 1, x1) :|: x1 > x
f7(x2, x3) -> f4(x2, x3) :|: x3 > 0 && x2 > 0 && x3 > x2

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(7) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f7 ] = 3*f7_2 + 2*f7_1 + 1
[ f4 ] = 2*f4_1 + 3*f4_2 + 1

The following rules are decreasing:
f4(x15:0, x16:0) -> f7(x15:0, x16:0 - 1) :|: x16:0 < x15:0
f4(x, x1) -> f7(x - 1, x1) :|: x1 > x

The following rules are bounded:
f7(x25:0, x26:0) -> f4(x25:0, x26:0) :|: x26:0 > 0 && x25:0 > 0 && x26:0 < x25:0


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(8)
Complex Obligation (AND)

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(9)
Obligation:
Rules:
f7(x25:0, x26:0) -> f4(x25:0, x26:0) :|: x26:0 > 0 && x25:0 > 0 && x26:0 < x25:0
f4(x17:0, x17:01) -> f7(x17:0, x17:0) :|: TRUE && x17:0 = x17:01
f7(x2, x3) -> f4(x2, x3) :|: x3 > 0 && x2 > 0 && x3 > x2

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

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(11)
YES

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(12)
Obligation:
Rules:
f4(x15:0, x16:0) -> f7(x15:0, x16:0 - 1) :|: x16:0 < x15:0
f4(x17:0, x17:01) -> f7(x17:0, x17:0) :|: TRUE && x17:0 = x17:01
f4(x, x1) -> f7(x - 1, x1) :|: x1 > x
f7(x2, x3) -> f4(x2, x3) :|: x3 > 0 && x2 > 0 && x3 > x2

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

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(14)
Obligation:
Rules:
f4(x15:0, x16:0) -> f7(x15:0, x16:0 - 1) :|: x16:0 < x15:0
f7(x2, x3) -> f4(x2, x3) :|: x3 > 0 && x2 > 0 && x3 > x2
f4(x, x1) -> f7(x - 1, x1) :|: x1 > x

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(15) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(16)
Obligation:
Rules:
f4(x15:0:0, x16:0:0) -> f4(x15:0:0, x16:0:0 - 1) :|: x16:0:0 - 1 > x15:0:0 && x16:0:0 < x15:0:0 && x15:0:0 > 0 && x16:0:0 > 1
f4(x:0, x1:0) -> f4(x:0 - 1, x1:0) :|: x:0 - 1 < x1:0 && x:0 < x1:0 && x:0 > 1 && x1:0 > 0

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f4(x, x1)] = d + x1

The following rules are decreasing:
f4(x15:0:0, x16:0:0) -> f4(x15:0:0, x16:0:0 - 1) :|: x16:0:0 - 1 > x15:0:0 && x16:0:0 < x15:0:0 && x15:0:0 > 0 && x16:0:0 > 1
The following rules are bounded:
f4(x15:0:0, x16:0:0) -> f4(x15:0:0, x16:0:0 - 1) :|: x16:0:0 - 1 > x15:0:0 && x16:0:0 < x15:0:0 && x15:0:0 > 0 && x16:0:0 > 1

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(18)
Obligation:
Rules:
f4(x:0, x1:0) -> f4(x:0 - 1, x1:0) :|: x:0 - 1 < x1:0 && x:0 < x1:0 && x:0 > 1 && x1:0 > 0

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(19) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(20)
Obligation:
Rules:
f4(x:0:0, x1:0:0) -> f4(x:0:0 - 1, x1:0:0) :|: x:0:0 > 1 && x1:0:0 > 0 && x:0:0 < x1:0:0 && x:0:0 - 1 < x1:0:0

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(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f4 ] = f4_1

The following rules are decreasing:
f4(x:0:0, x1:0:0) -> f4(x:0:0 - 1, x1:0:0) :|: x:0:0 > 1 && x1:0:0 > 0 && x:0:0 < x1:0:0 && x:0:0 - 1 < x1:0:0

The following rules are bounded:
f4(x:0:0, x1:0:0) -> f4(x:0:0 - 1, x1:0:0) :|: x:0:0 > 1 && x1:0:0 > 0 && x:0:0 < x1:0:0 && x:0:0 - 1 < x1:0:0


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(22)
YES