YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 66 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(10) AND
    (11) IntTRS
        (12) TerminationGraphProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IntTRS
        (15) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (16) YES


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(0)
Obligation:
c file /export/starexec/sandbox2/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, xtmp, res, restmp) -> f2(x_1, xtmp, res, restmp) :|: TRUE
f2(x1, x2, x3, x4) -> f3(x1, x2, 0, x4) :|: TRUE
f4(x5, x6, x7, x8) -> f5(x5, x5, x7, x8) :|: TRUE
f5(x9, x10, x11, x12) -> f6(x9, x10, x11, 0) :|: TRUE
f7(x13, x14, x15, x16) -> f8(x13, arith, x15, x16) :|: TRUE && arith = x14 - 2
f8(x53, x54, x55, x56) -> f9(x53, x54, x55, x57) :|: TRUE && x57 = x56 + 1
f6(x21, x22, x23, x24) -> f7(x21, x22, x23, x24) :|: x22 > 1
f9(x25, x26, x27, x28) -> f6(x25, x26, x27, x28) :|: TRUE
f6(x29, x30, x31, x32) -> f10(x29, x30, x31, x32) :|: x30 <= 1
f10(x33, x34, x35, x36) -> f11(x34, x34, x35, x36) :|: TRUE
f11(x58, x59, x60, x61) -> f12(x58, x59, x62, x61) :|: TRUE && x62 = x60 + 1
f3(x41, x42, x43, x44) -> f4(x41, x42, x43, x44) :|: x41 > 1
f12(x45, x46, x47, x48) -> f3(x45, x46, x47, x48) :|: TRUE
f3(x49, x50, x51, x52) -> f13(x49, x50, x51, x52) :|: x49 <= 1
Start term: f1(x, xtmp, res, restmp)

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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(x41, x42, x43, x44) -> f4(x41, x42, x43, x44) :|: x41 > 1
f12(x45, x46, x47, x48) -> f3(x45, x46, x47, x48) :|: TRUE
f11(x58, x59, x60, x61) -> f12(x58, x59, x62, x61) :|: TRUE && x62 = x60 + 1
f10(x33, x34, x35, x36) -> f11(x34, x34, x35, x36) :|: TRUE
f6(x29, x30, x31, x32) -> f10(x29, x30, x31, x32) :|: x30 <= 1
f5(x9, x10, x11, x12) -> f6(x9, x10, x11, 0) :|: TRUE
f4(x5, x6, x7, x8) -> f5(x5, x5, x7, x8) :|: TRUE
f9(x25, x26, x27, x28) -> f6(x25, x26, x27, x28) :|: TRUE
f8(x53, x54, x55, x56) -> f9(x53, x54, x55, x57) :|: TRUE && x57 = x56 + 1
f7(x13, x14, x15, x16) -> f8(x13, arith, x15, x16) :|: TRUE && arith = x14 - 2
f6(x21, x22, x23, x24) -> f7(x21, x22, x23, x24) :|: x22 > 1

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f6(x21:0, x22:0, x23:0, x24:0) -> f6(x21:0, x22:0 - 2, x23:0, x24:0 + 1) :|: x22:0 > 1
f6(x29:0, x30:0, x31:0, x32:0) -> f6(x30:0, x30:0, x31:0 + 1, 0) :|: x30:0 < 2 && x30:0 > 1

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

   f6(x1, x2, x3, x4) -> f6(x2)

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(8)
Obligation:
Rules:
f6(x22:0) -> f6(x22:0 - 2) :|: x22:0 > 1
f6(x30:0) -> f6(x30:0) :|: x30:0 < 2 && x30:0 > 1

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x)] = d + x

The following rules are decreasing:
f6(x22:0) -> f6(x22:0 - 2) :|: x22:0 > 1
The following rules are bounded:
f6(x30:0) -> f6(x30:0) :|: x30:0 < 2 && x30:0 > 1

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(10)
Complex Obligation (AND)

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(11)
Obligation:
Rules:
f6(x30:0) -> f6(x30:0) :|: x30:0 < 2 && x30:0 > 1

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

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(13)
YES

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(14)
Obligation:
Rules:
f6(x22:0) -> f6(x22:0 - 2) :|: x22:0 > 1

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(15) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x)] = -1 - x + x^2

The following rules are decreasing:
f6(x22:0) -> f6(x22:0 - 2) :|: x22:0 > 1
The following rules are bounded:
f6(x22:0) -> f6(x22:0 - 2) :|: x22:0 > 1

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(16)
YES