YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 64 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 15 ms]
(10) AND
    (11) IntTRS
        (12) TerminationGraphProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IntTRS
        (15) TerminationGraphProcessor [EQUIVALENT, 6 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, b) -> f2(x_1, b) :|: TRUE
f2(x1, x2) -> f3(x1, x3) :|: TRUE
f4(x4, x5) -> f5(x4, x6) :|: TRUE
f5(x7, x8) -> f6(arith, x8) :|: TRUE && arith = x7 - 1
f7(x9, x10) -> f10(x9, 1) :|: TRUE
f8(x11, x12) -> f11(x11, 0) :|: TRUE
f6(x13, x14) -> f7(x13, x14) :|: x13 >= 0
f6(x15, x16) -> f8(x15, x16) :|: x15 < 0
f10(x17, x18) -> f9(x17, x18) :|: TRUE
f11(x19, x20) -> f9(x19, x20) :|: TRUE
f3(x21, x22) -> f4(x21, x22) :|: x22 < 0
f3(x27, x28) -> f4(x27, x28) :|: x28 > 0
f9(x23, x24) -> f3(x23, x24) :|: TRUE
f3(x25, x26) -> f12(x25, x26) :|: x26 = 0
Start term: f1(x, b)

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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(x21, x22) -> f4(x21, x22) :|: x22 < 0
f9(x23, x24) -> f3(x23, x24) :|: TRUE
f10(x17, x18) -> f9(x17, x18) :|: TRUE
f7(x9, x10) -> f10(x9, 1) :|: TRUE
f6(x13, x14) -> f7(x13, x14) :|: x13 >= 0
f5(x7, x8) -> f6(arith, x8) :|: TRUE && arith = x7 - 1
f4(x4, x5) -> f5(x4, x6) :|: TRUE
f3(x27, x28) -> f4(x27, x28) :|: x28 > 0
f11(x19, x20) -> f9(x19, x20) :|: TRUE
f8(x11, x12) -> f11(x11, 0) :|: TRUE
f6(x15, x16) -> f8(x15, x16) :|: x15 < 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f9(x23:0, x24:0) -> f5(x23:0, x6:0) :|: x24:0 < 0
f5(x7:0, x8:0) -> f9(x7:0 - 1, 1) :|: x7:0 > 0
f5(x, x1) -> f9(x - 1, 0) :|: x < 1
f9(x2, x3) -> f5(x2, x4) :|: x3 > 0

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

   f5(x1, x2) -> f5(x1)

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(8)
Obligation:
Rules:
f9(x23:0, x24:0) -> f5(x23:0) :|: x24:0 < 0
f5(x7:0) -> f9(x7:0 - 1, 1) :|: x7:0 > 0
f5(x) -> f9(x - 1, 0) :|: x < 1
f9(x2, x3) -> f5(x2) :|: x3 > 0

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f9(x, x1)] = x
[f5(x2)] = -1 + x2

The following rules are decreasing:
f9(x23:0, x24:0) -> f5(x23:0) :|: x24:0 < 0
f9(x2, x3) -> f5(x2) :|: x3 > 0
The following rules are bounded:
f5(x7:0) -> f9(x7:0 - 1, 1) :|: x7:0 > 0

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(10)
Complex Obligation (AND)

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(11)
Obligation:
Rules:
f5(x7:0) -> f9(x7:0 - 1, 1) :|: x7:0 > 0
f5(x) -> f9(x - 1, 0) :|: x < 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:
f9(x23:0, x24:0) -> f5(x23:0) :|: x24:0 < 0
f5(x) -> f9(x - 1, 0) :|: x < 1
f9(x2, x3) -> f5(x2) :|: x3 > 0

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

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(16)
YES