/export/starexec/sandbox/solver/bin/starexec_run_c /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files


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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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 75 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 6 ms]
(10) IntTRS
(11) TerminationGraphProcessor [EQUIVALENT, 6 ms]
(12) 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(flag, c, x, y) -> f2(1, c, x, y) :|: TRUE
f2(x1, x2, x3, x4) -> f3(x1, 0, x3, x4) :|: TRUE
f3(x5, x6, x7, x8) -> f4(x5, x6, x9, x8) :|: TRUE
f4(x10, x11, x12, x13) -> f5(x10, x11, x12, x14) :|: TRUE
f7(x15, x16, x17, x18) -> f10(0, x16, x17, x18) :|: TRUE
f6(x19, x20, x21, x22) -> f7(x19, x20, x21, x22) :|: x21 >= x22
f6(x23, x24, x25, x26) -> f8(x23, x24, x25, x26) :|: x25 < x26
f10(x27, x28, x29, x30) -> f9(x27, x28, x29, x30) :|: TRUE
f8(x31, x32, x33, x34) -> f9(x31, x32, x33, x34) :|: TRUE
f9(x35, x36, x37, x38) -> f11(x35, x36, arith, x38) :|: TRUE && arith = x37 + 1
f11(x55, x56, x57, x58) -> f12(x55, x59, x57, x58) :|: TRUE && x59 = x56 + 1
f5(x43, x44, x45, x46) -> f6(x43, x44, x45, x46) :|: x43 < 0
f5(x60, x61, x62, x63) -> f6(x60, x61, x62, x63) :|: x60 > 0
f12(x47, x48, x49, x50) -> f5(x47, x48, x49, x50) :|: TRUE
f5(x51, x52, x53, x54) -> f13(x51, x52, x53, x54) :|: x51 = 0
Start term: f1(flag, c, 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:
f5(x43, x44, x45, x46) -> f6(x43, x44, x45, x46) :|: x43 < 0
f12(x47, x48, x49, x50) -> f5(x47, x48, x49, x50) :|: TRUE
f11(x55, x56, x57, x58) -> f12(x55, x59, x57, x58) :|: TRUE && x59 = x56 + 1
f9(x35, x36, x37, x38) -> f11(x35, x36, arith, x38) :|: TRUE && arith = x37 + 1
f10(x27, x28, x29, x30) -> f9(x27, x28, x29, x30) :|: TRUE
f7(x15, x16, x17, x18) -> f10(0, x16, x17, x18) :|: TRUE
f6(x19, x20, x21, x22) -> f7(x19, x20, x21, x22) :|: x21 >= x22
f5(x60, x61, x62, x63) -> f6(x60, x61, x62, x63) :|: x60 > 0
f8(x31, x32, x33, x34) -> f9(x31, x32, x33, x34) :|: TRUE
f6(x23, x24, x25, x26) -> f8(x23, x24, x25, x26) :|: x25 < x26

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f9(x35:0, x36:0, x37:0, x38:0) -> f6(x35:0, x36:0 + 1, x37:0 + 1, x38:0) :|: x35:0 > 0
f9(x, x1, x2, x3) -> f6(x, x1 + 1, x2 + 1, x3) :|: x < 0
f6(x23:0, x24:0, x25:0, x26:0) -> f9(x23:0, x24:0, x25:0, x26:0) :|: x26:0 > x25:0
f6(x19:0, x20:0, x21:0, x22:0) -> f9(0, x20:0, x21:0, x22:0) :|: x22:0 <= x21:0

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

   f9(x1, x2, x3, x4) -> f9(x1, x3, x4)
   f6(x1, x2, x3, x4) -> f6(x1, x3, x4)

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(8)
Obligation:
Rules:
f9(x35:0, x37:0, x38:0) -> f6(x35:0, x37:0 + 1, x38:0) :|: x35:0 > 0
f9(x, x2, x3) -> f6(x, x2 + 1, x3) :|: x < 0
f6(x23:0, x25:0, x26:0) -> f9(x23:0, x25:0, x26:0) :|: x26:0 > x25:0
f6(x19:0, x21:0, x22:0) -> f9(0, x21:0, x22:0) :|: x22:0 <= x21:0

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f9(x, x1, x2)] = -2 - x1 + x2
[f6(x3, x4, x5)] = -1 - x4 + x5

The following rules are decreasing:
f6(x23:0, x25:0, x26:0) -> f9(x23:0, x25:0, x26:0) :|: x26:0 > x25:0
f6(x19:0, x21:0, x22:0) -> f9(0, x21:0, x22:0) :|: x22:0 <= x21:0
The following rules are bounded:
f6(x23:0, x25:0, x26:0) -> f9(x23:0, x25:0, x26:0) :|: x26:0 > x25:0

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(10)
Obligation:
Rules:
f9(x35:0, x37:0, x38:0) -> f6(x35:0, x37:0 + 1, x38:0) :|: x35:0 > 0
f9(x, x2, x3) -> f6(x, x2 + 1, x3) :|: x < 0
f6(x19:0, x21:0, x22:0) -> f9(0, x21:0, x22:0) :|: x22:0 <= x21:0

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

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(12)
YES