/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 55 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 29 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) TerminationGraphProcessor [EQUIVALENT, 3 ms]
(10) IntTRS
(11) TerminationGraphProcessor [EQUIVALENT, 0 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(x, y, oldy) -> f2(x_1, y, oldy) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
f4(x5, x6, x7) -> f5(x6, x6, x7) :|: TRUE
f5(x8, x9, x10) -> f6(x8, x9, x9) :|: TRUE
f6(x11, x12, x13) -> f7(x11, x14, x13) :|: TRUE
f3(x15, x16, x17) -> f4(x15, x16, x17) :|: x15 > 0 && x16 <= 0 - x17
f7(x18, x19, x20) -> f3(x18, x19, x20) :|: TRUE
f3(x21, x22, x23) -> f8(x21, x22, x23) :|: x21 <= 0
f3(x24, x25, x26) -> f8(x24, x25, x26) :|: x25 > 0 - x26
Start term: f1(x, y, oldy)

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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(x15, x16, x17) -> f4(x15, x16, x17) :|: x15 > 0 && x16 <= 0 - x17
f7(x18, x19, x20) -> f3(x18, x19, x20) :|: TRUE
f6(x11, x12, x13) -> f7(x11, x14, x13) :|: TRUE
f5(x8, x9, x10) -> f6(x8, x9, x9) :|: TRUE
f4(x5, x6, x7) -> f5(x6, x6, x7) :|: TRUE

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x8:0, x9:0, x10:0) -> f5(x14:0, x14:0, x9:0) :|: x8:0 > 0 && x14:0 <= 0 - x9:0

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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, x3) -> f5(x1, x2)

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(8)
Obligation:
Rules:
f5(x8:0, x9:0) -> f5(x14:0, x14:0) :|: x8:0 > 0 && x14:0 <= 0 - x9:0

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

f5(x8:0, x9:0) -> f5(x14:0, x14:0) :|: x8:0 > 0 && x14:0 <= 0 - x9:0
has been transformed into
f5(x8:0, x9:0) -> f5(x14:0, x14:0) :|: x8:0 > 0 && x14:0 <= 0 - x9:0.


f5(x8:0, x9:0) -> f5(x14:0, x14:0) :|: x8:0 > 0 && x14:0 <= 0 - x9:0 and 
f5(x8:0, x9:0) -> f5(x14:0, x14:0) :|: x8:0 > 0 && x14:0 <= 0 - x9:0
have been merged into the new rule
f5(x15, x16) -> f5(x17, x17) :|: x15 > 0 && x18 <= 0 - x16 && (x18 > 0 && x17 <= 0 - x18)


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(10)
Obligation:
Rules:
f5(x19, x20) -> f5(x21, x21) :|: TRUE && x19 >= 1 && x22 + x20 <= 0 && x22 >= 1 && x21 + x22 <= 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