YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 54 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) RankingReductionPairProof [EQUIVALENT, 1 ms]
(10) 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(c, x) -> f2(c, x_1) :|: TRUE
f2(x1, x2) -> f3(0, x2) :|: TRUE
f4(x3, x4) -> f5(x3, arith) :|: TRUE && arith = x4 * x4
f5(x13, x14) -> f6(x15, x14) :|: TRUE && x15 = x13 + 1
f3(x7, x8) -> f4(x7, x8) :|: x8 > 1 && x8 < 100
f6(x9, x10) -> f3(x9, x10) :|: TRUE
f3(x11, x12) -> f7(x11, x12) :|: x12 <= 1
f3(x16, x17) -> f7(x16, x17) :|: x17 >= 100
Start term: f1(c, x)

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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(x7, x8) -> f4(x7, x8) :|: x8 > 1 && x8 < 100
f6(x9, x10) -> f3(x9, x10) :|: TRUE
f5(x13, x14) -> f6(x15, x14) :|: TRUE && x15 = x13 + 1
f4(x3, x4) -> f5(x3, arith) :|: TRUE && arith = x4 * x4

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x13:0, x14:0) -> f5(x13:0 + 1, x14:0 * x14:0) :|: x14:0 > 1 && x14:0 < 100

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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(x2)

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(8)
Obligation:
Rules:
f5(x14:0) -> f5(x14:0 * x14:0) :|: x14:0 > 1 && x14:0 < 100

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(9) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f5 ] = -1/2*f5_1

The following rules are decreasing:
f5(x14:0) -> f5(x14:0 * x14:0) :|: x14:0 > 1 && x14:0 < 100

The following rules are bounded:
f5(x14:0) -> f5(x14:0 * x14:0) :|: x14:0 > 1 && x14:0 < 100


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(10)
YES