/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 59 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 0 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(q, y) -> f2(x_1, y) :|: TRUE
f2(x, x1) -> f3(x, x2) :|: TRUE
f5(x3, x4) -> f8(x3, 0) :|: TRUE
f8(x5, x6) -> f9(x7, x6) :|: TRUE
f6(x8, x9) -> f10(x8, arith) :|: TRUE && arith = x9 - 1
f10(x26, x27) -> f11(x28, x27) :|: TRUE && x28 = x26 - 1
f4(x12, x13) -> f5(x12, x13) :|: x13 > 0
f4(x14, x15) -> f6(x14, x15) :|: x15 <= 0
f9(x16, x17) -> f7(x16, x17) :|: TRUE
f11(x18, x19) -> f7(x18, x19) :|: TRUE
f3(x20, x21) -> f4(x20, x21) :|: x20 > 0
f7(x22, x23) -> f3(x22, x23) :|: TRUE
f3(x24, x25) -> f12(x24, x25) :|: x24 <= 0
Start term: f1(q, 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:
f3(x20, x21) -> f4(x20, x21) :|: x20 > 0
f7(x22, x23) -> f3(x22, x23) :|: TRUE
f9(x16, x17) -> f7(x16, x17) :|: TRUE
f8(x5, x6) -> f9(x7, x6) :|: TRUE
f5(x3, x4) -> f8(x3, 0) :|: TRUE
f4(x12, x13) -> f5(x12, x13) :|: x13 > 0
f11(x18, x19) -> f7(x18, x19) :|: TRUE
f10(x26, x27) -> f11(x28, x27) :|: TRUE && x28 = x26 - 1
f6(x8, x9) -> f10(x8, arith) :|: TRUE && arith = x9 - 1
f4(x14, x15) -> f6(x14, x15) :|: x15 <= 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f7(x22:0, x23:0) -> f7(x22:0 - 1, x23:0 - 1) :|: x22:0 > 0 && x23:0 < 1
f7(x, x1) -> f7(x2, 0) :|: x > 0 && x1 > 0

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f7(x, x1)] = -1 + x1

The following rules are decreasing:
f7(x22:0, x23:0) -> f7(x22:0 - 1, x23:0 - 1) :|: x22:0 > 0 && x23:0 < 1
f7(x, x1) -> f7(x2, 0) :|: x > 0 && x1 > 0
The following rules are bounded:
f7(x, x1) -> f7(x2, 0) :|: x > 0 && x1 > 0

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(8)
Obligation:
Rules:
f7(x22:0, x23:0) -> f7(x22:0 - 1, x23:0 - 1) :|: x22:0 > 0 && x23:0 < 1

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f7(x, x1)] = x

The following rules are decreasing:
f7(x22:0, x23:0) -> f7(x22:0 - 1, x23:0 - 1) :|: x22:0 > 0 && x23:0 < 1
The following rules are bounded:
f7(x22:0, x23:0) -> f7(x22:0 - 1, x23:0 - 1) :|: x22:0 > 0 && x23:0 < 1

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(10)
YES