/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 49 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 19 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 9 ms]
(8) AND
    (9) IntTRS
        (10) TerminationGraphProcessor [EQUIVALENT, 2 ms]
        (11) YES
    (12) IntTRS
        (13) TerminationGraphProcessor [EQUIVALENT, 0 ms]
        (14) 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(a, b) -> f2(x_1, b) :|: TRUE
f2(x, x1) -> f3(x, x2) :|: TRUE
f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 + x4
f6(x23, x24) -> f9(x23, x25) :|: TRUE && x25 = 0 - x24 - 1
f7(x26, x27) -> f10(x26, x28) :|: TRUE && x28 = 0 - x27
f5(x9, x10) -> f6(x9, x10) :|: x10 >= 0
f5(x11, x12) -> f7(x11, x12) :|: x12 < 0
f9(x13, x14) -> f8(x13, x14) :|: TRUE
f10(x15, x16) -> f8(x15, x16) :|: TRUE
f3(x17, x18) -> f4(x17, x18) :|: x17 >= 0
f8(x19, x20) -> f3(x19, x20) :|: TRUE
f3(x21, x22) -> f11(x21, x22) :|: x21 < 0
Start term: f1(a, 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(x17, x18) -> f4(x17, x18) :|: x17 >= 0
f8(x19, x20) -> f3(x19, x20) :|: TRUE
f9(x13, x14) -> f8(x13, x14) :|: TRUE
f6(x23, x24) -> f9(x23, x25) :|: TRUE && x25 = 0 - x24 - 1
f5(x9, x10) -> f6(x9, x10) :|: x10 >= 0
f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 + x4
f10(x15, x16) -> f8(x15, x16) :|: TRUE
f7(x26, x27) -> f10(x26, x28) :|: TRUE && x28 = 0 - x27
f5(x11, x12) -> f7(x11, x12) :|: x12 < 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x9:0, x10:0) -> f5(x9:0 + (0 - x10:0 - 1), 0 - x10:0 - 1) :|: x10:0 > -1 && x9:0 > -1
f5(x11:0, x12:0) -> f5(x11:0 + (0 - x12:0), 0 - x12:0) :|: x12:0 < 0 && x11:0 > -1

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f5(x, x1)] = -1 + 2*x - x1

The following rules are decreasing:
f5(x9:0, x10:0) -> f5(x9:0 + (0 - x10:0 - 1), 0 - x10:0 - 1) :|: x10:0 > -1 && x9:0 > -1
The following rules are bounded:
f5(x11:0, x12:0) -> f5(x11:0 + (0 - x12:0), 0 - x12:0) :|: x12:0 < 0 && x11:0 > -1

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(8)
Complex Obligation (AND)

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(9)
Obligation:
Rules:
f5(x11:0, x12:0) -> f5(x11:0 + (0 - x12:0), 0 - x12:0) :|: x12:0 < 0 && x11:0 > -1

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

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(11)
YES

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(12)
Obligation:
Rules:
f5(x9:0, x10:0) -> f5(x9:0 + (0 - x10:0 - 1), 0 - x10:0 - 1) :|: x10:0 > -1 && x9:0 > -1

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

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(14)
YES