/export/starexec/sandbox2/solver/bin/starexec_run_c /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 67 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 23 ms]
(10) YES


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(0)
Obligation:
c file /export/starexec/sandbox2/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, i, j, k, tmp) -> f2(c, x_1, j, k, tmp) :|: TRUE
f2(x, x1, x2, x3, x4) -> f3(x, x1, x5, x3, x4) :|: TRUE
f3(x6, x7, x8, x9, x10) -> f4(x6, x7, x8, x11, x10) :|: TRUE
f4(x12, x13, x14, x15, x16) -> f5(x12, x13, x14, x15, x17) :|: TRUE
f5(x18, x19, x20, x21, x22) -> f6(0, x19, x20, x21, x22) :|: TRUE
f7(x23, x24, x25, x26, x27) -> f8(x23, x24, x25, x26, x24) :|: TRUE
f8(x28, x29, x30, x31, x32) -> f9(x28, x30, x30, x31, x32) :|: TRUE
f9(x33, x34, x35, x36, x37) -> f10(x33, x34, arith, x36, x37) :|: TRUE && arith = x37 + 1
f10(x63, x64, x65, x66, x67) -> f11(x63, x64, x65, x68, x67) :|: TRUE && x68 = x66 - 1
f11(x69, x70, x71, x72, x73) -> f12(x74, x70, x71, x72, x73) :|: TRUE && x74 = x69 + 1
f6(x48, x49, x50, x51, x52) -> f7(x48, x49, x50, x51, x52) :|: x49 <= 100 && x50 <= x51
f12(x53, x54, x55, x56, x57) -> f6(x53, x54, x55, x56, x57) :|: TRUE
f6(x58, x59, x60, x61, x62) -> f13(x58, x59, x60, x61, x62) :|: x59 > 100
f6(x75, x76, x77, x78, x79) -> f13(x75, x76, x77, x78, x79) :|: x77 > x78
Start term: f1(c, i, j, k, tmp)

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(3) TerminationGraphProcessor (SOUND)
Constructed the termination graph and obtained one non-trivial SCC.

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(4)
Obligation:
Rules:
f6(x48, x49, x50, x51, x52) -> f7(x48, x49, x50, x51, x52) :|: x49 <= 100 && x50 <= x51
f12(x53, x54, x55, x56, x57) -> f6(x53, x54, x55, x56, x57) :|: TRUE
f11(x69, x70, x71, x72, x73) -> f12(x74, x70, x71, x72, x73) :|: TRUE && x74 = x69 + 1
f10(x63, x64, x65, x66, x67) -> f11(x63, x64, x65, x68, x67) :|: TRUE && x68 = x66 - 1
f9(x33, x34, x35, x36, x37) -> f10(x33, x34, arith, x36, x37) :|: TRUE && arith = x37 + 1
f8(x28, x29, x30, x31, x32) -> f9(x28, x30, x30, x31, x32) :|: TRUE
f7(x23, x24, x25, x26, x27) -> f8(x23, x24, x25, x26, x24) :|: TRUE

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f8(x28:0, x29:0, x30:0, x31:0, x32:0) -> f8(x28:0 + 1, x30:0, x32:0 + 1, x31:0 - 1, x30:0) :|: x30:0 < 101 && x32:0 + 1 <= x31:0 - 1

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

   f8(x1, x2, x3, x4, x5) -> f8(x3, x4, x5)

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(8)
Obligation:
Rules:
f8(x30:0, x31:0, x32:0) -> f8(x32:0 + 1, x31:0 - 1, x30:0) :|: x30:0 < 101 && x32:0 + 1 <= x31:0 - 1

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f8(x, x1, x2)] = 98 - x + x1 - x2

The following rules are decreasing:
f8(x30:0, x31:0, x32:0) -> f8(x32:0 + 1, x31:0 - 1, x30:0) :|: x30:0 < 101 && x32:0 + 1 <= x31:0 - 1
The following rules are bounded:
f8(x30:0, x31:0, x32:0) -> f8(x32:0 + 1, x31:0 - 1, x30:0) :|: x30:0 < 101 && x32:0 + 1 <= x31:0 - 1

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(10)
YES