/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 72 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 21 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 1 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(a, x, max) -> f2(x_1, x, max) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE
f5(x9, x10, x11) -> f8(0, x10, x11) :|: TRUE
f8(x12, x13, x14) -> f9(x12, 1, x14) :|: TRUE
f11(x15, x16, x17) -> f14(arith, x16, x17) :|: TRUE && arith = x15 + 1
f12(x59, x60, x61) -> f15(x62, x60, x61) :|: TRUE && x62 = x59 - 1
f10(x21, x22, x23) -> f11(x21, x22, x23) :|: x24 < 0
f10(x63, x64, x65) -> f11(x63, x64, x65) :|: x66 > 0
f10(x25, x26, x27) -> f12(x25, x26, x27) :|: x28 = 0
f14(x29, x30, x31) -> f13(x29, x30, x31) :|: TRUE
f15(x32, x33, x34) -> f13(x32, x33, x34) :|: TRUE
f13(x67, x68, x69) -> f16(x67, x70, x69) :|: TRUE && x70 = x68 + 1
f9(x38, x39, x40) -> f10(x38, x39, x40) :|: x39 <= x40
f16(x41, x42, x43) -> f9(x41, x42, x43) :|: TRUE
f9(x44, x45, x46) -> f17(x44, x45, x46) :|: x45 > x46
f4(x47, x48, x49) -> f5(x47, x48, x49) :|: x49 > 0
f4(x50, x51, x52) -> f6(x50, x51, x52) :|: x52 <= 0
f17(x53, x54, x55) -> f7(x53, x54, x55) :|: TRUE
f6(x56, x57, x58) -> f7(x56, x57, x58) :|: TRUE
Start term: f1(a, x, max)

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

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(4)
Obligation:
Rules:
f9(x38, x39, x40) -> f10(x38, x39, x40) :|: x39 <= x40
f16(x41, x42, x43) -> f9(x41, x42, x43) :|: TRUE
f13(x67, x68, x69) -> f16(x67, x70, x69) :|: TRUE && x70 = x68 + 1
f14(x29, x30, x31) -> f13(x29, x30, x31) :|: TRUE
f11(x15, x16, x17) -> f14(arith, x16, x17) :|: TRUE && arith = x15 + 1
f10(x21, x22, x23) -> f11(x21, x22, x23) :|: x24 < 0
f10(x63, x64, x65) -> f11(x63, x64, x65) :|: x66 > 0
f15(x32, x33, x34) -> f13(x32, x33, x34) :|: TRUE
f12(x59, x60, x61) -> f15(x62, x60, x61) :|: TRUE && x62 = x59 - 1
f10(x25, x26, x27) -> f12(x25, x26, x27) :|: x28 = 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f13(x67:0, x68:0, x69:0) -> f13(x67:0 - 1, x68:0 + 1, x69:0) :|: x69:0 >= x68:0 + 1
f13(x, x1, x2) -> f13(x + 1, x1 + 1, x2) :|: x2 >= x1 + 1 && x3 > 0
f13(x4, x5, x6) -> f13(x4 + 1, x5 + 1, x6) :|: x6 >= x5 + 1 && x7 < 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:

   f13(x1, x2, x3) -> f13(x2, x3)

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(8)
Obligation:
Rules:
f13(x68:0, x69:0) -> f13(x68:0 + 1, x69:0) :|: x69:0 >= x68:0 + 1
f13(x1, x2) -> f13(x1 + 1, x2) :|: x2 >= x1 + 1 && x3 > 0
f13(x5, x6) -> f13(x5 + 1, x6) :|: x6 >= x5 + 1 && x7 < 0

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f13(x, x1)] = -x + x1

The following rules are decreasing:
f13(x68:0, x69:0) -> f13(x68:0 + 1, x69:0) :|: x69:0 >= x68:0 + 1
f13(x1, x2) -> f13(x1 + 1, x2) :|: x2 >= x1 + 1 && x3 > 0
f13(x5, x6) -> f13(x5 + 1, x6) :|: x6 >= x5 + 1 && x7 < 0
The following rules are bounded:
f13(x68:0, x69:0) -> f13(x68:0 + 1, x69:0) :|: x69:0 >= x68:0 + 1
f13(x1, x2) -> f13(x1 + 1, x2) :|: x2 >= x1 + 1 && x3 > 0
f13(x5, x6) -> f13(x5 + 1, x6) :|: x6 >= x5 + 1 && x7 < 0

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(10)
YES