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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 70 ms]
(2) IntTRS
(3) TerminationGraphProcessor [SOUND, 66 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 10 ms]
(10) IntTRS
(11) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(12) IntTRS
(13) RankingReductionPairProof [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, c, i, j, M, N) -> f2(a, b, c, x_1, j, M, N) :|: TRUE
f2(x, x1, x2, x3, x4, x5, x6) -> f3(x, x1, x2, x3, x7, x5, x6) :|: TRUE
f3(x8, x9, x10, x11, x12, x13, x14) -> f4(x8, x9, x10, x11, x12, x15, x14) :|: TRUE
f4(x16, x17, x18, x19, x20, x21, x22) -> f5(x16, x17, x18, x19, x20, x21, x23) :|: TRUE
f5(x24, x25, x26, x27, x28, x29, x30) -> f6(x27, x25, x26, x27, x28, x29, x30) :|: TRUE
f6(x31, x32, x33, x34, x35, x36, x37) -> f7(x31, x35, x33, x34, x35, x36, x37) :|: TRUE
f7(x38, x39, x40, x41, x42, x43, x44) -> f8(x38, x39, 0, x41, x42, x43, x44) :|: TRUE
f9(x45, x46, x47, x48, x49, x50, x51) -> f10(x45, x46, x47, arith, x49, x50, x51) :|: TRUE && arith = x48 + 1
f10(x87, x88, x89, x90, x91, x92, x93) -> f11(x87, x88, x89, x90, x94, x92, x93) :|: TRUE && x94 = x91 + 1
f11(x95, x96, x97, x98, x99, x100, x101) -> f12(x95, x96, x102, x98, x99, x100, x101) :|: TRUE && x102 = x97 + 1
f8(x66, x67, x68, x69, x70, x71, x72) -> f9(x66, x67, x68, x69, x70, x71, x72) :|: x69 < x71
f8(x103, x104, x105, x106, x107, x108, x109) -> f9(x103, x104, x105, x106, x107, x108, x109) :|: x107 < x109
f12(x73, x74, x75, x76, x77, x78, x79) -> f8(x73, x74, x75, x76, x77, x78, x79) :|: TRUE
f8(x80, x81, x82, x83, x84, x85, x86) -> f13(x80, x81, x82, x83, x84, x85, x86) :|: x83 >= x85 && x84 >= x86
Start term: f1(a, b, c, i, j, M, N)

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

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(4)
Obligation:
Rules:
f8(x66, x67, x68, x69, x70, x71, x72) -> f9(x66, x67, x68, x69, x70, x71, x72) :|: x69 < x71
f12(x73, x74, x75, x76, x77, x78, x79) -> f8(x73, x74, x75, x76, x77, x78, x79) :|: TRUE
f11(x95, x96, x97, x98, x99, x100, x101) -> f12(x95, x96, x102, x98, x99, x100, x101) :|: TRUE && x102 = x97 + 1
f10(x87, x88, x89, x90, x91, x92, x93) -> f11(x87, x88, x89, x90, x94, x92, x93) :|: TRUE && x94 = x91 + 1
f9(x45, x46, x47, x48, x49, x50, x51) -> f10(x45, x46, x47, arith, x49, x50, x51) :|: TRUE && arith = x48 + 1
f8(x103, x104, x105, x106, x107, x108, x109) -> f9(x103, x104, x105, x106, x107, x108, x109) :|: x107 < x109

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f10(x87:0, x88:0, x89:0, x90:0, x91:0, x92:0, x93:0) -> f10(x87:0, x88:0, x89:0 + 1, x90:0 + 1, x91:0 + 1, x92:0, x93:0) :|: x92:0 > x90:0
f10(x, x1, x2, x3, x4, x5, x6) -> f10(x, x1, x2 + 1, x3 + 1, x4 + 1, x5, x6) :|: x6 > x4 + 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:

   f10(x1, x2, x3, x4, x5, x6, x7) -> f10(x4, x5, x6, x7)

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(8)
Obligation:
Rules:
f10(x90:0, x91:0, x92:0, x93:0) -> f10(x90:0 + 1, x91:0 + 1, x92:0, x93:0) :|: x92:0 > x90:0
f10(x3, x4, x5, x6) -> f10(x3 + 1, x4 + 1, x5, x6) :|: x6 > x4 + 1

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f10(x, x1, x2, x3)] = -1 - x1 + x3

The following rules are decreasing:
f10(x90:0, x91:0, x92:0, x93:0) -> f10(x90:0 + 1, x91:0 + 1, x92:0, x93:0) :|: x92:0 > x90:0
f10(x3, x4, x5, x6) -> f10(x3 + 1, x4 + 1, x5, x6) :|: x6 > x4 + 1
The following rules are bounded:
f10(x3, x4, x5, x6) -> f10(x3 + 1, x4 + 1, x5, x6) :|: x6 > x4 + 1

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(10)
Obligation:
Rules:
f10(x90:0, x91:0, x92:0, x93:0) -> f10(x90:0 + 1, x91:0 + 1, x92:0, x93:0) :|: x92:0 > x90:0

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

   f10(x1, x2, x3, x4) -> f10(x1, x3)

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(12)
Obligation:
Rules:
f10(x90:0, x92:0) -> f10(x90:0 + 1, x92:0) :|: x92:0 > x90:0

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(13) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f10 ] = f10_2 + -1*f10_1

The following rules are decreasing:
f10(x90:0, x92:0) -> f10(x90:0 + 1, x92:0) :|: x92:0 > x90:0

The following rules are bounded:
f10(x90:0, x92:0) -> f10(x90:0 + 1, x92:0) :|: x92:0 > x90:0


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(14)
YES