YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(2) IntTRS
(3) TerminationGraphProcessor [SOUND, 67 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 50 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) RankingReductionPairProof [EQUIVALENT, 46 ms]
(10) IntTRS
(11) TerminationGraphProcessor [EQUIVALENT, 0 ms]
(12) 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(i, j, nondetNat, nondetPos) -> f2(x_1, j, nondetNat, nondetPos) :|: TRUE
f2(x, x1, x2, x3) -> f3(x, x4, x2, x3) :|: TRUE
f4(x5, x6, x7, x8) -> f5(x5, x6, x9, x8) :|: TRUE
f6(x10, x11, x12, x13) -> f9(x10, x11, arith, x13) :|: TRUE && arith = 0 - x12
f5(x14, x15, x16, x17) -> f6(x14, x15, x16, x17) :|: x16 < 0
f5(x18, x19, x20, x21) -> f7(x18, x19, x20, x21) :|: x20 >= 0
f9(x22, x23, x24, x25) -> f8(x22, x23, x24, x25) :|: TRUE
f7(x26, x27, x28, x29) -> f8(x26, x27, x28, x29) :|: TRUE
f8(x79, x80, x81, x82) -> f10(x83, x80, x81, x82) :|: TRUE && x83 = x79 - x81
f10(x34, x35, x36, x37) -> f11(x34, x35, x36, x38) :|: TRUE
f12(x84, x85, x86, x87) -> f15(x84, x85, x86, x88) :|: TRUE && x88 = 0 - x87
f11(x43, x44, x45, x46) -> f12(x43, x44, x45, x46) :|: x46 < 0
f11(x47, x48, x49, x50) -> f13(x47, x48, x49, x50) :|: x50 >= 0
f15(x51, x52, x53, x54) -> f14(x51, x52, x53, x54) :|: TRUE
f13(x55, x56, x57, x58) -> f14(x55, x56, x57, x58) :|: TRUE
f14(x89, x90, x91, x92) -> f16(x89, x90, x91, x93) :|: TRUE && x93 = x92 + 1
f16(x94, x95, x96, x97) -> f17(x94, x98, x96, x97) :|: TRUE && x98 = x95 + x97
f3(x67, x68, x69, x70) -> f4(x67, x68, x69, x70) :|: x67 - x68 >= 1
f17(x71, x72, x73, x74) -> f3(x71, x72, x73, x74) :|: TRUE
f3(x75, x76, x77, x78) -> f18(x75, x76, x77, x78) :|: x75 - x76 < 1
Start term: f1(i, j, nondetNat, nondetPos)

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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(x67, x68, x69, x70) -> f4(x67, x68, x69, x70) :|: x67 - x68 >= 1
f17(x71, x72, x73, x74) -> f3(x71, x72, x73, x74) :|: TRUE
f16(x94, x95, x96, x97) -> f17(x94, x98, x96, x97) :|: TRUE && x98 = x95 + x97
f14(x89, x90, x91, x92) -> f16(x89, x90, x91, x93) :|: TRUE && x93 = x92 + 1
f15(x51, x52, x53, x54) -> f14(x51, x52, x53, x54) :|: TRUE
f12(x84, x85, x86, x87) -> f15(x84, x85, x86, x88) :|: TRUE && x88 = 0 - x87
f11(x43, x44, x45, x46) -> f12(x43, x44, x45, x46) :|: x46 < 0
f10(x34, x35, x36, x37) -> f11(x34, x35, x36, x38) :|: TRUE
f8(x79, x80, x81, x82) -> f10(x83, x80, x81, x82) :|: TRUE && x83 = x79 - x81
f9(x22, x23, x24, x25) -> f8(x22, x23, x24, x25) :|: TRUE
f6(x10, x11, x12, x13) -> f9(x10, x11, arith, x13) :|: TRUE && arith = 0 - x12
f5(x14, x15, x16, x17) -> f6(x14, x15, x16, x17) :|: x16 < 0
f4(x5, x6, x7, x8) -> f5(x5, x6, x9, x8) :|: TRUE
f7(x26, x27, x28, x29) -> f8(x26, x27, x28, x29) :|: TRUE
f5(x18, x19, x20, x21) -> f7(x18, x19, x20, x21) :|: x20 >= 0
f13(x55, x56, x57, x58) -> f14(x55, x56, x57, x58) :|: TRUE
f11(x47, x48, x49, x50) -> f13(x47, x48, x49, x50) :|: x50 >= 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f8(x79:0, x80:0, x81:0, x82:0) -> f5(x79:0 - x81:0, x80:0 + (0 - x38:0 + 1), x9:0, 0 - x38:0 + 1) :|: x38:0 < 0 && x79:0 - x81:0 - (x80:0 + (0 - x38:0 + 1)) >= 1
f8(x, x1, x2, x3) -> f5(x - x2, x1 + (x4 + 1), x5, x4 + 1) :|: x4 > -1 && x - x2 - (x1 + (x4 + 1)) >= 1
f5(x18:0, x19:0, x20:0, x21:0) -> f8(x18:0, x19:0, x20:0, x21:0) :|: x20:0 > -1
f5(x14:0, x15:0, x16:0, x17:0) -> f8(x14:0, x15:0, 0 - x16:0, x17:0) :|: x16:0 < 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:

   f8(x1, x2, x3, x4) -> f8(x1, x2, x3)
   f5(x1, x2, x3, x4) -> f5(x1, x2, x3)

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(8)
Obligation:
Rules:
f8(x79:0, x80:0, x81:0) -> f5(x79:0 - x81:0, x80:0 + (0 - x38:0 + 1), x9:0) :|: x38:0 < 0 && x79:0 - x81:0 - (x80:0 + (0 - x38:0 + 1)) >= 1
f8(x, x1, x2) -> f5(x - x2, x1 + (x4 + 1), x5) :|: x4 > -1 && x - x2 - (x1 + (x4 + 1)) >= 1
f5(x18:0, x19:0, x20:0) -> f8(x18:0, x19:0, x20:0) :|: x20:0 > -1
f5(x14:0, x15:0, x16:0) -> f8(x14:0, x15:0, 0 - x16:0) :|: x16:0 < 0

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(9) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f8 ] = 2*f8_1 + -2*f8_3 + -2*f8_2
[ f5 ] = 2*f5_1 + -2*f5_2 + 1

The following rules are decreasing:
f8(x79:0, x80:0, x81:0) -> f5(x79:0 - x81:0, x80:0 + (0 - x38:0 + 1), x9:0) :|: x38:0 < 0 && x79:0 - x81:0 - (x80:0 + (0 - x38:0 + 1)) >= 1
f8(x, x1, x2) -> f5(x - x2, x1 + (x4 + 1), x5) :|: x4 > -1 && x - x2 - (x1 + (x4 + 1)) >= 1
f5(x18:0, x19:0, x20:0) -> f8(x18:0, x19:0, x20:0) :|: x20:0 > -1
f5(x14:0, x15:0, x16:0) -> f8(x14:0, x15:0, 0 - x16:0) :|: x16:0 < 0

The following rules are bounded:
f8(x79:0, x80:0, x81:0) -> f5(x79:0 - x81:0, x80:0 + (0 - x38:0 + 1), x9:0) :|: x38:0 < 0 && x79:0 - x81:0 - (x80:0 + (0 - x38:0 + 1)) >= 1
f8(x, x1, x2) -> f5(x - x2, x1 + (x4 + 1), x5) :|: x4 > -1 && x - x2 - (x1 + (x4 + 1)) >= 1


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(10)
Obligation:
Rules:
f5(x18:0, x19:0, x20:0) -> f8(x18:0, x19:0, x20:0) :|: x20:0 > -1
f5(x14:0, x15:0, x16:0) -> f8(x14:0, x15:0, 0 - x16:0) :|: x16:0 < 0

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

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(12)
YES