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


--------------------------------------------------------------------------------


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 53 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 34 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) RankingReductionPairProof [EQUIVALENT, 21 ms]
(10) YES


----------------------------------------

(0)
Obligation:
c file /export/starexec/sandbox/benchmark/theBenchmark.c
----------------------------------------

(1) CToIRSProof (EQUIVALENT)
Parsed C Integer Program as IRS.
----------------------------------------

(2)
Obligation:
Rules:
f1(x, y, z, oldx) -> f2(x_1, y, z, oldx) :|: TRUE
f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE
f3(x6, x7, x8, x9) -> f4(x6, x7, x10, x9) :|: TRUE
f5(x11, x12, x13, x14) -> f6(x11, x12, x13, x11) :|: TRUE
f6(x15, x16, x17, x18) -> f7(x19, x16, x17, x18) :|: TRUE
f7(x20, x21, x22, x23) -> f8(x20, x22, x22, x23) :|: TRUE
f4(x24, x25, x26, x27) -> f5(x24, x25, x26, x27) :|: x24 > 0 && x24 < x25 && x24 > 2 * x27
f8(x28, x29, x30, x31) -> f4(x28, x29, x30, x31) :|: TRUE
f4(x32, x33, x34, x35) -> f9(x32, x33, x34, x35) :|: x32 <= 2 * x35
f4(x36, x37, x38, x39) -> f9(x36, x37, x38, x39) :|: x36 <= 0
f4(x40, x41, x42, x43) -> f9(x40, x41, x42, x43) :|: x40 >= x41
Start term: f1(x, y, z, oldx)

----------------------------------------

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

----------------------------------------

(4)
Obligation:
Rules:
f4(x24, x25, x26, x27) -> f5(x24, x25, x26, x27) :|: x24 > 0 && x24 < x25 && x24 > 2 * x27
f8(x28, x29, x30, x31) -> f4(x28, x29, x30, x31) :|: TRUE
f7(x20, x21, x22, x23) -> f8(x20, x22, x22, x23) :|: TRUE
f6(x15, x16, x17, x18) -> f7(x19, x16, x17, x18) :|: TRUE
f5(x11, x12, x13, x14) -> f6(x11, x12, x13, x11) :|: TRUE

----------------------------------------

(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(6)
Obligation:
Rules:
f6(x15:0, x16:0, x17:0, x18:0) -> f6(x19:0, x17:0, x17:0, x19:0) :|: x19:0 > 0 && x19:0 < x17:0 && x19:0 > 2 * x18:0

----------------------------------------

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

   f6(x1, x2, x3, x4) -> f6(x3, x4)

----------------------------------------

(8)
Obligation:
Rules:
f6(x17:0, x18:0) -> f6(x17:0, x19:0) :|: x19:0 > 0 && x19:0 < x17:0 && x19:0 > 2 * x18:0

----------------------------------------

(9) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f6 ] = 1/2*f6_1 + -1*f6_2

The following rules are decreasing:
f6(x17:0, x18:0) -> f6(x17:0, x19:0) :|: x19:0 > 0 && x19:0 < x17:0 && x19:0 > 2 * x18:0

The following rules are bounded:
f6(x17:0, x18:0) -> f6(x17:0, x19:0) :|: x19:0 > 0 && x19:0 < x17:0 && x19:0 > 2 * x18:0


----------------------------------------

(10)
YES