/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 43 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 30 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 5 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) -> f2(x_1, y, z) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE
f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = x9 + x10 + x11
f6(x24, x25, x26) -> f7(x24, x27, x26) :|: TRUE && x27 = 0 - x26 - 1
f4(x15, x16, x17) -> f5(x15, x16, x17) :|: x15 >= 0 && x15 + x16 >= 0
f7(x18, x19, x20) -> f4(x18, x19, x20) :|: TRUE
f4(x21, x22, x23) -> f8(x21, x22, x23) :|: x21 < 0
f4(x28, x29, x30) -> f8(x28, x29, x30) :|: x28 + x29 < 0
Start term: f1(x, y, z)

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

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

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

(4)
Obligation:
Rules:
f4(x15, x16, x17) -> f5(x15, x16, x17) :|: x15 >= 0 && x15 + x16 >= 0
f7(x18, x19, x20) -> f4(x18, x19, x20) :|: TRUE
f6(x24, x25, x26) -> f7(x24, x27, x26) :|: TRUE && x27 = 0 - x26 - 1
f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = x9 + x10 + x11

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

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

(6)
Obligation:
Rules:
f6(x24:0, x25:0, x26:0) -> f6(x24:0 + (0 - x26:0 - 1) + x26:0, 0 - x26:0 - 1, x26:0) :|: x24:0 > -1 && x24:0 + (0 - x26:0 - 1) >= 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) -> f6(x1, x3)

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

(8)
Obligation:
Rules:
f6(x24:0, x26:0) -> f6(x24:0 + (0 - x26:0 - 1) + x26:0, x26:0) :|: x24:0 > -1 && x24:0 + (0 - x26:0 - 1) >= 0

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

(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x, x1)] = x

The following rules are decreasing:
f6(x24:0, x26:0) -> f6(x24:0 + (0 - x26:0 - 1) + x26:0, x26:0) :|: x24:0 > -1 && x24:0 + (0 - x26:0 - 1) >= 0
The following rules are bounded:
f6(x24:0, x26:0) -> f6(x24:0 + (0 - x26:0 - 1) + x26:0, x26:0) :|: x24:0 > -1 && x24:0 + (0 - x26:0 - 1) >= 0

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

(10)
YES