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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(2) IntTRS
(3) TerminationGraphProcessor [SOUND, 47 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) TerminationGraphProcessor [EQUIVALENT, 2 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 4 ms]
(12) 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) -> f2(x_1, y) :|: TRUE
f2(x1, x2) -> f3(x1, x3) :|: TRUE
f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5 - 5
f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = 0 - 2 * x15
f3(x8, x9) -> f4(x8, x9) :|: x8 > 0
f6(x10, x11) -> f3(x10, x11) :|: TRUE
f3(x12, x13) -> f7(x12, x13) :|: x12 <= 0
Start term: f1(x, y)

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

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

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

(4)
Obligation:
Rules:
f3(x8, x9) -> f4(x8, x9) :|: x8 > 0
f6(x10, x11) -> f3(x10, x11) :|: TRUE
f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = 0 - 2 * x15
f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5 - 5

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

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

(6)
Obligation:
Rules:
f5(x14:0, x15:0) -> f5(x14:0 + (0 - 2 * x15:0) - 5, 0 - 2 * x15:0) :|: x14:0 > 0

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

(7) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained one non-trivial SCC.

f5(x14:0, x15:0) -> f5(x14:0 + (0 - 2 * x15:0) - 5, 0 - 2 * x15:0) :|: x14:0 > 0
has been transformed into
f5(x14:0, x15:0) -> f5(x14:0 + (0 - 2 * x15:0) - 5, 0 - 2 * x15:0) :|: x14:0 > 0 && x4 > 0.


f5(x14:0, x15:0) -> f5(x14:0 + (0 - 2 * x15:0) - 5, 0 - 2 * x15:0) :|: x14:0 > 0 && x4 > 0 and 
f5(x14:0, x15:0) -> f5(x14:0 + (0 - 2 * x15:0) - 5, 0 - 2 * x15:0) :|: x14:0 > 0 && x4 > 0
have been merged into the new rule
f5(x12, x13) -> f5(x12 + (0 - 2 * x13) - 5 + (0 - 2 * (0 - 2 * x13)) - 5, 0 - 2 * (0 - 2 * x13)) :|: x12 > 0 && x14 > 0 && (x12 + (0 - 2 * x13) - 5 > 0 && x15 > 0)


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

(8)
Obligation:
Rules:
f5(x16, x17) -> f5(x16 + 2 * x17 + -10, 4 * x17) :|: TRUE && x16 >= 1 && x18 >= 1 && x16 + -2 * x17 >= 6 && x19 >= 1

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

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

(10)
Obligation:
Rules:
f5(x16:0, x17:0) -> f5(x16:0 + 2 * x17:0 - 10, 4 * x17:0) :|: x16:0 + -2 * x17:0 >= 6 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0

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

(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f5 ] = 1/10*f5_1 + -1/15*f5_2

The following rules are decreasing:
f5(x16:0, x17:0) -> f5(x16:0 + 2 * x17:0 - 10, 4 * x17:0) :|: x16:0 + -2 * x17:0 >= 6 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0

The following rules are bounded:
f5(x16:0, x17:0) -> f5(x16:0 + 2 * x17:0 - 10, 4 * x17:0) :|: x16:0 + -2 * x17:0 >= 6 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0


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

(12)
YES