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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 20 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 12 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 6 ms]
(8) 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 = x5 - x4
f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 + 1
f3(x8, x9) -> f4(x8, x9) :|: x8 - x9 > 0
f6(x10, x11) -> f3(x10, x11) :|: TRUE
f3(x12, x13) -> f7(x12, x13) :|: x12 - x13 <= 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 - x9 > 0
f6(x10, x11) -> f3(x10, x11) :|: TRUE
f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 + 1
f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x5 - x4

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

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

(6)
Obligation:
Rules:
f5(x14:0, x15:0) -> f5(x15:0 + 1 - x14:0, x15:0 + 1) :|: x14:0 - (x15:0 + 1) > 0

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

(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f5(x, x1)] = -4 + 2*x - 2*x1 + x1^2

The following rules are decreasing:
f5(x14:0, x15:0) -> f5(x15:0 + 1 - x14:0, x15:0 + 1) :|: x14:0 - (x15:0 + 1) > 0
The following rules are bounded:
f5(x14:0, x15:0) -> f5(x15:0 + 1 - x14:0, x15:0 + 1) :|: x14:0 - (x15:0 + 1) > 0

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

(8)
YES