NO
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could be disproven:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 135 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 38 ms]
(6) IRSwT
(7) IRSwTChainingProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) IRSwTTerminationDigraphProof [EQUIVALENT, 23 ms]
(10) AND
    (11) IRSwT
        (12) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (13) IRSwT
        (14) TempFilterProof [SOUND, 6 ms]
        (15) IntTRS
        (16) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) IRSwT
        (19) TempFilterProof [SOUND, 3 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) YES
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (25) IRSwT
        (26) FilterProof [EQUIVALENT, 0 ms]
        (27) IntTRS
        (28) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (29) IntTRS
        (30) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
        (31) NO


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

(0)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1, arg2) -> f79_0_main_GE(arg1P, arg2P) :|: 100 = arg2P && 0 = arg1P
f79_0_main_GE(x, x1) -> f79_0_main_GE(x2, x3) :|: x1 + 1 = x3 && x - 1 = x2 && x <= x1 - 1 && x1 <= 51
f79_0_main_GE(x4, x5) -> f79_0_main_GE(x6, x7) :|: x5 - 1 = x7 && x4 + 1 = x6 && x4 <= x5 - 1 && 51 <= x5 - 1
__init(x8, x9) -> f1_0_main_ConstantStackPush(x10, x11) :|: 0 <= 0
Start term: __init(arg1, arg2)

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

(1) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(2)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1, arg2) -> f79_0_main_GE(arg1P, arg2P) :|: 100 = arg2P && 0 = arg1P
f79_0_main_GE(x, x1) -> f79_0_main_GE(x2, x3) :|: x1 + 1 = x3 && x - 1 = x2 && x <= x1 - 1 && x1 <= 51
f79_0_main_GE(x4, x5) -> f79_0_main_GE(x6, x7) :|: x5 - 1 = x7 && x4 + 1 = x6 && x4 <= x5 - 1 && 51 <= x5 - 1
__init(x8, x9) -> f1_0_main_ConstantStackPush(x10, x11) :|: 0 <= 0
Start term: __init(arg1, arg2)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_ConstantStackPush(arg1, arg2) -> f79_0_main_GE(arg1P, arg2P) :|: 100 = arg2P && 0 = arg1P
(2) f79_0_main_GE(x, x1) -> f79_0_main_GE(x2, x3) :|: x1 + 1 = x3 && x - 1 = x2 && x <= x1 - 1 && x1 <= 51
(3) f79_0_main_GE(x4, x5) -> f79_0_main_GE(x6, x7) :|: x5 - 1 = x7 && x4 + 1 = x6 && x4 <= x5 - 1 && 51 <= x5 - 1
(4) __init(x8, x9) -> f1_0_main_ConstantStackPush(x10, x11) :|: 0 <= 0

Arcs:
(1) -> (3)
(2) -> (2), (3)
(3) -> (2), (3)
(4) -> (1)

This digraph is fully evaluated!
----------------------------------------

(4)
Obligation:

Termination digraph:
Nodes:
(1) f79_0_main_GE(x4, x5) -> f79_0_main_GE(x6, x7) :|: x5 - 1 = x7 && x4 + 1 = x6 && x4 <= x5 - 1 && 51 <= x5 - 1
(2) f79_0_main_GE(x, x1) -> f79_0_main_GE(x2, x3) :|: x1 + 1 = x3 && x - 1 = x2 && x <= x1 - 1 && x1 <= 51

Arcs:
(1) -> (1), (2)
(2) -> (1), (2)

This digraph is fully evaluated!

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

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

(6)
Obligation:
Rules:
f79_0_main_GE(x:0, x1:0) -> f79_0_main_GE(x:0 - 1, x1:0 + 1) :|: x1:0 < 52 && x:0 <= x1:0 - 1
f79_0_main_GE(x4:0, x5:0) -> f79_0_main_GE(x4:0 + 1, x5:0 - 1) :|: x5:0 > 51 && x5:0 - 1 >= x4:0

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

(7) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(8)
Obligation:
Rules:
f79_0_main_GE(x, x1) -> f79_0_main_GE(x + -2, x1 + 2) :|: TRUE && x + -1 * x1 <= -1 && x1 <= 50
f79_0_main_GE(x4:0, x5:0) -> f79_0_main_GE(x4:0 + 1, x5:0 - 1) :|: x5:0 > 51 && x5:0 - 1 >= x4:0
f79_0_main_GE(x4, x5) -> f79_0_main_GE(x4, x5) :|: TRUE && x5 <= 51 && x4 + -1 * x5 <= -1 && x5 >= 51

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

(9) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f79_0_main_GE(x, x1) -> f79_0_main_GE(x + -2, x1 + 2) :|: TRUE && x + -1 * x1 <= -1 && x1 <= 50
(2) f79_0_main_GE(x4:0, x5:0) -> f79_0_main_GE(x4:0 + 1, x5:0 - 1) :|: x5:0 > 51 && x5:0 - 1 >= x4:0
(3) f79_0_main_GE(x4, x5) -> f79_0_main_GE(x4, x5) :|: TRUE && x5 <= 51 && x4 + -1 * x5 <= -1 && x5 >= 51

Arcs:
(1) -> (1), (2), (3)
(2) -> (2), (3)
(3) -> (3)

This digraph is fully evaluated!
----------------------------------------

(10)
Complex Obligation (AND)

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

(11)
Obligation:

Termination digraph:
Nodes:
(1) f79_0_main_GE(x, x1) -> f79_0_main_GE(x + -2, x1 + 2) :|: TRUE && x + -1 * x1 <= -1 && x1 <= 50

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(13)
Obligation:
Rules:
f79_0_main_GE(x:0, x1:0) -> f79_0_main_GE(x:0 - 2, x1:0 + 2) :|: x1:0 < 51 && x:0 + -1 * x1:0 <= -1

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

(14) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f79_0_main_GE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(15)
Obligation:
Rules:
f79_0_main_GE(x:0, x1:0) -> f79_0_main_GE(c, c1) :|: c1 = x1:0 + 2 && c = x:0 - 2 && (x1:0 < 51 && x:0 + -1 * x1:0 <= -1)

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

(16) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f79_0_main_GE ] = -1/2*f79_0_main_GE_2

The following rules are decreasing:
f79_0_main_GE(x:0, x1:0) -> f79_0_main_GE(c, c1) :|: c1 = x1:0 + 2 && c = x:0 - 2 && (x1:0 < 51 && x:0 + -1 * x1:0 <= -1)

The following rules are bounded:
f79_0_main_GE(x:0, x1:0) -> f79_0_main_GE(c, c1) :|: c1 = x1:0 + 2 && c = x:0 - 2 && (x1:0 < 51 && x:0 + -1 * x1:0 <= -1)


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

(17)
YES

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

(18)
Obligation:

Termination digraph:
Nodes:
(1) f79_0_main_GE(x4:0, x5:0) -> f79_0_main_GE(x4:0 + 1, x5:0 - 1) :|: x5:0 > 51 && x5:0 - 1 >= x4:0

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f79_0_main_GE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
f79_0_main_GE(x4:0, x5:0) -> f79_0_main_GE(c, c1) :|: c1 = x5:0 - 1 && c = x4:0 + 1 && (x5:0 > 51 && x5:0 - 1 >= x4:0)

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

(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f79_0_main_GE(x, x1)] = -1 - x + x1

The following rules are decreasing:
f79_0_main_GE(x4:0, x5:0) -> f79_0_main_GE(c, c1) :|: c1 = x5:0 - 1 && c = x4:0 + 1 && (x5:0 > 51 && x5:0 - 1 >= x4:0)
The following rules are bounded:
f79_0_main_GE(x4:0, x5:0) -> f79_0_main_GE(c, c1) :|: c1 = x5:0 - 1 && c = x4:0 + 1 && (x5:0 > 51 && x5:0 - 1 >= x4:0)

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

(22)
YES

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

(23)
Obligation:

Termination digraph:
Nodes:
(1) f79_0_main_GE(x4, x5) -> f79_0_main_GE(x4, x5) :|: TRUE && x5 <= 51 && x4 + -1 * x5 <= -1 && x5 >= 51

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(25)
Obligation:
Rules:
f79_0_main_GE(x4:0, x5:0) -> f79_0_main_GE(x4:0, x5:0) :|: x4:0 + -1 * x5:0 <= -1 && x5:0 < 52 && x5:0 > 50

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

(26) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f79_0_main_GE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(27)
Obligation:
Rules:
f79_0_main_GE(x4:0, x5:0) -> f79_0_main_GE(x4:0, x5:0) :|: x4:0 + -1 * x5:0 <= -1 && x5:0 < 52 && x5:0 > 50

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

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

(29)
Obligation:
Rules:
f79_0_main_GE(x4:0:0, x5:0:0) -> f79_0_main_GE(x4:0:0, x5:0:0) :|: x4:0:0 + -1 * x5:0:0 <= -1 && x5:0:0 < 52 && x5:0:0 > 50

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

(30) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x4:0:0, x5:0:0) -> f(1, x4:0:0, x5:0:0) :|: pc = 1 && (x4:0:0 + -1 * x5:0:0 <= -1 && x5:0:0 < 52 && x5:0:0 > 50)
Witness term starting non-terminating reduction: f(1, -64, 51)
----------------------------------------

(31)
NO