TRS Standard pair #516965315

details

property	value
status	complete
benchmark	rybalchenko-nonloop-popl08.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n098.star.cs.uiowa.edu
space	EEG_IJCAR_12

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	25.0421180725 seconds
cpu usage	78.869208756
max memory	5.961211904E9

stage attributes

key	value
output-size	12970
starexec-result	NO

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination w.r.t. Q of the given QTRS could be disproven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) UsableRulesProof [EQUIVALENT, 0 ms]
        (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) NonLoopProof [COMPLETE, 9295 ms]
        (17) NO


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

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   notZero(pos(s(x))) -> true
   notZero(neg(s(x))) -> true
   notZero(neg(0)) -> false
   notZero(pos(0)) -> false
   greaterZero(pos(s(x))) -> true
   greaterZero(pos(0)) -> false
   greaterZero(neg(x)) -> false
   and(false, false) -> false
   and(false, true) -> false
   and(true, false) -> false
   and(true, true) -> true
   minusT(0, y) -> neg(y)
   minusT(x, 0) -> pos(x)
   minusT(s(x), s(y)) -> minusT(x, y)
   plusNat(0, y) -> y
   plusNat(s(x), y) -> plusNat(x, s(y))
   negate(pos(x)) -> neg(x)
   negate(neg(x)) -> pos(x)
   minus(pos(x), pos(y)) -> minusT(x, y)
   minus(neg(x), neg(y)) -> negate(minusT(x, y))
   minus(pos(x), neg(y)) -> pos(plusNat(x, y))
   minus(neg(x), pos(y)) -> neg(plusNat(x, y))
   while(true, i, y) -> while(and(notZero(y), greaterZero(i)), minus(i, y), y)

Q is empty.

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

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   MINUST(s(x), s(y)) -> MINUST(x, y)
   PLUSNAT(s(x), y) -> PLUSNAT(x, s(y))
   MINUS(pos(x), pos(y)) -> MINUST(x, y)
   MINUS(neg(x), neg(y)) -> NEGATE(minusT(x, y))
   MINUS(neg(x), neg(y)) -> MINUST(x, y)
   MINUS(pos(x), neg(y)) -> PLUSNAT(x, y)
   MINUS(neg(x), pos(y)) -> PLUSNAT(x, y)
   WHILE(true, i, y) -> WHILE(and(notZero(y), greaterZero(i)), minus(i, y), y)
   WHILE(true, i, y) -> AND(notZero(y), greaterZero(i))
   WHILE(true, i, y) -> NOTZERO(y)
   WHILE(true, i, y) -> GREATERZERO(i)
   WHILE(true, i, y) -> MINUS(i, y)

The TRS R consists of the following rules:

   notZero(pos(s(x))) -> true
   notZero(neg(s(x))) -> true
   notZero(neg(0)) -> false
   notZero(pos(0)) -> false
   greaterZero(pos(s(x))) -> true
   greaterZero(pos(0)) -> false
   greaterZero(neg(x)) -> false
   and(false, false) -> false

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