TRS Standard pair #615303547

details

property	value
status	complete
benchmark	thiemann26.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	58.9786667824 seconds
cpu usage	153.337852123
max memory	5.006503936E9

stage attributes

key	value
output-size	9195
starexec-result	"NO"

output

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


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NO
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished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, 1 ms]
        (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) NonTerminationLoopProof [COMPLETE, 36.3 s]
        (17) NO


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

   ge(x, 0) -> true
   ge(0, s(y)) -> false
   ge(s(x), s(y)) -> ge(x, y)
   minus(x, 0) -> x
   minus(0, y) -> 0
   minus(s(x), s(y)) -> minus(x, y)
   id_inc(x) -> x
   id_inc(x) -> s(x)
   quot(x, y) -> div(x, y, 0)
   div(x, y, z) -> if(ge(y, s(0)), ge(x, y), x, y, z)
   if(false, b, x, y, z) -> div_by_zero
   if(true, false, x, y, z) -> z
   if(true, true, x, y, z) -> div(minus(x, y), y, id_inc(z))

Q is empty.

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(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
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(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   GE(s(x), s(y)) -> GE(x, y)
   MINUS(s(x), s(y)) -> MINUS(x, y)
   QUOT(x, y) -> DIV(x, y, 0)
   DIV(x, y, z) -> IF(ge(y, s(0)), ge(x, y), x, y, z)
   DIV(x, y, z) -> GE(y, s(0))
   DIV(x, y, z) -> GE(x, y)
   IF(true, true, x, y, z) -> DIV(minus(x, y), y, id_inc(z))
   IF(true, true, x, y, z) -> MINUS(x, y)
   IF(true, true, x, y, z) -> ID_INC(z)

The TRS R consists of the following rules:

   ge(x, 0) -> true
   ge(0, s(y)) -> false
   ge(s(x), s(y)) -> ge(x, y)
   minus(x, 0) -> x
   minus(0, y) -> 0
   minus(s(x), s(y)) -> minus(x, y)
   id_inc(x) -> x
   id_inc(x) -> s(x)
   quot(x, y) -> div(x, y, 0)
   div(x, y, z) -> if(ge(y, s(0)), ge(x, y), x, y, z)
   if(false, b, x, y, z) -> div_by_zero
   if(true, false, x, y, z) -> z
   if(true, true, x, y, z) -> div(minus(x, y), y, id_inc(z))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(3) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 5 less nodes.
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