TRS Standard pair #615296540

details

property	value
status	complete
benchmark	round_nonterm.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n015.star.cs.uiowa.edu
space	AProVE_08

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	1.98790287971 seconds
cpu usage	5.266761641
max memory	2.88247808E8

stage attributes

key	value
output-size	5347
starexec-result	"NO"

output

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


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


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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished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, 0 ms]
        (12) QDP
        (13) NonTerminationLoopProof [COMPLETE, 0 ms]
        (14) NO


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

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

   f(s(x), x) -> f(s(x), round(x))
   round(0) -> 0
   round(0) -> s(0)
   round(s(0)) -> s(0)
   round(s(s(x))) -> s(s(round(x)))

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:

   F(s(x), x) -> F(s(x), round(x))
   F(s(x), x) -> ROUND(x)
   ROUND(s(s(x))) -> ROUND(x)

The TRS R consists of the following rules:

   f(s(x), x) -> f(s(x), round(x))
   round(0) -> 0
   round(0) -> s(0)
   round(s(0)) -> s(0)
   round(s(s(x))) -> s(s(round(x)))

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 2 SCCs with 1 less node.
----------------------------------------

(4)
Complex Obligation (AND)

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(5)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   ROUND(s(s(x))) -> ROUND(x)

The TRS R consists of the following rules:

   f(s(x), x) -> f(s(x), round(x))
   round(0) -> 0
   round(0) -> s(0)
   round(s(0)) -> s(0)
   round(s(s(x))) -> s(s(round(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

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