TRS Standard pair #615304961

details

property	value
status	complete
benchmark	4.32.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n035.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	4.78505086899 seconds
cpu usage	16.347239498
max memory	1.03262208E9

stage attributes

key	value
output-size	8399
starexec-result	"YES"

output

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


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


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

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 27 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 2 ms]
(6) QTRS
(7) QTRSRRRProof [EQUIVALENT, 1 ms]
(8) QTRS
(9) DependencyPairsProof [EQUIVALENT, 3 ms]
(10) QDP
(11) QDPOrderProof [EQUIVALENT, 69 ms]
(12) QDP
(13) DependencyGraphProof [EQUIVALENT, 0 ms]
(14) AND
    (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 1 ms]
        (19) YES
    (20) QDP
        (21) UsableRulesProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES


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

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

   a(b(x)) -> b(a(a(x)))
   b(c(x)) -> c(b(b(x)))
   c(a(x)) -> a(c(c(x)))
   u(a(x)) -> x
   v(b(x)) -> x
   w(c(x)) -> x
   a(u(x)) -> x
   b(v(x)) -> x
   c(w(x)) -> x

Q is empty.

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

(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   b(a(x)) -> a(a(b(x)))
   c(b(x)) -> b(b(c(x)))
   a(c(x)) -> c(c(a(x)))
   a(u(x)) -> x
   b(v(x)) -> x
   c(w(x)) -> x
   u(a(x)) -> x
   v(b(x)) -> x
   w(c(x)) -> x

Q is empty.

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

(3) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(a(x_1)) = x_1
   POL(b(x_1)) = x_1
   POL(c(x_1)) = x_1
   POL(u(x_1)) = 1 + x_1
   POL(v(x_1)) = x_1
   POL(w(x_1)) = x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   a(u(x)) -> x
   u(a(x)) -> x

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Standard