TRS Standard pair #615301384

details

property	value
status	complete
benchmark	ExAppendixB_AEL03_GM.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	Transformed_CSR_04

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	49.5439050198 seconds
cpu usage	180.342262144
max memory	1.838309376E9

stage attributes

key	value
output-size	146700
starexec-result	"YES"

output

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


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


YES
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished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 proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) QDPOrderProof [EQUIVALENT, 420 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) QDP
(7) QDPOrderProof [EQUIVALENT, 387 ms]
(8) QDP
(9) QDPOrderProof [EQUIVALENT, 364 ms]
(10) QDP
(11) DependencyGraphProof [EQUIVALENT, 0 ms]
(12) QDP
(13) QDPOrderProof [EQUIVALENT, 428 ms]
(14) QDP
(15) QDPOrderProof [EQUIVALENT, 452 ms]
(16) QDP
(17) DependencyGraphProof [EQUIVALENT, 0 ms]
(18) QDP
(19) QDPOrderProof [EQUIVALENT, 447 ms]
(20) QDP
(21) QDPOrderProof [EQUIVALENT, 423 ms]
(22) QDP
(23) QDPOrderProof [EQUIVALENT, 321 ms]
(24) QDP
(25) QDPOrderProof [EQUIVALENT, 311 ms]
(26) QDP
(27) QDPOrderProof [EQUIVALENT, 326 ms]
(28) QDP
(29) QDPOrderProof [EQUIVALENT, 389 ms]
(30) QDP
(31) QDPOrderProof [EQUIVALENT, 319 ms]
(32) QDP
(33) QDPOrderProof [EQUIVALENT, 410 ms]
(34) QDP
(35) QDPOrderProof [EQUIVALENT, 386 ms]
(36) QDP
(37) QDPOrderProof [EQUIVALENT, 338 ms]
(38) QDP
(39) QDPOrderProof [EQUIVALENT, 549 ms]
(40) QDP
(41) DependencyGraphProof [EQUIVALENT, 0 ms]
(42) QDP
(43) UsableRulesProof [EQUIVALENT, 0 ms]
(44) QDP
(45) QDPSizeChangeProof [EQUIVALENT, 0 ms]
(46) YES


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

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

   a__from(X) -> cons(mark(X), from(s(X)))
   a__2ndspos(0, Z) -> rnil
   a__2ndspos(s(N), cons(X, Z)) -> a__2ndspos(s(mark(N)), cons2(X, mark(Z)))
   a__2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
   a__2ndsneg(0, Z) -> rnil
   a__2ndsneg(s(N), cons(X, Z)) -> a__2ndsneg(s(mark(N)), cons2(X, mark(Z)))
   a__2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
   a__pi(X) -> a__2ndspos(mark(X), a__from(0))
   a__plus(0, Y) -> mark(Y)
   a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
   a__times(0, Y) -> 0
   a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
   a__square(X) -> a__times(mark(X), mark(X))
   mark(from(X)) -> a__from(mark(X))
   mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
   mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
   mark(pi(X)) -> a__pi(mark(X))
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
   mark(square(X)) -> a__square(mark(X))
   mark(0) -> 0
   mark(s(X)) -> s(mark(X))
   mark(posrecip(X)) -> posrecip(mark(X))
   mark(negrecip(X)) -> negrecip(mark(X))
   mark(nil) -> nil
   mark(cons(X1, X2)) -> cons(mark(X1), X2)
   mark(cons2(X1, X2)) -> cons2(X1, mark(X2))
   mark(rnil) -> rnil
   mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
   a__from(X) -> from(X)
   a__2ndspos(X1, X2) -> 2ndspos(X1, X2)

popout

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

job log

popout

actions all output return to TRS Standard