TRS Standard pair #615301538

details

property	value
status	complete
benchmark	ExIntrod_GM01_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	4.33327913284 seconds
cpu usage	12.429937573
max memory	7.24312064E8

stage attributes

key	value
output-size	55018
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished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) QTRSRRRProof [EQUIVALENT, 156 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 51 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 31 ms]
(6) QTRS
(7) DependencyPairsProof [EQUIVALENT, 0 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) UsableRulesProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QDP
        (17) UsableRulesProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (25) YES
    (26) QDP
        (27) UsableRulesProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (30) YES
    (31) QDP
        (32) UsableRulesProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (35) YES
    (36) QDP
        (37) UsableRulesProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (40) YES
    (41) QDP
        (42) MRRProof [EQUIVALENT, 51 ms]
        (43) QDP
        (44) MRRProof [EQUIVALENT, 66 ms]
        (45) QDP
        (46) MRRProof [EQUIVALENT, 35 ms]
        (47) QDP
        (48) QDPOrderProof [EQUIVALENT, 136 ms]
        (49) QDP
        (50) DependencyGraphProof [EQUIVALENT, 0 ms]
        (51) QDP
        (52) QDPOrderProof [EQUIVALENT, 33 ms]
        (53) QDP
        (54) QDPOrderProof [EQUIVALENT, 10 ms]
        (55) QDP
        (56) QDPOrderProof [EQUIVALENT, 36 ms]
        (57) QDP
        (58) QDPOrderProof [EQUIVALENT, 30 ms]
        (59) QDP
        (60) DependencyGraphProof [EQUIVALENT, 0 ms]
        (61) TRUE


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

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

   active(incr(nil)) -> mark(nil)
   active(incr(cons(X, L))) -> mark(cons(s(X), incr(L)))
   active(adx(nil)) -> mark(nil)
   active(adx(cons(X, L))) -> mark(incr(cons(X, adx(L))))
   active(nats) -> mark(adx(zeros))
   active(zeros) -> mark(cons(0, zeros))
   active(head(cons(X, L))) -> mark(X)
   active(tail(cons(X, L))) -> mark(L)
   mark(incr(X)) -> active(incr(mark(X)))
   mark(nil) -> active(nil)
   mark(cons(X1, X2)) -> active(cons(mark(X1), X2))
   mark(s(X)) -> active(s(mark(X)))
   mark(adx(X)) -> active(adx(mark(X)))
   mark(nats) -> active(nats)
   mark(zeros) -> active(zeros)
   mark(0) -> active(0)

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