TRS Standard pair #615301104

details

property	value
status	complete
benchmark	Ex1_Luc04b_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n164.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	3.6392800808 seconds
cpu usage	11.089979901
max memory	6.2758912E8

stage attributes

key	value
output-size	41340
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished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, 155 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 37 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 43 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (23) YES
    (24) QDP
        (25) UsableRulesProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (28) YES
    (29) QDP
        (30) UsableRulesProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (33) YES
    (34) QDP
        (35) MRRProof [EQUIVALENT, 52 ms]
        (36) QDP
        (37) MRRProof [EQUIVALENT, 37 ms]
        (38) QDP
        (39) QDPOrderProof [EQUIVALENT, 87 ms]
        (40) QDP
        (41) DependencyGraphProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) QDPOrderProof [EQUIVALENT, 172 ms]
        (44) QDP
        (45) QDPOrderProof [EQUIVALENT, 110 ms]
        (46) QDP
        (47) QDPOrderProof [EQUIVALENT, 0 ms]
        (48) QDP
        (49) UsableRulesProof [EQUIVALENT, 0 ms]
        (50) QDP
        (51) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (52) YES


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

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

   active(nats) -> mark(cons(0, incr(nats)))
   active(pairs) -> mark(cons(0, incr(odds)))
   active(odds) -> mark(incr(pairs))
   active(incr(cons(X, XS))) -> mark(cons(s(X), incr(XS)))
   active(head(cons(X, XS))) -> mark(X)
   active(tail(cons(X, XS))) -> mark(XS)
   mark(nats) -> active(nats)
   mark(cons(X1, X2)) -> active(cons(mark(X1), X2))
   mark(0) -> active(0)
   mark(incr(X)) -> active(incr(mark(X)))
   mark(pairs) -> active(pairs)
   mark(odds) -> active(odds)
   mark(s(X)) -> active(s(mark(X)))
   mark(head(X)) -> active(head(mark(X)))
   mark(tail(X)) -> active(tail(mark(X)))
   cons(mark(X1), X2) -> cons(X1, X2)
   cons(X1, mark(X2)) -> cons(X1, X2)
   cons(active(X1), X2) -> cons(X1, X2)
   cons(X1, active(X2)) -> cons(X1, X2)
   incr(mark(X)) -> incr(X)
   incr(active(X)) -> incr(X)
   s(mark(X)) -> s(X)
   s(active(X)) -> s(X)
   head(mark(X)) -> head(X)
   head(active(X)) -> head(X)

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