TRS Standard pair #487071353

details

property	value
status	complete
benchmark	Ex4_7_56_Bor03_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n182.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	10.5443 seconds
cpu usage	16.74
user time	16.1138
system time	0.626224
max virtual memory	1.8767292E7
max residence set size	1075340.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(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) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) UsableRulesProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) QDP
        (26) QDPOrderProof [EQUIVALENT, 64 ms]
        (27) QDP
        (28) QDPOrderProof [EQUIVALENT, 30 ms]
        (29) QDP
        (30) QDPOrderProof [EQUIVALENT, 140 ms]
        (31) QDP
        (32) QDPOrderProof [EQUIVALENT, 117 ms]
        (33) QDP
        (34) QDPOrderProof [EQUIVALENT, 141 ms]
        (35) QDP
        (36) QDPOrderProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) QDPOrderProof [EQUIVALENT, 8 ms]
        (39) QDP
        (40) QDPOrderProof [EQUIVALENT, 0 ms]
        (41) QDP
        (42) QDPOrderProof [EQUIVALENT, 521 ms]
        (43) QDP
        (44) DependencyGraphProof [EQUIVALENT, 0 ms]
        (45) TRUE


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

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

   active(from(X)) -> mark(cons(X, from(s(X))))
   active(after(0, XS)) -> mark(XS)
   active(after(s(N), cons(X, XS))) -> mark(after(N, XS))
   mark(from(X)) -> active(from(mark(X)))
   mark(cons(X1, X2)) -> active(cons(mark(X1), X2))
   mark(s(X)) -> active(s(mark(X)))
   mark(after(X1, X2)) -> active(after(mark(X1), mark(X2)))
   mark(0) -> active(0)
   from(mark(X)) -> from(X)
   from(active(X)) -> from(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)
   s(mark(X)) -> s(X)
   s(active(X)) -> s(X)
   after(mark(X1), X2) -> after(X1, X2)
   after(X1, mark(X2)) -> after(X1, X2)
   after(active(X1), X2) -> after(X1, X2)
   after(X1, active(X2)) -> after(X1, X2)

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:

   ACTIVE(from(X)) -> MARK(cons(X, from(s(X))))
   ACTIVE(from(X)) -> CONS(X, from(s(X)))
   ACTIVE(from(X)) -> FROM(s(X))
   ACTIVE(from(X)) -> S(X)

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