TRS Inner 89993 pair #381733779

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	n088.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.24567198753 seconds
cpu usage	17.076882481
max memory	1.10014464E9

stage attributes

key	value
output-size	57324
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) QReductionProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QReductionProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) QReductionProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (25) YES
    (26) QDP
        (27) UsableRulesProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) QReductionProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (32) YES
    (33) QDP
        (34) QDPOrderProof [EQUIVALENT, 56 ms]
        (35) QDP
        (36) QDPQMonotonicMRRProof [EQUIVALENT, 38 ms]
        (37) QDP
        (38) QDPOrderProof [EQUIVALENT, 105 ms]
        (39) QDP
        (40) QDPOrderProof [EQUIVALENT, 139 ms]
        (41) QDP
        (42) QDPOrderProof [EQUIVALENT, 129 ms]
        (43) QDP
        (44) QDPOrderProof [EQUIVALENT, 77 ms]
        (45) QDP
        (46) QDPOrderProof [EQUIVALENT, 50 ms]
        (47) QDP
        (48) DependencyGraphProof [EQUIVALENT, 0 ms]
        (49) AND
            (50) QDP
                (51) QDPQMonotonicMRRProof [EQUIVALENT, 24 ms]
                (52) QDP
                (53) DependencyGraphProof [EQUIVALENT, 0 ms]
                (54) TRUE
            (55) QDP
                (56) UsableRulesProof [EQUIVALENT, 0 ms]
                (57) QDP
                (58) QReductionProof [EQUIVALENT, 0 ms]
                (59) QDP
                (60) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (61) YES


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

(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)

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