TRS Innermost pair #487524295

details

property	value
status	complete
benchmark	Ex6_9_Luc02c_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n109.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	12.0704221725 seconds
cpu usage	18.515427506
max memory	1.131630592E9

stage attributes

key	value
output-size	63446
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 57 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) UsableRulesProof [EQUIVALENT, 0 ms]
        (35) QDP
        (36) QReductionProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (39) YES
    (40) QDP
        (41) QDPOrderProof [EQUIVALENT, 176 ms]
        (42) QDP
        (43) QDPQMonotonicMRRProof [EQUIVALENT, 77 ms]
        (44) QDP
        (45) QDPOrderProof [EQUIVALENT, 148 ms]
        (46) QDP
        (47) QDPOrderProof [EQUIVALENT, 81 ms]
        (48) QDP
        (49) DependencyGraphProof [EQUIVALENT, 0 ms]
        (50) QDP
        (51) QDPQMonotonicMRRProof [EQUIVALENT, 24 ms]
        (52) QDP
        (53) QDPOrderProof [EQUIVALENT, 40 ms]
        (54) QDP
        (55) DependencyGraphProof [EQUIVALENT, 0 ms]
        (56) AND
            (57) QDP
                (58) QDPOrderProof [EQUIVALENT, 73 ms]
                (59) QDP
                (60) DependencyGraphProof [EQUIVALENT, 0 ms]
                (61) TRUE
            (62) QDP
                (63) UsableRulesProof [EQUIVALENT, 0 ms]
                (64) QDP
                (65) QReductionProof [EQUIVALENT, 0 ms]
                (66) QDP
                (67) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (68) YES


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

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

   active(2nd(cons1(X, cons(Y, Z)))) -> mark(Y)
   active(2nd(cons(X, X1))) -> mark(2nd(cons1(X, X1)))
   active(from(X)) -> mark(cons(X, from(s(X))))
   mark(2nd(X)) -> active(2nd(mark(X)))
   mark(cons1(X1, X2)) -> active(cons1(mark(X1), mark(X2)))
   mark(cons(X1, X2)) -> active(cons(mark(X1), X2))
   mark(from(X)) -> active(from(mark(X)))
   mark(s(X)) -> active(s(mark(X)))
   2nd(mark(X)) -> 2nd(X)

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