TRS Innermost pair #487524575

details

property	value
status	complete
benchmark	ExProp7_Luc06_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n075.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.11903905869 seconds
cpu usage	8.487086827
max memory	5.97901312E8

stage attributes

key	value
output-size	45788
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) 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, 1 ms]
        (32) YES
    (33) QDP
        (34) MRRProof [EQUIVALENT, 31 ms]
        (35) QDP
        (36) QDPOrderProof [EQUIVALENT, 27 ms]
        (37) QDP
        (38) QDPOrderProof [EQUIVALENT, 0 ms]
        (39) QDP
        (40) DependencyGraphProof [EQUIVALENT, 0 ms]
        (41) AND
            (42) QDP
                (43) TransformationProof [EQUIVALENT, 0 ms]
                (44) QDP
                (45) QDPQMonotonicMRRProof [EQUIVALENT, 23 ms]
                (46) QDP
                (47) MRRProof [EQUIVALENT, 15 ms]
                (48) QDP
                (49) UsableRulesProof [EQUIVALENT, 0 ms]
                (50) QDP
                (51) QReductionProof [EQUIVALENT, 0 ms]
                (52) QDP
                (53) MRRProof [EQUIVALENT, 0 ms]
                (54) QDP
                (55) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms]
                (56) YES
            (57) QDP
                (58) UsableRulesProof [EQUIVALENT, 0 ms]
                (59) QDP
                (60) QReductionProof [EQUIVALENT, 0 ms]
                (61) QDP
                (62) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (63) YES


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

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

   active(f(0)) -> mark(cons(0, f(s(0))))
   active(f(s(0))) -> mark(f(p(s(0))))
   active(p(s(X))) -> mark(X)
   mark(f(X)) -> active(f(mark(X)))
   mark(0) -> active(0)
   mark(cons(X1, X2)) -> active(cons(mark(X1), X2))
   mark(s(X)) -> active(s(mark(X)))
   mark(p(X)) -> active(p(mark(X)))
   f(mark(X)) -> f(X)
   f(active(X)) -> f(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)

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