TRS Innermost pair #487093155

details

property	value
status	complete
benchmark	Ex49_GM04_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.01073 seconds
cpu usage	8.01857
user time	7.66379
system time	0.354785
max virtual memory	6.0211116E7
max residence set size	601872.0

stage attributes

key	value
starexec-result	YES

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 17 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, 1 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) UsableRulesProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) QReductionProof [EQUIVALENT, 0 ms]
        (44) QDP
        (45) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (46) QDP
        (47) PisEmptyProof [EQUIVALENT, 0 ms]
        (48) YES
    (49) QDP
        (50) UsableRulesProof [EQUIVALENT, 0 ms]
        (51) QDP
        (52) QReductionProof [EQUIVALENT, 0 ms]
        (53) QDP
        (54) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (55) QDP
        (56) PisEmptyProof [EQUIVALENT, 0 ms]
        (57) YES
    (58) QDP
        (59) UsableRulesProof [EQUIVALENT, 0 ms]
        (60) QDP
        (61) QDPOrderProof [EQUIVALENT, 105 ms]
        (62) QDP
        (63) QDPQMonotonicMRRProof [EQUIVALENT, 70 ms]
        (64) QDP
        (65) UsableRulesProof [EQUIVALENT, 0 ms]
        (66) QDP
        (67) QReductionProof [EQUIVALENT, 0 ms]
        (68) QDP
        (69) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (70) YES


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

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

   active(minus(0, Y)) -> mark(0)
   active(minus(s(X), s(Y))) -> mark(minus(X, Y))
   active(geq(X, 0)) -> mark(true)
   active(geq(0, s(Y))) -> mark(false)
   active(geq(s(X), s(Y))) -> mark(geq(X, Y))
   active(div(0, s(Y))) -> mark(0)
   active(div(s(X), s(Y))) -> mark(if(geq(X, Y), s(div(minus(X, Y), s(Y))), 0))
   active(if(true, X, Y)) -> mark(X)
   active(if(false, X, Y)) -> mark(Y)
   mark(minus(X1, X2)) -> active(minus(X1, X2))
   mark(0) -> active(0)
   mark(s(X)) -> active(s(mark(X)))
   mark(geq(X1, X2)) -> active(geq(X1, X2))

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