TRS Standard pair #487073828

details

property	value
status	complete
benchmark	8.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n181.star.cs.uiowa.edu
space	MNZ_10

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	93.4186 seconds
cpu usage	255.662
user time	250.405
system time	5.25768
max virtual memory	3.7244196E7
max residence set size	5708936.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QDP
(5) TransformationProof [EQUIVALENT, 0 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) TransformationProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) DependencyGraphProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) TransformationProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) TransformationProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) DependencyGraphProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) TransformationProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) DependencyGraphProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) TransformationProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) TransformationProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) DependencyGraphProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) TransformationProof [EQUIVALENT, 0 ms]
        (35) QDP
        (36) DependencyGraphProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) TransformationProof [EQUIVALENT, 118 ms]
        (39) QDP
        (40) DependencyGraphProof [EQUIVALENT, 0 ms]
        (41) QDP
        (42) TransformationProof [EQUIVALENT, 0 ms]
        (43) QDP
        (44) DependencyGraphProof [EQUIVALENT, 0 ms]
        (45) QDP
        (46) TransformationProof [EQUIVALENT, 21 ms]
        (47) QDP
        (48) DependencyGraphProof [EQUIVALENT, 0 ms]
        (49) QDP
        (50) QDPOrderProof [EQUIVALENT, 200 ms]
        (51) QDP
        (52) QDPOrderProof [EQUIVALENT, 4569 ms]
        (53) QDP
        (54) QDPOrderProof [EQUIVALENT, 3730 ms]
        (55) QDP
        (56) QDPOrderProof [EQUIVALENT, 4267 ms]
        (57) QDP
        (58) QDPOrderProof [EQUIVALENT, 4467 ms]
        (59) QDP
        (60) QDPOrderProof [EQUIVALENT, 3134 ms]
        (61) QDP
        (62) QDPOrderProof [EQUIVALENT, 3084 ms]
        (63) QDP
        (64) QDPOrderProof [EQUIVALENT, 3010 ms]
        (65) QDP
        (66) QDPOrderProof [EQUIVALENT, 1685 ms]
        (67) QDP
        (68) QDPOrderProof [EQUIVALENT, 966 ms]
        (69) QDP
        (70) DependencyGraphProof [EQUIVALENT, 0 ms]
        (71) TRUE
    (72) QDP
        (73) QDPOrderProof [EQUIVALENT, 129 ms]
        (74) QDP
        (75) DependencyGraphProof [EQUIVALENT, 0 ms]
        (76) QDP
        (77) UsableRulesProof [EQUIVALENT, 0 ms]
        (78) QDP
        (79) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (80) YES


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

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

   s(s(0)) -> f(s(0))
   g(x) -> h(x, x)
   s(x) -> h(x, 0)

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