TRS Standard pair #487073833

details

property	value
status	complete
benchmark	9.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	MNZ_10

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	233.143 seconds
cpu usage	428.833
user time	424.158
system time	4.6756
max virtual memory	3.73828E7
max residence set size	8029100.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1 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, 0 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, 171 ms]
        (47) QDP
        (48) DependencyGraphProof [EQUIVALENT, 0 ms]
        (49) QDP
        (50) TransformationProof [EQUIVALENT, 72 ms]
        (51) QDP
        (52) DependencyGraphProof [EQUIVALENT, 0 ms]
        (53) QDP
        (54) QDPOrderProof [EQUIVALENT, 213 ms]
        (55) QDP
        (56) QDPOrderProof [EQUIVALENT, 132 ms]
        (57) QDP
        (58) QDPOrderProof [EQUIVALENT, 55 ms]
        (59) QDP
        (60) QDPOrderProof [EQUIVALENT, 3460 ms]
        (61) QDP
        (62) QDPOrderProof [EQUIVALENT, 3122 ms]
        (63) QDP
        (64) QDPOrderProof [EQUIVALENT, 2054 ms]
        (65) QDP
        (66) QDPOrderProof [EQUIVALENT, 3150 ms]
        (67) QDP
        (68) QDPOrderProof [EQUIVALENT, 167.6 s]
        (69) QDP
        (70) DependencyGraphProof [EQUIVALENT, 0 ms]
        (71) TRUE
    (72) QDP
        (73) QDPOrderProof [EQUIVALENT, 122 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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