TRS Standard pair #487073863

details

property	value
status	complete
benchmark	2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n191.star.cs.uiowa.edu
space	MNZ_10

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	36.2716 seconds
cpu usage	98.4948
user time	95.8612
system time	2.63364
max virtual memory	3.7774652E7
max residence set size	5104444.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 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, 28 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) QDPOrderProof [EQUIVALENT, 67 ms]
        (43) QDP
        (44) QDPOrderProof [EQUIVALENT, 33 ms]
        (45) QDP
        (46) QDPOrderProof [EQUIVALENT, 1625 ms]
        (47) QDP
        (48) QDPOrderProof [EQUIVALENT, 1448 ms]
        (49) QDP
        (50) QDPOrderProof [EQUIVALENT, 669 ms]
        (51) QDP
        (52) QDPOrderProof [EQUIVALENT, 738 ms]
        (53) QDP
        (54) QDPOrderProof [EQUIVALENT, 1763 ms]
        (55) QDP
        (56) DependencyGraphProof [EQUIVALENT, 0 ms]
        (57) TRUE
    (58) QDP
        (59) QDPOrderProof [EQUIVALENT, 64 ms]
        (60) QDP
        (61) DependencyGraphProof [EQUIVALENT, 0 ms]
        (62) QDP
        (63) UsableRulesProof [EQUIVALENT, 0 ms]
        (64) QDP
        (65) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (66) 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)
   s(x) -> h(0, x)
   f(g(x)) -> g(g(f(x)))
   g(s(x)) -> s(s(g(x)))
   h(f(x), g(x)) -> f(s(x))
   s(s(0)) -> k(0)
   k(0) -> 0
   s(s(s(0))) -> k(s(0))
   k(s(0)) -> s(0)
   s(s(s(s(s(s(s(s(0)))))))) -> k(s(s(0)))
   k(s(s(0))) -> s(s(s(s(s(s(0))))))
   h(k(x), g(x)) -> k(s(x))

Q is empty.

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