TRS Standard pair #487073873

details

property	value
status	complete
benchmark	nvsr.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n178.star.cs.uiowa.edu
space	MNZ_10

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	120.728 seconds
cpu usage	250.095
user time	241.547
system time	8.54871
max virtual memory	3.7382692E7
max residence set size	1.1894792E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QDP
(9) QDPOrderProof [EQUIVALENT, 123 ms]
(10) QDP
(11) QDPOrderProof [EQUIVALENT, 89 ms]
(12) QDP
(13) TransformationProof [EQUIVALENT, 0 ms]
(14) QDP
(15) DependencyGraphProof [EQUIVALENT, 0 ms]
(16) QDP
(17) TransformationProof [EQUIVALENT, 0 ms]
(18) QDP
(19) DependencyGraphProof [EQUIVALENT, 0 ms]
(20) QDP
(21) TransformationProof [EQUIVALENT, 0 ms]
(22) QDP
(23) DependencyGraphProof [EQUIVALENT, 0 ms]
(24) QDP
(25) TransformationProof [EQUIVALENT, 0 ms]
(26) QDP
(27) DependencyGraphProof [EQUIVALENT, 0 ms]
(28) QDP
(29) TransformationProof [EQUIVALENT, 0 ms]
(30) QDP
(31) TransformationProof [EQUIVALENT, 0 ms]
(32) QDP
(33) DependencyGraphProof [EQUIVALENT, 0 ms]
(34) QDP
(35) TransformationProof [EQUIVALENT, 8 ms]
(36) QDP
(37) DependencyGraphProof [EQUIVALENT, 0 ms]
(38) QDP
(39) TransformationProof [EQUIVALENT, 0 ms]
(40) QDP
(41) DependencyGraphProof [EQUIVALENT, 0 ms]
(42) QDP
(43) QDPOrderProof [EQUIVALENT, 1996 ms]
(44) QDP
(45) QDPOrderProof [EQUIVALENT, 1447 ms]
(46) QDP
(47) DependencyGraphProof [EQUIVALENT, 0 ms]
(48) AND
    (49) QDP
        (50) UsableRulesProof [EQUIVALENT, 0 ms]
        (51) QDP
        (52) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (53) YES
    (54) QDP
        (55) QDPOrderProof [EQUIVALENT, 1335 ms]
        (56) QDP
        (57) QDPOrderProof [EQUIVALENT, 1111 ms]
        (58) QDP
        (59) QDPOrderProof [EQUIVALENT, 793 ms]
        (60) QDP
        (61) QDPOrderProof [EQUIVALENT, 841 ms]
        (62) QDP
        (63) DependencyGraphProof [EQUIVALENT, 0 ms]
        (64) QDP
        (65) QDPOrderProof [EQUIVALENT, 1482 ms]
        (66) QDP
        (67) DependencyGraphProof [EQUIVALENT, 0 ms]
        (68) QDP
        (69) UsableRulesProof [EQUIVALENT, 0 ms]
        (70) QDP
        (71) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (72) YES


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

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

   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(0) -> f(0)
   s(s(0)) -> f(s(0))
   f(s(0)) -> 0
   s(s(s(s(s(s(s(0))))))) -> f(s(s(0)))
   f(s(s(0))) -> s(s(s(s(s(0)))))

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