TRS Stand 20472 pair #381710979

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	n096.star.cs.uiowa.edu
space	MNZ_10

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	116.16027689 seconds
cpu usage	245.804809075
max memory	1.2060745728E10

stage attributes

key	value
output-size	57793
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 1 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, 120 ms]
(10) QDP
(11) QDPOrderProof [EQUIVALENT, 82 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, 9 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, 2034 ms]
(44) QDP
(45) QDPOrderProof [EQUIVALENT, 1405 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, 1310 ms]
        (56) QDP
        (57) QDPOrderProof [EQUIVALENT, 762 ms]
        (58) QDP
        (59) QDPOrderProof [EQUIVALENT, 790 ms]
        (60) QDP
        (61) QDPOrderProof [EQUIVALENT, 592 ms]
        (62) QDP
        (63) DependencyGraphProof [EQUIVALENT, 0 ms]
        (64) QDP
        (65) QDPOrderProof [EQUIVALENT, 1527 ms]
        (66) QDP
        (67) DependencyGraphProof [EQUIVALENT, 0 ms]
        (68) QDP
        (69) UsableRulesProof [EQUIVALENT, 0 ms]
        (70) QDP
        (71) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (72) YES


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(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)))

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