TRS Stand 20472 pair #381709634

details

property	value
status	complete
benchmark	0.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n075.star.cs.uiowa.edu
space	MNZ_10

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	31.5606579781 seconds
cpu usage	86.52772868
max memory	4.111417344E9

stage attributes

key	value
output-size	47730
starexec-result	YES

output

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


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YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 21 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, 103 ms]
(10) QDP
(11) DependencyGraphProof [EQUIVALENT, 0 ms]
(12) AND
    (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, 16 ms]
        (35) QDP
        (36) DependencyGraphProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) QDPOrderProof [EQUIVALENT, 41 ms]
        (39) QDP
        (40) QDPOrderProof [EQUIVALENT, 1365 ms]
        (41) QDP
        (42) QDPOrderProof [EQUIVALENT, 996 ms]
        (43) QDP
        (44) QDPOrderProof [EQUIVALENT, 936 ms]
        (45) QDP
        (46) QDPOrderProof [EQUIVALENT, 969 ms]
        (47) QDP
        (48) QDPOrderProof [EQUIVALENT, 773 ms]
        (49) QDP
        (50) QDPOrderProof [EQUIVALENT, 1203 ms]
        (51) QDP
        (52) DependencyGraphProof [EQUIVALENT, 0 ms]
        (53) TRUE
    (54) QDP
        (55) UsableRulesProof [EQUIVALENT, 0 ms]
        (56) QDP
        (57) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (58) YES


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

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

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

Q is empty.

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(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.

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