SRS Standard pair #516968206

details

property	value
status	complete
benchmark	aprove1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n090.star.cs.uiowa.edu
space	Secret_05_SRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	13.9329199791 seconds
cpu usage	42.393411488
max memory	1.534181376E9

stage attributes

key	value
output-size	15275
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 16 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) MNOCProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) DependencyGraphProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) QDPOrderProof [EQUIVALENT, 159 ms]
        (15) QDP
        (16) QDPOrderProof [EQUIVALENT, 164 ms]
        (17) QDP
        (18) QDPOrderProof [EQUIVALENT, 38 ms]
        (19) QDP
        (20) PisEmptyProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) QDP
        (23) QDPOrderProof [EQUIVALENT, 34 ms]
        (24) QDP
        (25) UsableRulesProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (28) YES


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

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

   p(0(x1)) -> 0(s(s(p(x1))))
   p(s(x1)) -> x1
   p(p(s(x1))) -> p(x1)
   f(s(x1)) -> g(s(x1))
   g(x1) -> i(s(half(x1)))
   i(x1) -> f(p(x1))
   half(0(x1)) -> 0(s(s(half(x1))))
   half(s(s(x1))) -> s(half(p(p(s(s(x1))))))
   0(x1) -> x1
   rd(0(x1)) -> 0(0(0(0(0(0(rd(x1)))))))

Q is empty.

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

(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   0(p(x1)) -> p(s(s(0(x1))))
   s(p(x1)) -> x1
   s(p(p(x1))) -> p(x1)
   s(f(x1)) -> s(g(x1))
   g(x1) -> half(s(i(x1)))
   i(x1) -> p(f(x1))
   0(half(x1)) -> half(s(s(0(x1))))
   s(s(half(x1))) -> s(s(p(p(half(s(x1))))))
   0(x1) -> x1
   0(rd(x1)) -> rd(0(0(0(0(0(0(x1)))))))

Q is empty.

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

(4)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(p(x1)) -> S(s(0(x1)))

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