SRS Standard pair #516968260

details

property	value
status	complete
benchmark	aprove3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n026.star.cs.uiowa.edu
space	Secret_05_SRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	5.18903303146 seconds
cpu usage	17.2088733
max memory	1.231982592E9

stage attributes

key	value
output-size	18080
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) Overlay + Local Confluence [EQUIVALENT, 1 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 26 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QReductionProof [EQUIVALENT, 8 ms]
        (13) QDP
        (14) QDPOrderProof [EQUIVALENT, 87 ms]
        (15) QDP
        (16) QDPOrderProof [EQUIVALENT, 58 ms]
        (17) QDP
        (18) DependencyGraphProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) QReductionProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QDPOrderProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) DependencyGraphProof [EQUIVALENT, 0 ms]
        (27) TRUE
    (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) QReductionProof [EQUIVALENT, 4 ms]
        (32) QDP
        (33) QDPOrderProof [EQUIVALENT, 114 ms]
        (34) QDP
        (35) UsableRulesProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) QReductionProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (40) YES


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

   p(0(x1)) -> s(s(0(s(s(p(x1))))))
   p(s(0(x1))) -> 0(x1)
   p(s(s(x1))) -> s(p(s(x1)))
   f(s(x1)) -> g(q(i(x1)))
   g(x1) -> f(p(p(x1)))
   q(i(x1)) -> q(s(x1))
   q(s(x1)) -> s(s(x1))
   i(x1) -> s(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(s(s(x1))))))
   0(s(p(x1))) -> 0(x1)
   s(s(p(x1))) -> s(p(s(x1)))
   s(f(x1)) -> i(q(g(x1)))
   g(x1) -> p(p(f(x1)))
   i(q(x1)) -> s(q(x1))
   s(q(x1)) -> s(s(x1))
   i(x1) -> s(x1)

Q is empty.

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(3) Overlay + Local Confluence (EQUIVALENT)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.

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