SRS Standard pair #487519745

details

property	value
status	complete
benchmark	z008.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n043.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	12.2418179512 seconds
cpu usage	44.039008489
max memory	4.774715392E9

stage attributes

key	value
output-size	10737
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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, 1 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 6 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 9 ms]
        (9) QDP
        (10) QDPOrderProof [EQUIVALENT, 59 ms]
        (11) QDP
        (12) DependencyGraphProof [EQUIVALENT, 0 ms]
        (13) AND
            (14) QDP
                (15) QDPOrderProof [EQUIVALENT, 6 ms]
                (16) QDP
                (17) PisEmptyProof [EQUIVALENT, 0 ms]
                (18) YES
            (19) QDP
                (20) QDPOrderProof [EQUIVALENT, 5 ms]
                (21) QDP
                (22) PisEmptyProof [EQUIVALENT, 0 ms]
                (23) YES
    (24) QDP
        (25) UsableRulesProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) MRRProof [EQUIVALENT, 27 ms]
        (28) QDP
        (29) PisEmptyProof [EQUIVALENT, 0 ms]
        (30) YES


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

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

   a(s(x1)) -> s(a(x1))
   b(a(b(s(x1)))) -> a(b(s(a(x1))))
   b(a(b(b(x1)))) -> a(b(a(b(x1))))
   a(b(a(a(x1)))) -> b(a(b(a(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:

   s(a(x1)) -> a(s(x1))
   s(b(a(b(x1)))) -> a(s(b(a(x1))))
   b(b(a(b(x1)))) -> b(a(b(a(x1))))
   a(a(b(a(x1)))) -> a(b(a(b(x1))))

Q is empty.

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

(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:

   S(a(x1)) -> A(s(x1))
   S(a(x1)) -> S(x1)
   S(b(a(b(x1)))) -> A(s(b(a(x1))))
   S(b(a(b(x1)))) -> S(b(a(x1)))
   S(b(a(b(x1)))) -> B(a(x1))
   S(b(a(b(x1)))) -> A(x1)
   B(b(a(b(x1)))) -> B(a(b(a(x1))))
   B(b(a(b(x1)))) -> A(b(a(x1)))
   B(b(a(b(x1)))) -> B(a(x1))
   B(b(a(b(x1)))) -> A(x1)
   A(a(b(a(x1)))) -> A(b(a(b(x1))))

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