SRS Stand 10685 pair #381717813

details

property	value
status	timeout (cpu)
benchmark	x07.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
space	Secret_07_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	301.007974863 seconds
cpu usage	1624.49837092
max memory	2.056521728E10

stage attributes

unavailable

output

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


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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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 23 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) QDPOrderProof [EQUIVALENT, 334 ms]
        (12) QDP
        (13) DependencyGraphProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QDPOrderProof [EQUIVALENT, 66 ms]
        (16) QDP
        (17) QDPOrderProof [EQUIVALENT, 65.4 s]
        (18) QDP
        (19) DependencyGraphProof [EQUIVALENT, 0 ms]
        (20) TRUE


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

   a(a(b(x1))) -> c(d(x1))
   b(e(b(x1))) -> e(d(x1))
   b(d(x1)) -> e(b(x1))
   b(b(b(x1))) -> e(e(x1))
   e(e(e(x1))) -> d(e(x1))
   d(x1) -> b(e(x1))
   c(d(a(x1))) -> c(x1)
   d(c(x1)) -> c(d(a(x1)))
   a(x1) -> e(b(x1))

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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(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   A(a(b(x1))) -> C(d(x1))
   A(a(b(x1))) -> D(x1)
   B(e(b(x1))) -> E(d(x1))
   B(e(b(x1))) -> D(x1)
   B(d(x1)) -> E(b(x1))
   B(d(x1)) -> B(x1)
   B(b(b(x1))) -> E(e(x1))
   B(b(b(x1))) -> E(x1)
   E(e(e(x1))) -> D(e(x1))
   D(x1) -> B(e(x1))
   D(x1) -> E(x1)
   C(d(a(x1))) -> C(x1)
   D(c(x1)) -> C(d(a(x1)))
   D(c(x1)) -> D(a(x1))
   D(c(x1)) -> A(x1)
   A(x1) -> E(b(x1))
   A(x1) -> B(x1)

The TRS R consists of the following rules:

   a(a(b(x1))) -> c(d(x1))
   b(e(b(x1))) -> e(d(x1))
   b(d(x1)) -> e(b(x1))
   b(b(b(x1))) -> e(e(x1))
   e(e(e(x1))) -> d(e(x1))
   d(x1) -> b(e(x1))
   c(d(a(x1))) -> c(x1)
   d(c(x1)) -> c(d(a(x1)))
   a(x1) -> e(b(x1))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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