SRS Stand 10685 pair #381717535

details

property	value
status	complete
benchmark	jw3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n047.star.cs.uiowa.edu
space	Waldmann_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.14376187325 seconds
cpu usage	19.988372692
max memory	2.404110336E9

stage attributes

key	value
output-size	8313
starexec-result	YES

output

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


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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 17 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) QDPOrderProof [EQUIVALENT, 22 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 1 ms]
        (9) YES
    (10) QDP
        (11) QDPOrderProof [EQUIVALENT, 69 ms]
        (12) QDP
        (13) QDPOrderProof [EQUIVALENT, 247 ms]
        (14) QDP
        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (16) YES


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

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

   a(b(b(x1))) -> P(a(b(x1)))
   a(P(x1)) -> P(a(x(x1)))
   a(x(x1)) -> x(a(x1))
   b(P(x1)) -> b(Q(x1))
   Q(x(x1)) -> a(Q(x1))
   Q(a(x1)) -> b(b(a(x1)))

Q is empty.

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

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

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

   A(b(b(x1))) -> A(b(x1))
   A(P(x1)) -> A(x(x1))
   A(x(x1)) -> A(x1)
   B(P(x1)) -> B(Q(x1))
   B(P(x1)) -> Q^1(x1)
   Q^1(x(x1)) -> A(Q(x1))
   Q^1(x(x1)) -> Q^1(x1)
   Q^1(a(x1)) -> B(b(a(x1)))
   Q^1(a(x1)) -> B(a(x1))

The TRS R consists of the following rules:

   a(b(b(x1))) -> P(a(b(x1)))
   a(P(x1)) -> P(a(x(x1)))
   a(x(x1)) -> x(a(x1))
   b(P(x1)) -> b(Q(x1))
   Q(x(x1)) -> a(Q(x1))
   Q(a(x1)) -> b(b(a(x1)))

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

(3) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node.
----------------------------------------

(4)
Complex Obligation (AND)

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

(5)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   A(P(x1)) -> A(x(x1))
   A(x(x1)) -> A(x1)
   A(b(b(x1))) -> A(b(x1))

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