SRS Standard pair #516973180

details

property	value
status	complete
benchmark	x06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n166.star.cs.uiowa.edu
space	Secret_07_SRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	17.7394058704 seconds
cpu usage	66.306039374
max memory	5.592498176E9

stage attributes

key	value
output-size	12759
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 14 ms]
(2) QDP
(3) QDPOrderProof [EQUIVALENT, 209 ms]
(4) QDP
(5) QDPOrderProof [EQUIVALENT, 129 ms]
(6) QDP
(7) QDPOrderProof [EQUIVALENT, 148 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) QDP
(11) QDPOrderProof [EQUIVALENT, 34 ms]
(12) QDP
(13) DependencyGraphProof [EQUIVALENT, 0 ms]
(14) TRUE


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

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

   a(b(x1)) -> c(b(x1))
   c(c(x1)) -> d(b(x1))
   d(x1) -> c(e(x1))
   b(b(x1)) -> f(x1)
   c(b(x1)) -> g(x1)
   e(x1) -> f(x1)
   e(x1) -> b(b(x1))
   f(g(x1)) -> a(c(x1))
   g(f(x1)) -> e(x1)
   a(x1) -> b(c(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(x1)) -> C(b(x1))
   C(c(x1)) -> D(b(x1))
   C(c(x1)) -> B(x1)
   D(x1) -> C(e(x1))
   D(x1) -> E(x1)
   B(b(x1)) -> F(x1)
   C(b(x1)) -> G(x1)
   E(x1) -> F(x1)
   E(x1) -> B(b(x1))
   E(x1) -> B(x1)
   F(g(x1)) -> A(c(x1))
   F(g(x1)) -> C(x1)
   G(f(x1)) -> E(x1)
   A(x1) -> B(c(x1))
   A(x1) -> C(x1)

The TRS R consists of the following rules:

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

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

(3) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

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