TRS Stand 20472 pair #381709793

details

property	value
status	complete
benchmark	linear2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n023.star.cs.uiowa.edu
space	Endrullis_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.59455513954 seconds
cpu usage	11.08079839
max memory	6.78862848E8

stage attributes

key	value
output-size	7843
starexec-result	YES

output

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


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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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) MRRProof [EQUIVALENT, 27 ms]
        (7) QDP
        (8) QDPOrderProof [EQUIVALENT, 33 ms]
        (9) QDP
        (10) PisEmptyProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) MRRProof [EQUIVALENT, 19 ms]
        (14) QDP
        (15) QDPOrderProof [EQUIVALENT, 392 ms]
        (16) QDP
        (17) PisEmptyProof [EQUIVALENT, 0 ms]
        (18) YES


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

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

   f(a, f(a, f(a, f(x, b)))) -> f(f(a, f(a, f(a, x))), b)
   f(f(f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b)

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:

   F(a, f(a, f(a, f(x, b)))) -> F(f(a, f(a, f(a, x))), b)
   F(a, f(a, f(a, f(x, b)))) -> F(a, f(a, f(a, x)))
   F(a, f(a, f(a, f(x, b)))) -> F(a, f(a, x))
   F(a, f(a, f(a, f(x, b)))) -> F(a, x)
   F(f(f(a, x), b), b) -> F(f(a, f(f(x, b), b)), b)
   F(f(f(a, x), b), b) -> F(a, f(f(x, b), b))
   F(f(f(a, x), b), b) -> F(f(x, b), b)
   F(f(f(a, x), b), b) -> F(x, b)

The TRS R consists of the following rules:

   f(a, f(a, f(a, f(x, b)))) -> f(f(a, f(a, f(a, x))), b)
   f(f(f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b)

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 2 less nodes.
----------------------------------------

(4)
Complex Obligation (AND)

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

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

   F(f(f(a, x), b), b) -> F(f(x, b), b)
   F(f(f(a, x), b), b) -> F(f(a, f(f(x, b), b)), b)
   F(f(f(a, x), b), b) -> F(x, b)

The TRS R consists of the following rules:

   f(a, f(a, f(a, f(x, b)))) -> f(f(a, f(a, f(a, x))), b)
   f(f(f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b)

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

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