TRS Standard pair #615302798

details

property	value
status	complete
benchmark	tpa2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n010.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	2.02671194077 seconds
cpu usage	5.439709022
max memory	2.90717696E8

stage attributes

key	value
output-size	9833
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


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

(0) QTRS
(1) AAECC Innermost [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QReductionProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPOrderProof [EQUIVALENT, 46 ms]
        (20) QDP
        (21) QDPOrderProof [EQUIVALENT, 14 ms]
        (22) QDP
        (23) PisEmptyProof [EQUIVALENT, 0 ms]
        (24) YES


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

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

   -(x, 0) -> x
   -(s(x), s(y)) -> -(x, y)
   p(s(x)) -> x
   f(s(x), y) -> f(p(-(s(x), y)), p(-(y, s(x))))
   f(x, s(y)) -> f(p(-(x, s(y))), p(-(s(y), x)))

Q is empty.

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

(1) AAECC Innermost (EQUIVALENT)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
   -(x, 0) -> x
   -(s(x), s(y)) -> -(x, y)
   p(s(x)) -> x

The TRS R 2 is 
   f(s(x), y) -> f(p(-(s(x), y)), p(-(y, s(x))))
   f(x, s(y)) -> f(p(-(x, s(y))), p(-(s(y), x)))

The signature Sigma is {f_2}
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   -(x, 0) -> x
   -(s(x), s(y)) -> -(x, y)
   p(s(x)) -> x
   f(s(x), y) -> f(p(-(s(x), y)), p(-(y, s(x))))
   f(x, s(y)) -> f(p(-(x, s(y))), p(-(s(y), x)))

The set Q consists of the following terms:

   -(x0, 0)
   -(s(x0), s(x1))
   p(s(x0))
   f(s(x0), x1)
   f(x0, s(x1))


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(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:

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