TRS Standard pair #516965220

details

property	value
status	complete
benchmark	emmes-nonloop-ex1_5.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n069.star.cs.uiowa.edu
space	EEG_IJCAR_12

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	12.769933939 seconds
cpu usage	43.96900157
max memory	1.3681664E9

stage attributes

key	value
output-size	12809
starexec-result	NO

output

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


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


NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(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) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) MNOCProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) NonLoopProof [COMPLETE, 232 ms]
        (25) NO


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

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

   f(true, x, y) -> f(gt(x, y), plus2(x), plus1(y))
   gt(s(x), 0) -> true
   gt(0, y) -> false
   gt(s(x), s(y)) -> gt(x, y)
   plus1(x) -> plus(s(0), x)
   plus2(x) -> plus(s(s(0)), x)
   plus(0, y) -> y
   plus(s(x), y) -> s(plus(x, y))

Q is empty.

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

(1) AAECC Innermost (EQUIVALENT)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
   gt(s(x), 0) -> true
   gt(0, y) -> false
   gt(s(x), s(y)) -> gt(x, y)
   plus1(x) -> plus(s(0), x)
   plus2(x) -> plus(s(s(0)), x)
   plus(0, y) -> y
   plus(s(x), y) -> s(plus(x, y))

The TRS R 2 is 
   f(true, x, y) -> f(gt(x, y), plus2(x), plus1(y))

The signature Sigma is {f_3}
----------------------------------------

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

   f(true, x, y) -> f(gt(x, y), plus2(x), plus1(y))
   gt(s(x), 0) -> true
   gt(0, y) -> false
   gt(s(x), s(y)) -> gt(x, y)
   plus1(x) -> plus(s(0), x)
   plus2(x) -> plus(s(s(0)), x)
   plus(0, y) -> y
   plus(s(x), y) -> s(plus(x, y))

The set Q consists of the following terms:

   f(true, x0, x1)
   gt(s(x0), 0)
   gt(0, x0)
   gt(s(x0), s(x1))
   plus1(x0)
   plus2(x0)
   plus(0, x0)

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