TRS Standard pair #615305941

details

property	value
status	complete
benchmark	cade07.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	3.36951684952 seconds
cpu usage	9.027509439
max memory	3.78023936E8

stage attributes

key	value
output-size	23775
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished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) NonInfProof [EQUIVALENT, 64 ms]
        (20) AND
            (21) QDP
                (22) NonInfProof [EQUIVALENT, 18 ms]
                (23) QDP
                (24) DependencyGraphProof [EQUIVALENT, 0 ms]
                (25) TRUE
            (26) QDP
                (27) DependencyGraphProof [EQUIVALENT, 0 ms]
                (28) TRUE


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

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

   f(true, x, y, z) -> g(gt(x, y), x, y, z)
   g(true, x, y, z) -> f(gt(x, z), x, s(y), z)
   g(true, x, y, z) -> f(gt(x, z), x, y, s(z))
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)

Q is empty.

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

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

The TRS R 2 is 
   f(true, x, y, z) -> g(gt(x, y), x, y, z)
   g(true, x, y, z) -> f(gt(x, z), x, s(y), z)
   g(true, x, y, z) -> f(gt(x, z), x, y, s(z))

The signature Sigma is {f_4, g_4}
----------------------------------------

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

   f(true, x, y, z) -> g(gt(x, y), x, y, z)
   g(true, x, y, z) -> f(gt(x, z), x, s(y), z)
   g(true, x, y, z) -> f(gt(x, z), x, y, s(z))
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)

The set Q consists of the following terms:

   f(true, x0, x1, x2)
   g(true, x0, x1, x2)
   gt(0, x0)
   gt(s(x0), 0)
   gt(s(x0), s(x1))


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(3) DependencyPairsProof (EQUIVALENT)

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