SRS Stand 10685 pair #381724652

details

property	value
status	complete
benchmark	214169.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n081.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	11.4280190468 seconds
cpu usage	42.089823219
max memory	4.132143104E9

stage attributes

key	value
output-size	39434
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 277 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 10 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 1 ms]
        (9) QDP
        (10) QDPOrderProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) PisEmptyProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) QDPOrderProof [EQUIVALENT, 152 ms]
        (16) QDP
        (17) QDPOrderProof [EQUIVALENT, 57 ms]
        (18) QDP
        (19) PisEmptyProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (23) YES
    (24) QDP
        (25) QDPOrderProof [EQUIVALENT, 143 ms]
        (26) QDP
        (27) QDPOrderProof [EQUIVALENT, 72 ms]
        (28) QDP
        (29) PisEmptyProof [EQUIVALENT, 0 ms]
        (30) YES


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

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

   0(0(1(x1))) -> 0(0(2(1(3(x1)))))
   0(0(1(x1))) -> 0(0(2(2(3(1(x1))))))
   0(4(1(x1))) -> 0(4(2(2(1(x1)))))
   0(4(1(x1))) -> 0(2(3(1(4(2(x1))))))
   1(0(1(x1))) -> 0(2(1(1(x1))))
   1(0(1(x1))) -> 0(2(1(1(2(x1)))))
   1(0(1(x1))) -> 1(0(3(2(1(x1)))))
   1(4(0(x1))) -> 1(0(3(2(4(2(x1))))))
   1(4(1(x1))) -> 4(2(1(1(x1))))
   1(4(1(x1))) -> 4(2(1(1(2(1(x1))))))
   4(0(1(x1))) -> 4(0(2(1(x1))))
   5(0(1(x1))) -> 5(0(2(1(x1))))
   5(0(1(x1))) -> 0(2(1(5(3(x1)))))
   5(0(1(x1))) -> 0(3(2(1(5(5(x1))))))
   5(0(1(x1))) -> 3(0(2(3(5(1(x1))))))
   5(0(5(x1))) -> 0(3(2(5(3(5(x1))))))
   5(4(1(x1))) -> 2(4(2(5(1(3(x1))))))
   5(4(1(x1))) -> 4(5(2(1(3(3(x1))))))
   0(0(4(5(x1)))) -> 0(5(0(2(4(2(x1))))))
   0(1(2(0(x1)))) -> 2(0(2(1(0(x1)))))
   0(2(0(1(x1)))) -> 0(0(2(1(3(x1)))))
   0(3(4(0(x1)))) -> 3(2(4(0(0(3(x1))))))
   0(4(0(4(x1)))) -> 0(0(3(2(4(4(x1))))))
   1(0(1(4(x1)))) -> 2(3(1(1(4(0(x1))))))
   1(0(3(1(x1)))) -> 4(2(3(1(1(0(x1))))))
   1(2(0(4(x1)))) -> 1(4(2(0(3(2(x1))))))
   1(3(0(4(x1)))) -> 4(0(3(2(1(3(x1))))))
   1(4(1(5(x1)))) -> 2(1(2(5(1(4(x1))))))
   4(0(5(1(x1)))) -> 0(2(4(2(1(5(x1))))))
   4(1(0(0(x1)))) -> 3(2(1(4(0(0(x1))))))
   4(1(0(4(x1)))) -> 4(4(0(2(1(x1)))))
   5(0(0(1(x1)))) -> 0(3(2(5(1(0(x1))))))
   5(0(3(1(x1)))) -> 0(5(3(2(1(x1)))))
   5(0(3(1(x1)))) -> 0(3(5(2(2(1(x1))))))
   5(0(5(1(x1)))) -> 5(2(5(3(1(0(x1))))))
   5(2(4(1(x1)))) -> 2(1(4(2(5(x1)))))
   5(4(1(5(x1)))) -> 4(5(5(2(1(x1)))))
   5(4(1(5(x1)))) -> 2(1(5(4(2(5(x1))))))
   5(4(3(1(x1)))) -> 5(4(2(1(3(x1)))))
   5(4(3(1(x1)))) -> 3(5(2(4(2(1(x1))))))
   5(4(3(1(x1)))) -> 5(2(4(3(2(1(x1))))))
   5(5(0(4(x1)))) -> 5(0(2(5(4(2(x1))))))
   0(0(3(3(1(x1))))) -> 0(3(0(1(2(3(x1))))))
   0(2(4(3(1(x1))))) -> 0(2(3(1(4(2(x1))))))
   0(5(4(1(1(x1))))) -> 4(0(2(5(1(1(x1))))))
   1(2(4(3(1(x1))))) -> 1(2(3(3(1(4(x1))))))
   4(0(0(3(1(x1))))) -> 4(0(3(2(1(0(x1))))))

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