SRS Stand 10685 pair #381720120

details

property	value
status	complete
benchmark	z092.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	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.70688605309 seconds
cpu usage	10.914031474
max memory	9.43919104E8

stage attributes

key	value
output-size	14117
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) QTRSRRRProof [EQUIVALENT, 52 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 2 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 11 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (23) YES
    (24) QDP
        (25) UsableRulesProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (28) YES
    (29) QDP
        (30) UsableRulesProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (33) YES


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

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

   q0(0(x1)) -> 0'(q1(x1))
   q1(0(x1)) -> 0(q1(x1))
   q1(1'(x1)) -> 1'(q1(x1))
   0(q1(1(x1))) -> q2(0(1'(x1)))
   0'(q1(1(x1))) -> q2(0'(1'(x1)))
   1'(q1(1(x1))) -> q2(1'(1'(x1)))
   0(q2(0(x1))) -> q2(0(0(x1)))
   0'(q2(0(x1))) -> q2(0'(0(x1)))
   1'(q2(0(x1))) -> q2(1'(0(x1)))
   0(q2(1'(x1))) -> q2(0(1'(x1)))
   0'(q2(1'(x1))) -> q2(0'(1'(x1)))
   1'(q2(1'(x1))) -> q2(1'(1'(x1)))
   q2(0'(x1)) -> 0'(q0(x1))
   q0(1'(x1)) -> 1'(q3(x1))
   q3(1'(x1)) -> 1'(q3(x1))
   q3(b(x1)) -> b(q4(x1))

Q is empty.

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

(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(0'(x_1)) = x_1
   POL(1(x_1)) = 3 + x_1
   POL(1'(x_1)) = x_1
   POL(b(x_1)) = x_1
   POL(q0(x_1)) = 2 + x_1
   POL(q1(x_1)) = x_1
   POL(q2(x_1)) = 3 + x_1
   POL(q3(x_1)) = 1 + x_1
   POL(q4(x_1)) = x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   q0(0(x1)) -> 0'(q1(x1))
   q2(0'(x1)) -> 0'(q0(x1))
   q0(1'(x1)) -> 1'(q3(x1))
   q3(b(x1)) -> b(q4(x1))

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