TRS Inner 89993 pair #381733446

details

property	value
status	complete
benchmark	cade05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n042.star.cs.uiowa.edu
space	Mixed_innermost

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.58640599251 seconds
cpu usage	6.642110053
max memory	3.88685824E8

stage attributes

key	value
output-size	22741
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) DependencyPairsProof [EQUIVALENT, 26 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QReductionProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QReductionProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) QReductionProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QDPQMonotonicMRRProof [EQUIVALENT, 23 ms]
        (25) QDP
        (26) NonInfProof [EQUIVALENT, 60 ms]
        (27) AND
            (28) QDP
                (29) DependencyGraphProof [EQUIVALENT, 0 ms]
                (30) TRUE
            (31) QDP
                (32) DependencyGraphProof [EQUIVALENT, 0 ms]
                (33) TRUE


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

   minus(x, x) -> 0
   minus(x, y) -> cond(equal(min(x, y), y), x, y)
   cond(true, x, y) -> s(minus(x, s(y)))
   min(0, v) -> 0
   min(u, 0) -> 0
   min(s(u), s(v)) -> s(min(u, v))
   equal(0, 0) -> true
   equal(s(x), 0) -> false
   equal(0, s(y)) -> false
   equal(s(x), s(y)) -> equal(x, y)

The set Q consists of the following terms:

   minus(x0, x1)
   cond(true, x0, x1)
   min(0, x0)
   min(x0, 0)
   min(s(x0), s(x1))
   equal(0, 0)
   equal(s(x0), 0)
   equal(0, s(x0))
   equal(s(x0), s(x1))


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(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   MINUS(x, y) -> COND(equal(min(x, y), y), x, y)
   MINUS(x, y) -> EQUAL(min(x, y), y)
   MINUS(x, y) -> MIN(x, y)
   COND(true, x, y) -> MINUS(x, s(y))
   MIN(s(u), s(v)) -> MIN(u, v)
   EQUAL(s(x), s(y)) -> EQUAL(x, y)

The TRS R consists of the following rules:

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