TRS Contextsensitive pair #487092595

details

property	value
status	complete
benchmark	MYNAT_nokinds-noand.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	Maude_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.38967 seconds
cpu usage	3.75406
user time	3.60024
system time	0.153821
max virtual memory	1.8343376E7
max residence set size	245684.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given CSR could be proven:

(0) CSR
(1) CSDependencyPairsProof [EQUIVALENT, 0 ms]
(2) QCSDP
(3) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QCSDP
        (6) QCSDPSubtermProof [EQUIVALENT, 16 ms]
        (7) QCSDP
        (8) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (9) TRUE
    (10) QCSDP
        (11) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (12) QCSDP
        (13) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (14) TRUE
    (15) QCSDP
        (16) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (17) QCSDP
        (18) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (19) TRUE


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

(0)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V2) -> U12(isNat(V2))
   U12(tt) -> tt
   U21(tt) -> tt
   U31(tt, V2) -> U32(isNat(V2))
   U32(tt) -> tt
   U41(tt, N) -> N
   U51(tt, M, N) -> U52(isNat(N), M, N)
   U52(tt, M, N) -> s(plus(N, M))
   U61(tt) -> 0
   U71(tt, M, N) -> U72(isNat(N), M, N)
   U72(tt, M, N) -> plus(x(N, M), N)
   isNat(0) -> tt
   isNat(plus(V1, V2)) -> U11(isNat(V1), V2)
   isNat(s(V1)) -> U21(isNat(V1))
   isNat(x(V1, V2)) -> U31(isNat(V1), V2)
   plus(N, 0) -> U41(isNat(N), N)
   plus(N, s(M)) -> U51(isNat(M), M, N)
   x(N, 0) -> U61(isNat(N))
   x(N, s(M)) -> U71(isNat(M), M, N)

The replacement map contains the following entries:

U11: {1}
tt: empty set
U12: {1}
isNat: empty set
U21: {1}
U31: {1}
U32: {1}
U41: {1}
U51: {1}
U52: {1}
s: {1}
plus: {1, 2}
U61: {1}
0: empty set
U71: {1}
U72: {1}
x: {1, 2}

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

(1) CSDependencyPairsProof (EQUIVALENT)
Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem.
----------------------------------------

(2)
Obligation:
Q-restricted context-sensitive dependency pair problem:
The symbols in {U12_1, U21_1, U32_1, s_1, plus_2, U61_1, x_2, U12'_1, U32'_1, PLUS_2, X_2, U21'_1, U61'_1} are replacing on all positions.
For all symbols f in {U11_2, U31_2, U41_2, U51_3, U52_3, U71_3, U72_3, U11'_2, U31'_2, U52'_3, U51'_3, U72'_3, U71'_3, U41'_2} we have mu(f) = {1}.
The symbols in {isNat_1, ISNAT_1, U_1} are not replacing on any position.

The ordinary context-sensitive dependency pairs DP_o are:
   U11'(tt, V2) -> U12'(isNat(V2))
   U11'(tt, V2) -> ISNAT(V2)
   U31'(tt, V2) -> U32'(isNat(V2))
   U31'(tt, V2) -> ISNAT(V2)
   U51'(tt, M, N) -> U52'(isNat(N), M, N)
   U51'(tt, M, N) -> ISNAT(N)
   U52'(tt, M, N) -> PLUS(N, M)
   U71'(tt, M, N) -> U72'(isNat(N), M, N)
   U71'(tt, M, N) -> ISNAT(N)
   U72'(tt, M, N) -> PLUS(x(N, M), N)

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