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TRS Innermost pair #516979243
details
property
value
status
complete
benchmark
LengthOfFiniteLists_complete_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n170.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
43.777687788 seconds
cpu usage
145.432999036
max memory
8.086560768E9
stage attributes
key
value
output-size
100603
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [SOUND, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 128 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 24 ms] (6) CSR (7) CSRRRRProof [EQUIVALENT, 37 ms] (8) CSR (9) CSRRRRProof [EQUIVALENT, 0 ms] (10) CSR (11) CSRRRRProof [EQUIVALENT, 23 ms] (12) CSR (13) CSRRRRProof [EQUIVALENT, 5 ms] (14) CSR (15) CSRRRRProof [EQUIVALENT, 4 ms] (16) CSR (17) Incomplete Giesl Middeldorp-Transformation [SOUND, 0 ms] (18) QTRS (19) DependencyPairsProof [EQUIVALENT, 0 ms] (20) QDP (21) DependencyGraphProof [EQUIVALENT, 0 ms] (22) QDP (23) QDPOrderProof [EQUIVALENT, 249 ms] (24) QDP (25) DependencyGraphProof [EQUIVALENT, 0 ms] (26) AND (27) QDP (28) QDPOrderProof [EQUIVALENT, 94 ms] (29) QDP (30) DependencyGraphProof [EQUIVALENT, 0 ms] (31) TRUE (32) QDP (33) QDPOrderProof [EQUIVALENT, 153 ms] (34) QDP (35) DependencyGraphProof [EQUIVALENT, 0 ms] (36) QDP (37) UsableRulesProof [EQUIVALENT, 0 ms] (38) QDP (39) QDPSizeChangeProof [EQUIVALENT, 0 ms] (40) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(zeros) -> mark(cons(0, zeros)) active(U11(tt, V1)) -> mark(U12(isNatList(V1))) active(U12(tt)) -> mark(tt) active(U21(tt, V1)) -> mark(U22(isNat(V1))) active(U22(tt)) -> mark(tt) active(U31(tt, V)) -> mark(U32(isNatList(V))) active(U32(tt)) -> mark(tt) active(U41(tt, V1, V2)) -> mark(U42(isNat(V1), V2)) active(U42(tt, V2)) -> mark(U43(isNatIList(V2))) active(U43(tt)) -> mark(tt) active(U51(tt, V1, V2)) -> mark(U52(isNat(V1), V2)) active(U52(tt, V2)) -> mark(U53(isNatList(V2))) active(U53(tt)) -> mark(tt) active(U61(tt, L)) -> mark(s(length(L))) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1), V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V), V)) active(isNatIList(zeros)) -> mark(tt) active(isNatIList(cons(V1, V2))) -> mark(U41(and(isNatKind(V1), isNatIListKind(V2)), V1, V2)) active(isNatIListKind(nil)) -> mark(tt) active(isNatIListKind(zeros)) -> mark(tt) active(isNatIListKind(cons(V1, V2))) -> mark(and(isNatKind(V1), isNatIListKind(V2))) active(isNatKind(0)) -> mark(tt) active(isNatKind(length(V1))) -> mark(isNatIListKind(V1)) active(isNatKind(s(V1))) -> mark(isNatKind(V1)) active(isNatList(nil)) -> mark(tt) active(isNatList(cons(V1, V2))) -> mark(U51(and(isNatKind(V1), isNatIListKind(V2)), V1, V2)) active(length(nil)) -> mark(0) active(length(cons(N, L))) -> mark(U61(and(and(isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L)) active(cons(X1, X2)) -> cons(active(X1), X2) active(U11(X1, X2)) -> U11(active(X1), X2) active(U12(X)) -> U12(active(X)) active(U21(X1, X2)) -> U21(active(X1), X2) active(U22(X)) -> U22(active(X)) active(U31(X1, X2)) -> U31(active(X1), X2)
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