Deriv Compl Full Rewri 33144 pair #381922613

details

property	value
status	complete
benchmark	2.61.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n075.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_dc
runtime (wallclock)	0.862226009369 seconds
cpu usage	3.361315113
max memory	7.7070336E7

stage attributes

key	value
output-size	2985
starexec-result	WORST_CASE(?,O(n^1))

output

/export/starexec/sandbox/solver/bin/starexec_run_tct_dc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(n^1))
* Step 1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(x,h1(y,z)) -> h2(0(),x,h1(y,z))
            f(j(x,y),y) -> g(f(x,k(y)))
            g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u))
            h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u))
            i(f(x,h(y))) -> y
            i(h2(s(x),y,h1(x,z))) -> z
            k(h(x)) -> h1(0(),x)
            k(h1(x,y)) -> h1(s(x),y)
        - Signature:
            {f/2,g/1,h2/3,i/1,k/1} / {0/0,h/1,h1/2,j/2,s/1}
        - Obligation:
             derivational complexity wrt. signature {0,f,g,h,h1,h2,i,j,k,s}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 1
          0_1() -> 2
          0_2() -> 7
          f_0(1,1) -> 1
          f_1(1,5) -> 4
          g_0(1) -> 1
          g_1(4) -> 1
          g_1(4) -> 4
          h_0(1) -> 1
          h1_0(1,1) -> 1
          h1_1(1,1) -> 3
          h1_1(2,1) -> 1
          h1_1(2,1) -> 3
          h1_1(2,1) -> 5
          h1_1(6,1) -> 3
          h1_2(2,1) -> 8
          h1_2(6,1) -> 5
          h2_0(1,1,1) -> 1
          h2_1(2,1,3) -> 1
          h2_1(2,1,5) -> 4
          h2_1(10,1,5) -> 4
          h2_2(6,1,5) -> 1
          h2_2(6,1,5) -> 4
          h2_2(6,1,8) -> 1
          h2_2(6,1,8) -> 4
          h2_2(7,1,5) -> 4
          h2_2(7,1,8) -> 4
          h2_2(9,1,5) -> 1
          h2_2(9,1,5) -> 4
          h2_2(9,1,8) -> 1
          h2_2(9,1,8) -> 4
          i_0(1) -> 1
          j_0(1,1) -> 1
          k_0(1) -> 1
          k_1(1) -> 5
          s_0(1) -> 1
          s_1(1) -> 2
          s_1(2) -> 2
          s_1(6) -> 2
          s_1(7) -> 10
          s_1(9) -> 2
          s_1(10) -> 2
          s_2(2) -> 6
          s_2(6) -> 6
          s_2(7) -> 9
          s_2(9) -> 6
          s_2(10) -> 6
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(x,h1(y,z)) -> h2(0(),x,h1(y,z))
            f(j(x,y),y) -> g(f(x,k(y)))
            g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u))
            h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u))
            i(f(x,h(y))) -> y
            i(h2(s(x),y,h1(x,z))) -> z
            k(h(x)) -> h1(0(),x)
            k(h1(x,y)) -> h1(s(x),y)
        - Signature:
            {f/2,g/1,h2/3,i/1,k/1} / {0/0,h/1,h1/2,j/2,s/1}
        - Obligation:
             derivational complexity wrt. signature {0,f,g,h,h1,h2,i,j,k,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))

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