YES
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could be proven:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 314 ms]
(4) TRUE


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

(0)
Obligation:
Rules:
l0(__len9HAT0, __val8HAT0, tmp10HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0) -> l1(__len9HATpost, __val8HATpost, tmp10HATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost) :|: tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmp10HAT0 = tmp10HATpost && tmpHAT0 = tmpHATpost && __val8HAT0 = __val8HATpost && __len9HAT0 = __len9HATpost
l2(x, x1, x2, x3, x4, x5) -> l0(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x2 = x8 && x3 = x9 && x1 = x7 && x = x6 && x10 = x10
l3(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x20 = x20 && x18 = x18 && x19 = 0 && -1 <= x17 && x17 <= -1
l3(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x26 = x32 && x27 = x33 && x25 = x31 && x24 = x30 && 0 <= x29
l3(x36, x37, x38, x39, x40, x41) -> l2(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x39 = x45 && x37 = x43 && x36 = x42 && 1 + x41 <= -1
l4(x48, x49, x50, x51, x52, x53) -> l3(x54, x55, x56, x57, x58, x59) :|: x52 = x58 && x50 = x56 && x49 = x55 && x48 = x54 && x59 = x59 && x57 = x57
l5(x60, x61, x62, x63, x64, x65) -> l4(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x62 = x68 && x63 = x69 && x61 = x67 && x60 = x66
Start term: l5(__len9HAT0, __val8HAT0, tmp10HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0)

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

(1) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(2)
Obligation:
Rules:
l0(__len9HAT0, __val8HAT0, tmp10HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0) -> l1(__len9HATpost, __val8HATpost, tmp10HATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost) :|: tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmp10HAT0 = tmp10HATpost && tmpHAT0 = tmpHATpost && __val8HAT0 = __val8HATpost && __len9HAT0 = __len9HATpost
l2(x, x1, x2, x3, x4, x5) -> l0(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x2 = x8 && x3 = x9 && x1 = x7 && x = x6 && x10 = x10
l3(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x20 = x20 && x18 = x18 && x19 = 0 && -1 <= x17 && x17 <= -1
l3(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x26 = x32 && x27 = x33 && x25 = x31 && x24 = x30 && 0 <= x29
l3(x36, x37, x38, x39, x40, x41) -> l2(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x39 = x45 && x37 = x43 && x36 = x42 && 1 + x41 <= -1
l4(x48, x49, x50, x51, x52, x53) -> l3(x54, x55, x56, x57, x58, x59) :|: x52 = x58 && x50 = x56 && x49 = x55 && x48 = x54 && x59 = x59 && x57 = x57
l5(x60, x61, x62, x63, x64, x65) -> l4(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x62 = x68 && x63 = x69 && x61 = x67 && x60 = x66
Start term: l5(__len9HAT0, __val8HAT0, tmp10HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(__len9HAT0, __val8HAT0, tmp10HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0) -> l1(__len9HATpost, __val8HATpost, tmp10HATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost) :|: tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmp10HAT0 = tmp10HATpost && tmpHAT0 = tmpHATpost && __val8HAT0 = __val8HATpost && __len9HAT0 = __len9HATpost
(2) l2(x, x1, x2, x3, x4, x5) -> l0(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x2 = x8 && x3 = x9 && x1 = x7 && x = x6 && x10 = x10
(3) l3(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x20 = x20 && x18 = x18 && x19 = 0 && -1 <= x17 && x17 <= -1
(4) l3(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x26 = x32 && x27 = x33 && x25 = x31 && x24 = x30 && 0 <= x29
(5) l3(x36, x37, x38, x39, x40, x41) -> l2(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x39 = x45 && x37 = x43 && x36 = x42 && 1 + x41 <= -1
(6) l4(x48, x49, x50, x51, x52, x53) -> l3(x54, x55, x56, x57, x58, x59) :|: x52 = x58 && x50 = x56 && x49 = x55 && x48 = x54 && x59 = x59 && x57 = x57
(7) l5(x60, x61, x62, x63, x64, x65) -> l4(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x62 = x68 && x63 = x69 && x61 = x67 && x60 = x66

Arcs:
(2) -> (1)
(3) -> (1)
(4) -> (2)
(5) -> (2)
(6) -> (3), (4), (5)
(7) -> (6)

This digraph is fully evaluated!
----------------------------------------

(4)
TRUE